A short recording of a semi-improvized 3D comma pump

Hey, guys,

this is unbelievable ... Finally, after spending almost a year finding formulas for the shortest triadic comma pumps in 2D temperaments (still not definitely settled), I've managed to find a 3D comma pump. :-D
The vanishing interval here is the 676/675 which seems to have been highly discussed some time ago.
BTW: Sorry for a few mistakes, it's just an immediate result of my thoughts, hope I'll do something more out of it one day.
/tuning/files/PetrParizek/pp_pump_675.mp3

Petr

PS: I think I would never *ever* be able to find this chord progression if I didn't know what I'm actually tempering out. This is a possible answer to the question why I prefer vanishing intervals over EDO combinations when it comes to defining a temperament.

2011/4/10 Petr Pařízek <petrparizek2000@...>
>
> Hey, guys,
>
> this is unbelievable ... Finally, after spending almost a year finding
> formulas for the shortest triadic comma pumps in 2D temperaments (still not
> definitely settled), I've managed to find a 3D comma pump. :-D
> The vanishing interval here is the 676/675 which seems to have been highly
> discussed some time ago.
> BTW: Sorry for a few mistakes, it's just an immediate result of my thoughts,
> hope I'll do something more out of it one day.
> /tuning/files/PetrParizek/pp_pump_675.mp3
>
> Petr
>
> PS: I think I would never *ever* be able to find this chord progression if I
> didn't know what I'm actually tempering out. This is a possible answer to
> the question why I prefer vanishing intervals over EDO combinations when it
> comes to defining a temperament.

Nice! If you can get used to 10:13:15 triads, there might be some even
trippier possibilities. Tempering out 91/90 is a good choice as well,
as it makes it so that the inversion of 10:13:15 is 6:7:9. May not be
too compatible with 676/675 though, as it necessarily means that 49/48
vanishes...

-Mike

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:
/tuning/files/PetrParizek/pp_pump_675.mp3

Interesting! What's the tuning? And could I use it on the Achipelago page?

Petr, your examples are always the most clear (I remember Run the Whistle Down and others) in demonstrating the sound of the piece "turning back in on itself" as the comma in question is tempered out. I doubt if I could transcibe and analize this without putting in some hours, but I can hear what's going on plain as day. I think any musician could. These comma examples should be linked to from the xenwiki page.

That being said, I'm suprised the comma "return" sounds so heavy, considering the tiny size of the comma.

--- In tuning@yahoogroups.com, Petr PaÅo?=ízek <petrparizek2000@...> wrote:
>
> Hey, guys,
>
> this is unbelievable ... Finally, after spending almost a year finding
> formulas for the shortest triadic comma pumps in 2D temperaments (still not
> definitely settled), I've managed to find a 3D comma pump. :-D
> The vanishing interval here is the 676/675 which seems to have been highly
> discussed some time ago.
> BTW: Sorry for a few mistakes, it's just an immediate result of my thoughts,
> hope I'll do something more out of it one day.
> /tuning/files/PetrParizek/pp_pump_675.mp3
>
> Petr
>
> PS: I think I would never *ever* be able to find this chord progression if I
> didn't know what I'm actually tempering out. This is a possible answer to
> the question why I prefer vanishing intervals over EDO combinations when it
> comes to defining a temperament.
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> That being said, I'm suprised the comma "return" sounds so heavy, considering the tiny size of the comma.

It would be nice to know the tuning. You don't need to temper drastically to temper out 676/675; good ole 270et will do the job, for instance, or hemiennealimmal. It will slice the fourth in two, but don't call it semaphore.

Gene wrote:

> Interesting! What's the tuning?

It's the 3D temperament where one generator is a tempered 15/13 (stacked as many times as you desire) and another generator is a tempered 5/4 (used only once).

> And could I use it on the Achipelago page?

I think you've already included that, haven't you?

Petr

Lobawad wrote:

> Petr, your examples are always the most clear (I remember Run the Whistle > Down and others) in demonstrating
> the sound of the piece "turning back in on itself" as the comma in > question is tempered out.

Hoh, Thanks. :-)

> I doubt if I could
> transcibe and analize this without putting in some hours, but I can hear > what's going on plain as day. I think any
> musician could. These comma examples should be linked to from the xenwiki > page.

That's a very encouraging thing to hear. Very much so -- as that's just what I'm intending.
I'll tell you something.
Some time ago, I examined the comma pump sequence files which were part of the Scala bundle and I realized there wasn't an example of a "kleisma pump" there. So I wrote one. 8-) So if you now download the latest version of Scala, one of the sequence examples is called "pump_kleisma.seq". - And I'm going to make some others in the future.

> That being said, I'm suprised the comma "return" sounds so heavy, > considering the tiny size of the comma.

Well, it doesn't.
To make a long story short, try these steps:
3/4, 5/3, 3/4, 16/13, 3/4, 5/3, 3/4, 16/13, 3/4.
Where do you end up?

Petr

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Gene wrote:
>
> > Interesting! What's the tuning?
>
> It's the 3D temperament where one generator is a tempered 15/13 (stacked as
> many times as you desire) and another generator is a tempered 5/4 (used only
> once).
>
> > And could I use it on the Achipelago page?
>
> I think you've already included that, haven't you?

If it's a subgroup temperament using no 7 or 11, it would be parizekmic temperament, yes. But I have no musical example for that at the moment, so I'd need a permanent home for the mp3 and permission to use it.

Everyone drop what you're doing and listen to this now!

Also, I second the motion that Petr's complete catalog of
comma pump examples be permanently installed on the xenwiki.

And, I second the motion that normal comma lists (and/or
comma sequences) be standard when identifying temperaments
on the xenwiki.

-Carl

--- Petr Pařízek <petrparizek2000@...> wrote:

> Hey, guys,
> this is unbelievable ... Finally, after spending almost a year
> finding formulas for the ...
[snip]
> /tuning/files/PetrParizek/pp_pump_675.mp3

Of course if needed I can host these.
-----Original Message-----
From: "Carl Lumma" <carl@lumma.org>
Sender: tuning@yahoogroups.com
Date: Sun, 10 Apr 2011 22:37:47
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: A short recording of a semi-improvized 3D comma pump

Everyone drop what you're doing and listen to this now!

Also, I second the motion that Petr's complete catalog of
comma pump examples be permanently installed on the xenwiki.

And, I second the motion that normal comma lists (and/or
comma sequences) be standard when identifying temperaments
on the xenwiki.

-Carl

--- Petr Pařízek <petrparizek2000@...> wrote:

> Hey, guys,
> this is unbelievable ... Finally, after spending almost a year
> finding formulas for the ...
[snip]
> /tuning/files/PetrParizek/pp_pump_675.mp3

   Pardon my criticism...but (at least as music rather than a sound example) this simply seems like transposed melodies over five chords to my ears...the bassline doesn't even appear to have its own phrasing and thus sounds like just part of the chords rather than a separate entity.  The one parts that seems really cool is the transition from the end of the five chord motif to the beginning where it almost sounds "in between keys". 

Petr>"The vanishing interval here is the 676/675 which seems to have been highly discussed some time ago."

Perhaps this is due to my own lack of knowledge as to the significance of comma pumps (simply a chord progression where each chord has at least one chord in common with the last, correct?)
However, as a sound example (rather than a piece of music), isn't this a bit less than 3 cents and...how/why would such a small difference matter musically in composition?

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> Of course if needed I can host these.

If Petr gives permission that would be good.

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Lobawad wrote:
>
> > Petr, your examples are always the most clear (I remember Run the Whistle
> > Down and others) in demonstrating
> > the sound of the piece "turning back in on itself" as the comma in
> > question is tempered out.
>
> Hoh, Thanks. :-)

Well thank you- there has to be a clear way of explaining temperament without having to use words, so that musicians can simply hear and understand even if they can't articulate how it's done or even point out precisely where the "trick" happens.

> That's a very encouraging thing to hear. Very much so -- as that's just what
> I'm intending.
> I'll tell you something.
> Some time ago, I examined the comma pump sequence files which were part of
> the Scala bundle and I realized there wasn't an example of a "kleisma pump"
> there. So I wrote one. 8-) So if you now download the latest version of
> Scala, one of the sequence examples is called "pump_kleisma.seq". - And I'm
> going to make some others in the future.

That's a good idea, so we get to analize these as well.
>

> > That being said, I'm suprised the comma "return" sounds so heavy,
> > considering the tiny size of the comma.
>
> Well, it doesn't.
> To make a long story short, try these steps:
> 3/4, 5/3, 3/4, 16/13, 3/4, 5/3, 3/4, 16/13, 3/4.
> Where do you end up?
>
> Petr
>

I know it returns "naturally" almost exactly, it's a tiny comma, that't why I said I'm suprised by it's (relative) heaviness. There must be something else creating the effect, perhaps a different "implied" comma. Maybe I'm scanning a "M3" and feeling a 65/64 as a comma...hmmm, I'll have to analize it after all. :-)

The small commas may be even more important than big ones, if you want the sound of near-perfect rational intonation in a finite tuning in which you can make "returns" rather than spiral infinitely. A good "naturally occuring" example is 1029/1024. If you move three steps of 8/7, you get 512/343, about 8.4 cents flat of 3/2. You can see that this can be a key point of fitting simple ratios of 7 together with simple ratios of 3.

Petr is linking 2,3 and 5 with 13 here.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
>    Pardon my criticism...but (at least as music rather than a sound example) this simply seems like transposed melodies over five chords to my ears...the bassline doesn't even appear to have its own phrasing and thus sounds like just part of the chords rather than a separate entity.  The one parts that seems really cool is the transition from the end of the five chord motif to the beginning where it almost sounds "in between keys". 
>
>
> Petr>"The vanishing interval here is the 676/675 which seems to have been highly discussed some time ago."
>
> Perhaps this is due to my own lack of knowledge as to the significance of comma pumps (simply a chord progression where each chord has at least one chord in common with the last, correct?)
> However, as a sound example (rather than a piece of music), isn't this a bit less than 3 cents and...how/why would such a small difference matter musically in composition?
>

Listening again several times, I found what's "heavy", it's not a 65/64 comma shift feeling. But, it's not something I can explain technically. Or even in words at all. I'd like to hear a Just rendition.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@> wrote:
> >
> > Lobawad wrote:
> >
> > > Petr, your examples are always the most clear (I remember Run the Whistle
> > > Down and others) in demonstrating
> > > the sound of the piece "turning back in on itself" as the comma in
> > > question is tempered out.
> >
> > Hoh, Thanks. :-)
>
> Well thank you- there has to be a clear way of explaining temperament without having to use words, so that musicians can simply hear and understand even if they can't articulate how it's done or even point out precisely where the "trick" happens.
>
>
> > That's a very encouraging thing to hear. Very much so -- as that's just what
> > I'm intending.
> > I'll tell you something.
> > Some time ago, I examined the comma pump sequence files which were part of
> > the Scala bundle and I realized there wasn't an example of a "kleisma pump"
> > there. So I wrote one. 8-) So if you now download the latest version of
> > Scala, one of the sequence examples is called "pump_kleisma.seq". - And I'm
> > going to make some others in the future.
>
> That's a good idea, so we get to analize these as well.
> >
>
> > > That being said, I'm suprised the comma "return" sounds so heavy,
> > > considering the tiny size of the comma.
> >
> > Well, it doesn't.
> > To make a long story short, try these steps:
> > 3/4, 5/3, 3/4, 16/13, 3/4, 5/3, 3/4, 16/13, 3/4.
> > Where do you end up?
> >
> > Petr
> >
>
> I know it returns "naturally" almost exactly, it's a tiny comma, that't why I said I'm suprised by it's (relative) heaviness. There must be something else creating the effect, perhaps a different "implied" comma. Maybe I'm scanning a "M3" and feeling a 65/64 as a comma...hmmm, I'll have to analize it after all. :-)
>

Lobawad wrote:

> I'd like to hear a Just rendition.

If most of the target intervals are about half a cent away from JI (or even less), the difference would be almost unrecognizable.

Petr

Gene wrote:

> If Petr gives permission that would be good.

Okay, let's agree that Chris can upload it then.

Petr

Obviously- I'm curious as to what I'm hearing. Since this community at least pretends to be "scientific", it is necessary to rule out the discrepancy between Just and tempered as the source.

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Lobawad wrote:
>
> > I'd like to hear a Just rendition.
>
> If most of the target intervals are about half a cent away from JI (or even
> less), the difference would be almost unrecognizable.
>
> Petr
>

On Sun, Apr 10, 2011 at 1:20 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> > That being said, I'm suprised the comma "return" sounds so heavy, considering the tiny size of the comma.
>
> It would be nice to know the tuning. You don't need to temper drastically to temper out 676/675; good ole 270et will do the job, for instance, or hemiennealimmal. It will slice the fourth in two, but don't call it semaphore.

53-equal is pretty good for this if you're not using 7.

I'm trying to find a decent scale that encapsulates and generalizes
this chord progression. In 53-tet, the whole thing octave-reduces to 6
5 6 5 6 3 8 3 6 5, which is a strictly-proper scale. Might there not
be some related MODMOS lurking nearby with some additional tempering?
The 24-tet version is 3 2 3 2 3 1 4 1 3 2, which I'm not sure makes
anything much clearer.

One perhaps crappy option is to Negri temper it, which (in 29-equal)
gives you 3 3 3 3 3 2 4 2 3 3, which is a MODMOS of Negri[10]. It has
a periodicity block that looks something like this:

_ ___________ _
!_! !___________! !_!

(not to scale)

It sharps the second note in the chain of generators, so maybe
Negri[10] #2G is a good notation for this. Alternately, it flattens
the second last note, so Negri[10] b9G is another name for it.

There may be a better way to get to a rank 2 MODMOS than to go the
Negri route though.

-Mike

Hi Petr,

I took the liberty of setting you up with a folder on micro.soonlabel.com
http://micro.soonlabel.com/petr_parizek/

and put your files from the tuning list file section into that folder. I
also made a simple HTML file to preserve your comments:
http://micro.soonlabel.com/petr_parizek/~Petr_Parizek_Files.html

If I need to change something please let me know.

Have a great day,

Chris

On Mon, Apr 11, 2011 at 5:34 AM, Petr Parízek <petrparizek2000@...>wrote:

>
>
> Gene wrote:
>
> > If Petr gives permission that would be good.
>
> Okay, let's agree that Chris can upload it then.
>
> Petr
>
>
>
>

Thanks Chris, I'll look into that.

Petr

lobawad>"If you move three steps of 8/7, you get 512/343, about 8.4 cents flat
of 3/2. You can see that this can be a key point of fitting simple
ratios of 7 together with simple ratios of 3. "

   Meaning if you take a chain of 8/7's you can more-or-less link them with a chain of 3/2's?   Makes numerical sense...I assume the full use is to get chains of virtually-JI ratios almost perfectly intersecting each other so as to provide both the accuracy of JI and compositional flexibility of temperament?

     If so this begs a full explanation...what four (x/2, x/3, x/5, x/13?) chains is Petr linking?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> 53-equal is pretty good for this if you're not using 7.
>
> I'm trying to find a decent scale that encapsulates and generalizes
> this chord progression. In 53-tet, the whole thing octave-reduces to 6
> 5 6 5 6 3 8 3 6 5, which is a strictly-proper scale. Might there not
> be some related MODMOS lurking nearby with some additional tempering?

It fits into Cata[19], which is basically Hanson[19] except that you pay attention to the 13's. That is, it's a 2.3.5.13 subgroup temperament. By tempering out the kleisma and 676/675, it also tempers
out 625/624 and 325/324. It also fits into the 19-note hobbit for Madagascar temperament, a rank three temperament but the hobbit reduces to a MOS in 53, and catakleismic, a rank two temperament, and the no-11s version of catakleimsic, since you don't get much milage from 11 out of 19 notes. Within a MOS of 19 notes, catakleismic is giving you a lot of 3 and 5, considerable 13, a little 7 in the form of 13/7, 7/6 and 7/5, and kiss off the 11.

Gene>"a little 7 in the form of 13/7, 7/6 and 7/5, and kiss off the 11."

13/7 is 13-limit not 7-limit.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Petr,
>
> I took the liberty of setting you up with a folder on micro.soonlabel.com
> http://micro.soonlabel.com/petr_parizek/

There's a lot there about a crazed and evil temperament which tempers out 3125/2196, which could finally give the answer to the vexing question of how to find something nice enough to say about 32edo to be able to write a xenwiki entry for it. Since Petr pretty well owns this temperament, it should be either "petr temperament" or whatever else he wants to call it. Same for adding 64/63 to the bag and extending to the 7-limit. The generator is a very sharp 6/5, or at least you are supposed to pretend it counts as a 6/5, of about 338 cents, which can be tuned in 32 or 39 edo. Don't call it 17/14!

Gene (about 32EDO)>"The generator is a very sharp 6/5, or at least you are supposed to
pretend it counts as a 6/5, of about 338 cents, which can be tuned in 32
or 39 edo. Don't call it 17/14!"

  In fact, I'll even go so far as to say that, in general, anything over 13-odd-limit is beyond the scope of "Just resolution" of human hearing.  Plus even in 11-limit there exist things like 14/11 where it is rather tempting to say "it's just an out-of-tune/skewed 9/7".  I wouldn't dream of calling anything in 17-limit recognizable from something very close that's much lower limit.  Well, ok, 15/11, despite being 15-limit, has its own sound distinct from the 4/3 and 11/8 surrounding it...but it sounds, to me, more like an 11-limit interval than a 15-limit one.

On Mon, Apr 11, 2011 at 3:34 PM, Michael <djtrancendance@...> wrote:
>
> Gene (about 32EDO)>"The generator is a very sharp 6/5, or at least you are supposed to pretend it counts as a 6/5, of about 338 cents, which can be tuned in 32 or 39 edo. Don't call it 17/14!"
>
>   In fact, I'll even go so far as to say that, in general, anything over 13-odd-limit is beyond the scope of "Just resolution" of human hearing.  Plus even in 11-limit there exist things like 14/11 where it is rather tempting to say "it's just an out-of-tune/skewed 9/7".  I wouldn't dream of calling anything in 17-limit recognizable from something very close that's much lower limit.  Well, ok, 15/11, despite being 15-limit, has its own sound distinct from the 4/3 and 11/8 surrounding it...but it sounds, to me, more like an 11-limit interval than a 15-limit one.

I don't know about that. I've been digging the sound of 33/16 lately,
as in 11/8 * 3/2. Try 8:14:22:33, for example. It appears in one of
the zero-order MODMOS's of porcupine[8], and it's a really nice sound.

-Mike

MikeB>"I don't know about that. I've been digging the sound of 33/16 lately,

as in 11/8 * 3/2. Try 8:14:22:33, for example."

  Agreed but, well...that's over 2 octaves up.   25/6 seems like a not-too-far match from 33/8, though.  It does seem to beg the question how much higher limits become valid as you go across higher and higher numbers of octaves.

  It's funny that the chord you mentioned has 11/8 * 2 and 11/8 * 3 in it...makes me wonder what would happen it you simply took 11/8 22/8 33/8 = 8:11:22:33 as a sort of funky equal-beating type of chord.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Gene>"a little 7 in the form of 13/7, 7/6 and 7/5, and kiss off the 11."
>
> 13/7 is 13-limit not 7-limit.

Which doesn't change the fact that there's a 7 in it.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I don't know about that. I've been digging the sound of 33/16 lately,
> as in 11/8 * 3/2. Try 8:14:22:33, for example. It appears in one of
> the zero-order MODMOS's of porcupine[8], and it's a really nice sound.

Whatever you think the minor third+ generator is, you get one of those temperaments you or Herman could did out of it.

> Gene>"a little 7 in the form of 13/7, 7/6 and 7/5, and kiss off the 11."

>

> 13/7 is 13-limit not 7-limit.

>Which doesn't change the fact that there's a 7 in it.

  Interesting.  On that note...I'll say/admit that 9/7 sounds 7-ish and 15/11 sounds 11-ish.  But it seems to be hit-or-miss because while something like 15/11 sounds 11-ish to me, 17/11 really doesn't and even 20/11 doesn't (despite the fact it truly is 11-odd-limit, it seems much tenser).

  So trying to reduce this all to a distinct numeric pattern seems tricky...begs the question if there is a pattern you can use for anything over 9-limit beside listening tests.  It all seems so arbitrary beyond 9-limit...

On Mon, Apr 11, 2011 at 4:16 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I don't know about that. I've been digging the sound of 33/16 lately,
> > as in 11/8 * 3/2. Try 8:14:22:33, for example. It appears in one of
> > the zero-order MODMOS's of porcupine[8], and it's a really nice sound.
>
> Whatever you think the minor third+ generator is, you get one of those temperaments you or Herman could did out of it.

Holy crap, this sentence has destroyed my brain. I was following until
the comma. What does "you get one of those temperaments you or Herman
could did out of it" mean?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > Whatever you think the minor third+ generator is, you get one of those temperaments you or Herman could did out of it.
>
> Holy crap, this sentence has destroyed my brain. I was following until
> the comma. What does "you get one of those temperaments you or Herman
> could did out of it" mean?

It means I made a typo. Can you dig it?

On Mon, Apr 11, 2011 at 5:15 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > > Whatever you think the minor third+ generator is, you get one of those temperaments you or Herman could did out of it.
> >
> > Holy crap, this sentence has destroyed my brain. I was following until
> > the comma. What does "you get one of those temperaments you or Herman
> > could did out of it" mean?
>
> It means I made a typo. Can you dig it?

LOL, yes, of course, but I still don't understand what you meant...

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> There's a lot there about a crazed and evil temperament which tempers out 3125/2196,
> which could finally give the answer to the vexing question of how to find something nice
> enough to say about 32edo to be able to write a xenwiki entry for it.

Yeah, 32's a funky one. I don't think I'd recommend it for anything. That 336.5-cent generator is about the best thing going for it, unless you like a really extreme Superpyth, or some really large scales with very mediocre harmonies. I think I'd prefer 16.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> There's a lot there about a crazed and evil temperament which tempers out 3125/2196,
> which could finally give the answer to the vexing question of how to find something nice
> enough to say about 32edo to be able to write a xenwiki entry for it.

Yeah, 32's a funky one. I don't think I'd recommend it for anything. That 336.5-cent generator is about the best thing going for it, unless you like a really extreme Superpyth, or some really large scales with very mediocre harmonies. I think I'd prefer 16.

-Igs

Gene wrote:

> Since Petr pretty well owns this temperament,

Well, to be honest, some months ago, I was quite surprised that those like bug and father were often discussed and this one wasn't. As I was unable to answer the question why that was the case, I was courious what it sounded like -- since I knew the error is smaller there than in bug or father. You know what, if there's something that can persuade me to play in mavila, then ... What else can stop me? - Yeah, I'll tell you ... Father and dicot. Or at least there's only one recording where I used 7-EDO which could count as dicot as well.

> it should be either "petr temperament" or whatever else he wants to call > it.

I've just realized it easily "mutates" into amity and a generator like (8/3)^(1/5) could be actually used for both. Nevertheless, the two differ in mistuning and in complexity and when combined, they give you, hah, 7-EDO. :-D
So ... What about something like "sixix"? Meaning that an "octave + minor sixth" is split into 6 equal parts, therefore an octave equivalent of 5/1 is mapped to -6 generators. That would distinguish it from amity where 5/1 is mapped to -13 generators.

> Same for adding 64/63 to the bag and extending to the 7-limit.

For the time being, I'll go for the 5-limit application and let others to make their extensions.

> The generator is a very sharp 6/5, or at least you are supposed to pretend > it counts as a 6/5, of about
> 338 cents, which can be tuned in 32 or 39 edo. Don't call it 17/14!

I won't. For me it's a 5-limit temperament.

Petr

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> lobawad>"If you move three steps of 8/7, you get 512/343, about 8.4 cents flat
> of 3/2. You can see that this can be a key point of fitting simple
> ratios of 7 together with simple ratios of 3. "
>
>    Meaning if you take a chain of 8/7's you can more-or-less link them with a chain of 3/2's?   Makes numerical sense...I assume the full use is to get chains of virtually-JI ratios almost perfectly intersecting each other so as to provide both the accuracy of JI and compositional flexibility of temperament?

With a little temperament you can even link them very well. Look at the "miracle" temperament. What it does is take an interval which is in magnitude a tiny touch sharper than 1/2 of an 8/7, and use it as a generator. This interval is also 1/6 of a slightly flat 3/2 (which is how it was concieved) so six of them are going to generate a "fifth".

This makes not only numerical sense, but works acoustically very smoothly, because the comma of 1029/1024 is not only pretty small, but "tempered out" by sharping here and flatting there. With a well-chosen generator size, the 8/7 is only bit sharp and the 3/2 only a bit flat. Pretty slick.

>
>      If so this begs a full explanation...what four (x/2, x/3, x/5, x/13?) chains is Petr linking?
>

Petr gave a skeleton Just interval progression earlier. But he's working in more esoteric regions, it won't make much sense until you have basic concepts down.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Yeah, 32's a funky one. I don't think I'd recommend it for anything.

I did the 32 entry. But 30 is worse--the patent val, which seems to be about the best it has to offer, is contorted until you get to the 13-limit. 30 is, in other words, basically 15 in a false mustache and trying hard to be difficult to play. The best idea I can come up with for it is that the 680 cent fifth is a great pelogic fifth, and I will probably run with that unless you have something to add.

On Wed, Apr 13, 2011 at 1:48 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> > Yeah, 32's a funky one. I don't think I'd recommend it for anything.
>
> I did the 32 entry. But 30 is worse--the patent val, which seems to be about the best it has to offer, is contorted until you get to the 13-limit. 30 is, in other words, basically 15 in a false mustache and trying hard to be difficult to play. The best idea I can come up with for it is that the 680 cent fifth is a great pelogic fifth, and I will probably run with that unless you have something to add.

How ironic that you say that, because I decided earlier today that
15-equal was my favorite temperament in the entire world, but that its
biggest flaw was its lack of a decent major second. 30-tet solves this
problem by treating it as a deliberately inconsistent 2.3.7.9'.11
temperament. You treat the 9' as though it were its own prime, for use
in making really nice, "fused" sonorities like 8:9:10:11. But, when
you're making something like a major 9 chord, you'd use the 9 that's
equal to 3*3, because that's the capacity that it's functioning in.

Which is another reason why I think that inconsistent temperaments
aren't all that bad. If we're using abelian groups to generalize the
concept of the whole rational number system and prime numbers and so
on, might as well go all the way with it.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> How ironic that you say that, because I decided earlier today that
> 15-equal was my favorite temperament in the entire world, but that its
> biggest flaw was its lack of a decent major second. 30-tet solves this
> problem by treating it as a deliberately inconsistent 2.3.7.9'.11
> temperament.

Thanks, Mike--between this and the mavila idea, I've now got plenty!

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Which is another reason why I think that inconsistent temperaments
> aren't all that bad.

That's one for the zeta function, which is perfectly happy with the inconsistency.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> I did the 32 entry. But 30 is worse--the patent val, which seems to be about the best it has > to offer, is contorted until you get to the 13-limit. 30 is, in other words, basically 15 in a
> false mustache and trying hard to be difficult to play. The best idea I can come up with for > it is that the 680 cent fifth is a great pelogic fifth, and I will probably run with that unless
> you have something to add.

Well, it has an interesting decatonic scale that is to Blackwood as Superpyth is to Meantone (i.e. where triads approximate 6:7:9 and 14:18:21 instead of 10:12:15 and 4:5:6), and which is also pretty good for 11:13:15 triads. It's also--I think?--a rather unremarkable sensi temperament. But yeah, the only thing it really has going for it is that it gives you 10-EDO and 15-EDO together, for people who are fans of those two and want them on the same instrument. That's pretty much the only thing I can see recommending 30.

-Igs

On Wed, Apr 13, 2011 at 2:37 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Well, it has an interesting decatonic scale that is to Blackwood as Superpyth is to Meantone (i.e. where triads approximate 6:7:9 and 14:18:21 instead of 10:12:15 and 4:5:6)

I believe I called this one "Driftwood."

-Mike

On Wed, Apr 13, 2011 at 2:21 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > How ironic that you say that, because I decided earlier today that
> > 15-equal was my favorite temperament in the entire world, but that its
> > biggest flaw was its lack of a decent major second. 30-tet solves this
> > problem by treating it as a deliberately inconsistent 2.3.7.9'.11
> > temperament.
>
> Thanks, Mike--between this and the mavila idea, I've now got plenty!

Typo above - I meant 2.3.5.7.9'.11, sorry.

It's also worth noting that mavila itself lends to a 2.3.5.9'
interpretation - just equate 9'/8 and a mavila 10/9, and you're on
your way (meaning 81'/80 vanishes... this notation is going to get
weird). I've been treating that as the canonical approach to mavila
this whole time anyway, where the large steps in 2L5s are ~9/8,
although they're really 10/9. You can also go up to 2.3.5.7.9' by
tempering out 135/128, 81'/80, and 64/63', while leaving regular 81/80
and 64/63 untempered.

-Mike

MikeB>"How ironic that you say that, because I decided earlier today that

15-equal was my favorite temperament in the entire world, but that its

biggest flaw was its lack of a decent major second."

  Right, you are "stuck" with the neutral second...which is good for clusters but not great (IE I've found chaining two neutral seconds is fine, but 3 just doesn't cut it).

   15EDO has other cool features: the fifth and third are just on the edge of what I consider decent (thanks largely to a strong field of attraction around the major fourth), there is a great 6th and pretty good neutral seventh plus you get the cool, rather flexible neutral seventh near 11/6 and a not-so-bad 11/8.  Not to mention  a good minor third, a no-worse-than-12TET major third, and a good 8/7.  Far as possibilities per note...15EDO is quite strong already.   And 30EDO adds a strong 13/9, 14/9...making 13:14:15 chords possible.  But far as "possibilities per note", 15EDO has some serious game...under 19EDO or so you'd be hard-pressed to match its flexibility. 

MikeB (referring to what 30EDO does over 15EDO)>"making really nice, "fused" sonorities like 8:9:10:11"

   Agreed!  anything involving fractions from 9/8 to 12/11 IE 8:9:10:11 or 9:10:11:12 makes an ideal clustered chord IMVHO.   It solves my old issue with 12EDO and so many other tunings of the inability to chain semitones (IE A A# B) without creating a chaotic sound.  30EDO is a quite good fairly tuning for clusters.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

>You treat the 9' as though it were its own prime, for use
> in making really nice, "fused" sonorities like 8:9:10:11. But, when
> you're making something like a major 9 chord, you'd use the 9 that's
> equal to 3*3, because that's the capacity that it's functioning in.

You can fake this by making 9' an actual prime, for example, 18433 which I just tried, and it seems to work. 18433/16384 is 204.004 cents, as opposed to 203.910 cents for 9/8. The val for 30 in the 2.3.5.7.18433.11 subgroup is <30 48 70 84 425 104|, which isn't contorted. On the other hand, temperament finders will want to zero in on the comma 18433/18432, corresponding to 9'/3, and this is precisely what 30 doesn't have.

This is an open question for Chris V or anyone else. I noticed that 15-EDO
is not included in the list of audio files at http://micro.soonlabel.com/ and
am curious of the likely cause for this..?

Regarding the rule of thumb for "favored EDOs" I was considering in another
thread, 5 and 15 were the only ones mentioned by both Carl and Gene that did
not appear in the list I was using, so I do have a sort of numerological
bias against it.

On Wed, Apr 13, 2011 at 4:31 PM, Daniel Nielsen <nielsed@...> wrote:
>
> This is an open question for Chris V or anyone else. I noticed that 15-EDO is not included in the list of audio files at http://micro.soonlabel.com/ and am curious of the likely cause for this..?
>
> Regarding the rule of thumb for "favored EDOs" I was considering in another thread, 5 and 15 were the only ones mentioned by both Carl and Gene that did not appear in the list I was using, so I do have a sort of numerological bias against it.

Start playing around with major and minor 9 chords in blackwood[10] in
15 or 20-EDO and you'll get over that bias real quick.

-Mike

MikeB>"Start playing around with major and minor 9 chords in blackwood[10] in

15 or 20-EDO and you'll get over that bias real quick"

    Indeed...the 9th chords are sweet in 15EDO.  Question though: how do you get around the fact there is no tritone of sorts in 15EDO?  Or what kind of different chords do you make out of the area surrounding the tritone (IE 13/9 and 11/8)?  8:11:14 and 9:13:15 sound fairly good to me in that department...but I was wondering what other chords in 15EDO come across well to you?

I've just not got around to 15edo yet. No other reason. So many tunings and so little time.

I'll be happy to host any examples you or someone else has made.

Chris
-----Original Message-----
From: Mike Battaglia <battaglia01@gmail.com>
Sender: tuning@yahoogroups.com
Date: Wed, 13 Apr 2011 16:32:14
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: Re: [tuning] 15EDO is a sweet tuning...

On Wed, Apr 13, 2011 at 4:31 PM, Daniel Nielsen <nielsed@uah.edu> wrote:
>
> This is an open question for Chris V or anyone else. I noticed that 15-EDO is not included in the list of audio files at http://micro.soonlabel.com/ and am curious of the likely cause for this..?
>
> Regarding the rule of thumb for "favored EDOs" I was considering in another thread, 5 and 15 were the only ones mentioned by both Carl and Gene that did not appear in the list I was using, so I do have a sort of numerological bias against it.

Start playing around with major and minor 9 chords in blackwood[10] in
15 or 20-EDO and you'll get over that bias real quick.

-Mike

On Wed, Apr 13, 2011 at 4:50 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"Start playing around with major and minor 9 chords in blackwood[10] in
> 15 or 20-EDO and you'll get over that bias real quick"
>
>     Indeed...the 9th chords are sweet in 15EDO.  Question though: how do you get around the fact there is no tritone of sorts in 15EDO?  Or what kind of different chords do you make out of the area surrounding the tritone (IE 13/9 and 11/8)?  8:11:14 and 9:13:15 sound fairly good to me in that department...but I was wondering what other chords in 15EDO come across well to you?

That there is no clear tritone is one of the problems with 15EDO. But
15EDO seems to be perfectly set up to break my 12EDO, chromatic based
categorical perception of intervals in the perfect way so as to be
interesting and awesome and xenharmonic, rather than confusing and
irritating. Sometimes, the 640 cent interval sounds like a tritone to
me. Other times, it sounds like a flat pelog fifth. Most recently,
I've been trying to train myself to compulsively hear it as a 16/11;
that is, to imagine it as an "otonal" 11/8 in an inversion. Not having
much success with this yet because the field of attraction of 3/2 is
so strong.

On the other hand, sometimes the 560 cent interval sounds like a
tritone to me. Other times it'll sound like an "acute fourth." Yet
other times it'll sound like an "otonal" 11/8. So I don't know. The
fact that there's no really good tritone is fairly irritating, and
parallels that there's also no good 9/8. 30-EDO gets around that
issue. But the main point is that that's also just one of the
"features" of 15-EDO - some useful intervals that we have in 12 don't
work, but then there are other things we can do that don't work in 12.
So it forces you to try new stuff. Maybe it's not so bad.

-Mike

On 4/13/2011 4:57 PM, chrisvaisvil@... wrote:
> I've just not got around to 15edo yet. No other reason. So many tunings and so little time.
>
> I'll be happy to host any examples you or someone else has made.
>
> Chris

I've got a few examples on my Google site actually (http://sites.google.com/site/teamouse/).

http://sites.google.com/site/teamouse/Porcupine-orchestral-GPO.mp3
A recent orchestral version of my Mizarian Porcupine Overture, rendered with Garritan Personal Orchestra; *

http://sites.google.com/site/teamouse/MizarianPorcupineOverture.mp3
The original 1999 version of Mizarian Porcupine Overture;

http://sites.google.com/site/teamouse/mlgt3-15.mp3
The 3rd movement of Beethoven's "Moonlight" sonata, retuned in 15-ET;

http://sites.google.com/site/teamouse/15guitartest.mp3
And a brief experiment using the Rock Band 3 pro guitar as a controller to play in 15-ET.

*(strictly speaking, the GPO orchestral version of Mizarian Porcupine Overture is in 5-limit TOP 15-ET, with octaves of 1194.334 cents, not 15-EDO if you're assuming octaves are 1200 cents)

On Wed, Apr 13, 2011 at 9:50 PM, Herman Miller <hmiller@...> wrote:
>
> http://sites.google.com/site/teamouse/mlgt3-15.mp3
> The 3rd movement of Beethoven's "Moonlight" sonata, retuned in 15-ET;

I'd never heard this one before! This is awesome.

> http://sites.google.com/site/teamouse/15guitartest.mp3
> And a brief experiment using the Rock Band 3 pro guitar as a controller
> to play in 15-ET.

This one is interesting, as I'm about to get a 15-ET guitar, and I'm
not sure how that's going to go down. I can see that 256/243 vanishing
makes for major chords everywhere from what you played.

-Mike

Hi,

I wanted to try live input in Sibelius and this was a good excuse. Not
my best improvisation and Sibelius mangled what I played a bit.
Nonetheless I give you the mp3, midi file, and score under creative
commons, attribution, non-commercial.

http://micro.soonlabel.com/15-ET/Improv_on_15edo/

Chris

On Wed, Apr 13, 2011 at 4:31 PM, Daniel Nielsen <nielsed@...> wrote:
>
>
>
> This is an open question for Chris V or anyone else. I noticed that 15-EDO is not included in the list of audio files at http://micro.soonlabel.com/ and am curious of the likely cause for this..?
>
> Regarding the rule of thumb for "favored EDOs" I was considering in another thread, 5 and 15 were the only ones mentioned by both Carl and Gene that did not appear in the list I was using, so I do have a sort of numerological bias against it.

On Thu, Apr 14, 2011 at 10:44 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi,
>
> I wanted to try live input in Sibelius and this was a good excuse. Not
> my best improvisation and Sibelius mangled what I played a bit.
> Nonetheless I give you the mp3, midi file, and score under creative
> commons, attribution, non-commercial.
>
> http://micro.soonlabel.com/15-ET/Improv_on_15edo/
>
> Chris

Thanks Chris - really interesting! Did you find it easier to mess
around in 15-TET than other tunings? You might also want to look at
the Blackwood scale in it, which is basically a symmetricized diatonic
scale - you start with 5-equal, then you just create a second chain of
5-equal a major third off from the first chain. So you can do "circle
of fifths" chord progressions like this

Cmaj -> Gmaj -> Dmaj -> Amaj -> Emaj -> Bmaj

If you do this, you fill suddenly find this "Bmaj" that you arrive at
at the end is the same as the Cmaj you started with, because all of
the fifths are sharp and that's how it works. Furthermore, what I
called "Emaj" above will actually be the same as Fmaj. In other words,
you have a "circle of fifths" which is only 5-notes long, unlike in
12-equal where you have one that's 12 notes long. Rumor has it that
extra mojo is produced if you do this with major 7 chords instead of
major chords.

The whole thing ends up smushing into an octave to form a
"symmetrical" 10 note scale, which in 15-equal follows the pattern of

2 1 2 1 2 1 2 1 2 1

Kind of like the diminished scale, except there are 5 periods per
octave instead of 4, which makes the whole thing sound a lot
different.

-Mike

> http://sites.google.com/site/teamouse/mlgt3-15.mp3

> The 3rd movement of Beethoven's "Moonlight" sonata, retuned in 15-ET;

    Hot d-mn!!  This sound just as poised, if not more than the original: way to do 15EDO!   Would you believe the video game Earthworm Jim 2 used this song for a chase sequence?   And I feel bad because I have heard this song several times...just didn't know it name.   Ok, guilty as charged, this is one of those few classical pieces that's seriously fun to listen to for me...plus a great example of phrasing so loaded with attitude and swing, no rhythm section is needed. :-) 

   I swear...this is one of those rare retunings I bet you could show to any 12EDO listener and they'd have no doubt in their minds it's "very very musical" plus accessible and simply great...rather than "deliberately avant garde and made for study only" so to speak.

I would have to work with it more to really tell. However, I *do* want to
work with it more so that is a positive. The lack of tritone wasn't a
problem for me. In fact when I saw that discussion it reminded me of my
conclusion that much of common practice theory is about how to handle a
tritone - so its pretty xen not to have one.

I'll get back to 15 edo more in a bit - Oh I should say I like the whole
tone scale (on my regular keyboard) with a "minor" second - you should be
able to see that part in my score or midi file.

Chris

On Thu, Apr 14, 2011 at 10:53 AM, Mike Battaglia <battaglia01@gmail.com>wrote:

>
>
> On Thu, Apr 14, 2011 at 10:44 AM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> >
> > Hi,
> >
> > I wanted to try live input in Sibelius and this was a good excuse. Not
> > my best improvisation and Sibelius mangled what I played a bit.
> > Nonetheless I give you the mp3, midi file, and score under creative
> > commons, attribution, non-commercial.
> >
> > http://micro.soonlabel.com/15-ET/Improv_on_15edo/
> >
> > Chris
>
> Thanks Chris - really interesting! Did you find it easier to mess
> around in 15-TET than other tunings? You might also want to look at
> the Blackwood scale in it, which is basically a symmetricized diatonic
> scale - you start with 5-equal, then you just create a second chain of
> 5-equal a major third off from the first chain. So you can do "circle
> of fifths" chord progressions like this
>
> Cmaj -> Gmaj -> Dmaj -> Amaj -> Emaj -> Bmaj
>
> If you do this, you fill suddenly find this "Bmaj" that you arrive at
> at the end is the same as the Cmaj you started with, because all of
> the fifths are sharp and that's how it works. Furthermore, what I
> called "Emaj" above will actually be the same as Fmaj. In other words,
> you have a "circle of fifths" which is only 5-notes long, unlike in
> 12-equal where you have one that's 12 notes long. Rumor has it that
> extra mojo is produced if you do this with major 7 chords instead of
> major chords.
>
> The whole thing ends up smushing into an octave to form a
> "symmetrical" 10 note scale, which in 15-equal follows the pattern of
>
> 2 1 2 1 2 1 2 1 2 1
>
> Kind of like the diminished scale, except there are 5 periods per
> octave instead of 4, which makes the whole thing sound a lot
> different.
>
> -Mike
>
>

Chris>"In fact when I saw that discussion it reminded me of my conclusion that
much of common practice theory is about how to handle a tritone - so
its pretty xen not to have one. "

    I'm very interested...would this imply that a lot of chord theory is simply about how to make chords without tritones (in most cases)?  This seems to go back a discussion Igs and I had a good while ago about the tritone and critical-band-narrow semitone being the two primary things that can make a chord sour, with the tritone often being the "sourest" because some chords like C E F A with the 17/16-ish semitone can sound fairly sweet.

On Thu, Apr 14, 2011 at 12:21 PM, Michael <djtrancendance@...> wrote:
>
> Chris>"In fact when I saw that discussion it reminded me of my conclusion that much of common practice theory is about how to handle a tritone - so its pretty xen not to have one. "
>
>     I'm very interested...would this imply that a lot of chord theory is simply about how to make chords without tritones (in most cases)?  This seems to go back a discussion Igs and I had a good while ago about the tritone and critical-band-narrow semitone being the two primary things that can make a chord sour, with the tritone often being the "sourest" because some chords like C E F A with the 17/16-ish semitone can sound fairly sweet.

C E F# B D' B' sounds pretty sweet to me. So does C G E' Bb' C'' F#''.

-Mike

On Thu, Apr 14, 2011 at 11:21 AM, Michael <djtrancendance@...> wrote:

>
>
> Chris>"In fact when I saw that discussion it reminded me of my conclusion
> that much of common practice theory is about how to handle a tritone - so
> its pretty xen not to have one. "
>
> I'm very interested...would this imply that a lot of chord theory is
> simply about how to make chords without tritones (in most cases)? This
> seems to go back a discussion Igs and I had a good while ago about the
> tritone and critical-band-narrow semitone being the two primary things that
> can make a chord sour, with the tritone often being the "sourest" because
> some chords like C E F A with the 17/16-ish semitone can sound fairly sweet.
>

Confused - that seems to speak against the common (contemporary) Western
interpretation of the tritone as an interval that is simply "ambiguous" in
character. Is it really a primary source of sourness in chordal structure?
Why, due to its irrationality? I'd be interested in a cf. to the discussion.

Here is the short story. In A major the dominate 7th is e g# b d. G# is the leading tone to a. It is also a member of the tritone g#-d.

The dominant 7th is used extensively to define tonality and therefore modulations etc. How this chord is prepared for, used and resolved is a substantial part of common practice.
-----Original Message-----
From: Michael <djtrancendance@yahoo.com>
Sender: tuning@yahoogroups.com
Date: Thu, 14 Apr 2011 09:21:58
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] re: Much of common practice theory is about how to handle a tritone

Chris>"In fact when I saw that discussion it reminded me of my conclusion that
much of common practice theory is about how to handle a tritone - so
its pretty xen not to have one. "

    I'm very interested...would this imply that a lot of chord theory is simply about how to make chords without tritones (in most cases)?  This seems to go back a discussion Igs and I had a good while ago about the tritone and critical-band-narrow semitone being the two primary things that can make a chord sour, with the tritone often being the "sourest" because some chords like C E F A with the 17/16-ish semitone can sound fairly sweet.

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> Here is the short story. In A major the dominate 7th is e g# b d. G# is the leading tone to > a. It is also a member of the tritone g#-d.
>
> The dominant 7th is used extensively to define tonality and therefore modulations etc.
> How this chord is prepared for, used and resolved is a substantial part of common
> practice.

And this is why I don't think the septimal otonal tetrad (4:5:6:7) is a viable analogue to the 5-limit triad as a harmonic basis for making tonal music. 4:5:6:7 is basically a Justly-tuned dominant 7th chord, and it seems that there is something psychoacoustically tense about dom7's that causes them to want to resolve cadentially (downward by a 3/2). Can anyone demonstrate a short chord progression where you can resolve *to* a dom7 chord, rather than *from* one?

-Igs

On Thu, Apr 14, 2011 at 1:23 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
> >
> > Here is the short story. In A major the dominate 7th is e g# b d. G# is the leading tone to > a. It is also a member of the tritone g#-d.
> >
> > The dominant 7th is used extensively to define tonality and therefore modulations etc.
> > How this chord is prepared for, used and resolved is a substantial part of common
> > practice.
>
> And this is why I don't think the septimal otonal tetrad (4:5:6:7) is a viable analogue to the 5-limit triad as a harmonic basis for making tonal music. 4:5:6:7 is basically a Justly-tuned dominant 7th chord, and it seems that there is something psychoacoustically tense about dom7's that causes them to want to resolve cadentially (downward by a 3/2). Can anyone demonstrate a short chord progression where you can resolve *to* a dom7 chord, rather than *from* one?
>
> -Igs

C7 | C7 | C7 | C7
F7 | F7 | C7 | C7
G7 | F7 | C7 | C7

-Mike

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>    I swear...this is one of those rare retunings I bet you could show to any 12EDO listener and they'd have no doubt in their minds it's "very very musical" plus accessible and simply great...rather than "deliberately avant garde and made for study only" so to speak.

I believe the reaction of a lot of classical music people would be that it's simply way out of tune. I suspect something like my Night on Porcupine Mountain, which isn't a retuning so much as a reworking, would stand a better chance with them.

--- "cityoftheasleep" <igliashon@...> wrote:

> And this is why I don't think the septimal otonal tetrad (4:5:6:7)
> is a viable analogue to the 5-limit triad as a harmonic basis for
> making tonal music. 4:5:6:7 is basically a Justly-tuned dominant
> 7th chord, and it seems that there is something psychoacoustically
> tense about dom7's that causes them to want to resolve cadentially
> (downward by a 3/2). Can anyone demonstrate a short chord
> progression where you can resolve *to* a dom7 chord, rather than
> *from* one?

I don't hear otonal tetrads as tense in the least. Barbershop
is loaded with functional progressions based on them.

-Carl

> C7 | C7 | C7 | C7
> F7 | F7 | C7 | C7
> G7 | F7 | C7 | C7
>
> -Mike

Yeah, or that. :) -Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I would have to work with it more to really tell. However, I *do* want to
> work with it more so that is a positive. The lack of tritone wasn't a
> problem for me. In fact when I saw that discussion it reminded me of my
> conclusion that much of common practice theory is about how to handle a
> tritone - so its pretty xen not to have one.

The common-practice definition of a tritone is that it is three tones making up an augmented fourth, not an interval of 600 cents.

Thanks for sending the chromosounds renderings. I think you did a great job, and want to know if I should put them on my chromosounds page or if you had something else in mind. What's a JABB rendering?

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> And this is why I don't think the septimal otonal tetrad (4:5:6:7) is a viable analogue to the 5-limit triad as a harmonic basis for making tonal music. 4:5:6:7 is basically a Justly-tuned dominant 7th chord, and it seems that there is something psychoacoustically tense about dom7's that causes them to want to resolve cadentially (downward by a 3/2).

And yet, that isn't how they were treated in common practice in terms of resolution. Of course, augmented sixth chords only occurred in certain contexts and that influenced things.

"I am the walrus". It breaks all of the rules and still works.
-----Original Message-----
From: "cityoftheasleep" <igliashon@sbcglobal.net>
Sender: tuning@yahoogroups.com
Date: Thu, 14 Apr 2011 17:23:02
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: Much of common practice theory is about how to handle a tritone

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> Here is the short story. In A major the dominate 7th is e g# b d. G# is the leading tone to > a. It is also a member of the tritone g#-d.
>
> The dominant 7th is used extensively to define tonality and therefore modulations etc.
> How this chord is prepared for, used and resolved is a substantial part of common
> practice.

And this is why I don't think the septimal otonal tetrad (4:5:6:7) is a viable analogue to the 5-limit triad as a harmonic basis for making tonal music. 4:5:6:7 is basically a Justly-tuned dominant 7th chord, and it seems that there is something psychoacoustically tense about dom7's that causes them to want to resolve cadentially (downward by a 3/2). Can anyone demonstrate a short chord progression where you can resolve *to* a dom7 chord, rather than *from* one?

-Igs

>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> > And this is why I don't think the septimal otonal tetrad (4:5:6:7) is a
> viable analogue to the 5-limit triad as a harmonic basis for making tonal
> music. 4:5:6:7 is basically a Justly-tuned dominant 7th chord, and it seems
> that there is something psychoacoustically tense about dom7's that causes
> them to want to resolve cadentially (downward by a 3/2).
>

I tend to think about this in 2 different ways that don't on the surface
seem well related.

The first is simply that of voice-leading - e.g. in GBDF, BDF fills around
and through CE, defining those notes.

The other is that, if one cuts a strip of the 2D harmonic lattice from,
e.g., F and A on one edge and A and F# at the opposite, and then connects
the ends of the strip in Moebius fashion so that what would normally be F#
becomes F instead, it forms a nice harmonic space in which to move around
(until one modulates to another strip higher or lower). Adding the F to GBD
then makes the next step along an edge of fifths the tonic chord CEG.

On Thu, Apr 14, 2011 at 1:36 PM, Carl Lumma <carl@...> wrote:
>
> > C7 | C7 | C7 | C7
> > F7 | F7 | C7 | C7
> > G7 | F7 | C7 | C7
> >
> > -Mike
>
> Yeah, or that. :) -Carl

Some more examples

The Beatles - Get Back
http://www.youtube.com/watch?v=pdBnNzQz67A

Stevie Wonder - Uptight
http://www.youtube.com/watch?v=wDbyOLzEyfk

Marvin Gaye - Got To Give It Up, Part 1
http://www.youtube.com/watch?v=wRcVQDELAd4

Martha And The Vandellas - Dancing In The Streets
http://www.youtube.com/watch?v=CdvITn5cAVc

Jimi Hendrix - Manic Depression
http://www.youtube.com/watch?v=QYdq0ABH3so

Some jerk improvising on Youtube
http://www.youtube.com/watch?v=mXX3-t_4jRU&t=2m49s <-- note how it
"resolves" to something like C#dom9 omit 5 at 2:52, and then to B9
omit5

Little Richard - Lucille
http://www.youtube.com/watch?v=z3-OaNevkfg

James Brown - Sex Machine
http://www.youtube.com/watch?v=GrFzB3CvU9M

Red Hot Chili Peppers - Mellowship Slinky
http://www.youtube.com/watch?v=UVNJtNUoUsY

Tool - Reflection
http://www.youtube.com/watch?v=CvFN1p6dzNk

Radiohead - Bodysnatchers
http://www.youtube.com/watch?v=YVDSdDoD4Sg

Pearl Jam - Even Flow
http://www.youtube.com/watch?v=eE_fr8Vgn_k

Van Halen - Running with the Devil
http://www.youtube.com/watch?v=73sKNUa4M-E

Van Halen - Jamie's Cryin
http://www.youtube.com/watch?v=pA07U_Gx0Bg

Yes - Long Distance Runaround
http://www.youtube.com/watch?v=XUzpX-KxNLg

The Who - My Generation
http://www.youtube.com/watch?v=594WLzzb3JI

Claude Debussy - Prelude to the Afternoon of a Faun
http://www.youtube.com/watch?v=9_7loz-HWUM <-- Bb7 at 0:27 doesn't
sound unstable to me

Claude Debussy - Feuilles Mortes
http://www.youtube.com/watch?v=ixtZD3ybyT8 <-- after the initial
stuff, it resolves to A9 at 0:24, which is a nice break from all of
the diminished[12] type of stuff we had heard prior to this. Then, at
0:44, we hear a Gsus9 chord which sounds more like it wants to
resolve. Finally, at 1:04, it resolves to Db7#9, which is a roughly
19-limit chord, finally then moving to Eb7#9, which is another
19-limit chord. These don't sound as "resolved," but give you a nice
idea of what 19-limit harmony might one day sound like.

Leroy Anderson - Blue Tango
http://www.youtube.com/watch?v=oue8zZyrFic <-- flirts with dominant 7
chords over nearly every chord of the song

George Gershwin - Rhapsody in Blue
http://www.youtube.com/watch?v=1U40xBSz6Dc <-- same as above

Oscar Peterson - Oscar's Boogie
http://www.youtube.com/watch?v=XhQjwPI6H0k

Lee Morgan - The Sidewinder
http://www.youtube.com/watch?v=yf1Eo-6sDIE

That should include a little something for everyone, except for those
who only like common practice music pre about 1900.

-Mike

Gene,

A tritone is a diminished fifth or augmented. Fourth depending on contex which deterimines the enharmonic spelling. The interval in 12edo is the same and resolves differently again depending on context.

it was expedient for me to use the name tritone and I did not intend to invoke the definition you quoted.
-----Original Message-----
From: "genewardsmith" <genewardsmith@sbcglobal.net>
Sender: tuning@yahoogroups.com
Date: Thu, 14 Apr 2011 17:47:34
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: 15EDO is a sweet tuning...

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I would have to work with it more to really tell. However, I *do* want to
> work with it more so that is a positive. The lack of tritone wasn't a
> problem for me. In fact when I saw that discussion it reminded me of my
> conclusion that much of common practice theory is about how to handle a
> tritone - so its pretty xen not to have one.

The common-practice definition of a tritone is that it is three tones making up an augmented fourth, not an interval of 600 cents.

Thanks for sending the chromosounds renderings. I think you did a great job, and want to know if I should put them on my chromosounds page or if you had something else in mind. What's a JABB rendering?

On Thu, Apr 14, 2011 at 2:30 PM, Daniel Nielsen <nielsed@...> wrote:
>
> I tend to think about this in 2 different ways that don't on the surface seem well related.

I follow this...

> The first is simply that of voice-leading - e.g. in GBDF, BDF fills around and through CE, defining those notes.
> The other is that, if one cuts a strip of the 2D harmonic lattice from, e.g., F and A on one edge and A and F# at the opposite, and then connects the ends of the strip in Moebius fashion so that what would normally be F# becomes F instead, it forms a nice harmonic space in which to move around (until one modulates to another strip higher or lower). Adding the F to GBD then makes the next step along an edge of fifths the tonic chord CEG.

If you were talk about tempering 15/8 equal to 16/9, then that would
mean you're eliminating 135/128, and the name for that is "mavila"
temperament. But, on the other hand, if you're talking about tempering
15/8 equal to 9/5, then 25/24 vanishes, which is called "dicot"
temperament. A good tuning that can handle dicot temperament, but also
has leading tones, is 14-equal. Knowsur wrote an album in 14-equal
here:

http://split-notes.com/spnt004.php

"Haneru" is a standout track.

-Mike

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> Gene,
>
> A tritone is a diminished fifth or augmented. Fourth depending on contex which deterimines the enharmonic spelling.

I was talking about the traditional definition, which does not recognize enharmonics. The tritone in Western music goes back to the Middle Ages, where (according to the theorist Jacobus) the 3-limit tritone was 729/512, an augmented fourth, and the "semitritone" 1024/512, a diminished fifth. Only the augmented fourth consisted of three tones, and so was actually a tri tone, and that continued to be true throughout the Renaissance. Who first used "tritone" for an augmented fifth I don't know.

> The interval in 12edo is the same and resolves differently again depending on context.

A fact which doesn't much interest me.

> it was expedient for me to use the name tritone and I did not intend to invoke the definition you quoted.

When you say something doesn't have a tritone, it's not exactly clear what is meant. Traditionally, once again, the tritone arose inside a diatonic scale, so if you say 22edo has a tritone, which scale and which interval do you mean?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> A good tuning that can handle dicot temperament, but also
> has leading tones, is 14-equal.

According to one person's definition of "good tuning".

>
> If you were talk about tempering 15/8 equal to 16/9, then that would
> mean you're eliminating 135/128, and the name for that is "mavila"
> temperament. But, on the other hand, if you're talking about tempering
> 15/8 equal to 9/5, then 25/24 vanishes, which is called "dicot"
> temperament. A good tuning that can handle dicot temperament, but also
> has leading tones, is 14-equal. Knowsur wrote an album in 14-equal
> here:
>
> http://split-notes.com/spnt004.php
>
> "Haneru" is a standout track.
>
> -Mike
>

That's interesting. 14 is the only EDO that appeared in my numerological
list of "favored EDOs" that did not appear in either Gene or Carl's lists.
That's not to say I know what I'm talking about, but I do have a mushy
reason for wanting to look into it.

In that particular comment, I was just thinking about the simple (3,5)-prime
repeating octave-equivalent lattice (http://x31eq.com/lattice.htm), i.e.
12-ET.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

>Who first used "tritone" for an augmented fifth I don't know.

Of course a more relevant question would be who first used it for a diminished fifth.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> C7 | C7 | C7 | C7
> F7 | F7 | C7 | C7
> G7 | F7 | C7 | C7
>
> -Mike

Not so fast, Mr. 12-bar-blues. Try that whole progression, and then add an F major after the last C7...whoa, makes the F sound like the tonic, doesn't it?

-Igs

Nope. Don't buy it. In all these songs, they do treat a dom7 as the tonic, but in every case I still hear it wanting to resolve cadentially. The progressions that end on the dom7 tonics all feel unfinished to me. There's nowhere in any of these where they hit a dom7 and I feel that "ah..." (sigh of satisfaction) that that a V7-I cadence brings. Not that I think these tracks sound "wrong" or anything, it's a whole different kind of musical logic. My point is not that a 4:5:6:7 can't be used as a tonic chord (that's patently false), just that you can't resolve to a 4:5:6:7 with the same drop in tension as when resolving to a straight 4:5:6...unless perhaps you're coming from an even higher-tension chord, maybe some kind of 9th or 11th chord. But there is a tension that comes from that 5:7 tritone that's undeniable...I always hear a leading tone that wants to resolve upward.

Try this as an experiment: take a chord progression that ends on a dom7 tonic from any of these songs, then tack on a major triad that's a fifth below (or a fourth above) after the last chord and tell me what you think.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Apr 14, 2011 at 1:36 PM, Carl Lumma <carl@...> wrote:
> >
> > > C7 | C7 | C7 | C7
> > > F7 | F7 | C7 | C7
> > > G7 | F7 | C7 | C7
> > >
> > > -Mike
> >
> > Yeah, or that. :) -Carl
>
> Some more examples
>
> The Beatles - Get Back
> http://www.youtube.com/watch?v=pdBnNzQz67A
>
> Stevie Wonder - Uptight
> http://www.youtube.com/watch?v=wDbyOLzEyfk
>
> Marvin Gaye - Got To Give It Up, Part 1
> http://www.youtube.com/watch?v=wRcVQDELAd4
>
> Martha And The Vandellas - Dancing In The Streets
> http://www.youtube.com/watch?v=CdvITn5cAVc
>
> Jimi Hendrix - Manic Depression
> http://www.youtube.com/watch?v=QYdq0ABH3so
>
> Some jerk improvising on Youtube
> http://www.youtube.com/watch?v=mXX3-t_4jRU&t=2m49s <-- note how it
> "resolves" to something like C#dom9 omit 5 at 2:52, and then to B9
> omit5
>
> Little Richard - Lucille
> http://www.youtube.com/watch?v=z3-OaNevkfg
>
> James Brown - Sex Machine
> http://www.youtube.com/watch?v=GrFzB3CvU9M
>
> Red Hot Chili Peppers - Mellowship Slinky
> http://www.youtube.com/watch?v=UVNJtNUoUsY
>
> Tool - Reflection
> http://www.youtube.com/watch?v=CvFN1p6dzNk
>
> Radiohead - Bodysnatchers
> http://www.youtube.com/watch?v=YVDSdDoD4Sg
>
> Pearl Jam - Even Flow
> http://www.youtube.com/watch?v=eE_fr8Vgn_k
>
> Van Halen - Running with the Devil
> http://www.youtube.com/watch?v=73sKNUa4M-E
>
> Van Halen - Jamie's Cryin
> http://www.youtube.com/watch?v=pA07U_Gx0Bg
>
> Yes - Long Distance Runaround
> http://www.youtube.com/watch?v=XUzpX-KxNLg
>
> The Who - My Generation
> http://www.youtube.com/watch?v=594WLzzb3JI
>
> Claude Debussy - Prelude to the Afternoon of a Faun
> http://www.youtube.com/watch?v=9_7loz-HWUM <-- Bb7 at 0:27 doesn't
> sound unstable to me
>
> Claude Debussy - Feuilles Mortes
> http://www.youtube.com/watch?v=ixtZD3ybyT8 <-- after the initial
> stuff, it resolves to A9 at 0:24, which is a nice break from all of
> the diminished[12] type of stuff we had heard prior to this. Then, at
> 0:44, we hear a Gsus9 chord which sounds more like it wants to
> resolve. Finally, at 1:04, it resolves to Db7#9, which is a roughly
> 19-limit chord, finally then moving to Eb7#9, which is another
> 19-limit chord. These don't sound as "resolved," but give you a nice
> idea of what 19-limit harmony might one day sound like.
>
> Leroy Anderson - Blue Tango
> http://www.youtube.com/watch?v=oue8zZyrFic <-- flirts with dominant 7
> chords over nearly every chord of the song
>
> George Gershwin - Rhapsody in Blue
> http://www.youtube.com/watch?v=1U40xBSz6Dc <-- same as above
>
> Oscar Peterson - Oscar's Boogie
> http://www.youtube.com/watch?v=XhQjwPI6H0k
>
> Lee Morgan - The Sidewinder
> http://www.youtube.com/watch?v=yf1Eo-6sDIE
>
> That should include a little something for everyone, except for those
> who only like common practice music pre about 1900.
>
> -Mike
>

Yes, and if you go back to C7, then in retrospect it sounds like ut was just
the IV chord all along. Check out the Martha and the Vandellas tune I posted
for an example of a song that does exactly that in the bridge.

Sent from my iPhone

On Apr 14, 2011, at 3:37 PM, "cityoftheasleep" <igliashon@sbcglobal.net>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> C7 | C7 | C7 | C7
> F7 | F7 | C7 | C7
> G7 | F7 | C7 | C7
>
> -Mike

Not so fast, Mr. 12-bar-blues. Try that whole progression, and then add an F
major after the last C7...whoa, makes the F sound like the tonic, doesn't
it?

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> And yet, that isn't how they were treated in common practice in terms of resolution. Of
> course, augmented sixth chords only occurred in certain contexts and that influenced
> things.

I don't get it...are you saying that since in Meantone a 4:7 is an augmented 6th, dom7 chords aren't really approximating 4:5:6:7's?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Not so fast, Mr. 12-bar-blues. Try that whole progression,
> and then add an F major after the last C7...whoa, makes the
> F sound like the tonic, doesn't it?

Whether or not it does, it's hardly a fair comparison.
There are functional progressions of triads that you can
tack a power chord on the end of too. -Carl

Gene,

this is falling quickly into the abyss of absurdities. I prefaced my remark
with "common practice" and I'm pretty sure you know more than enough music
theory to know what I meant.

So... I'm dropping this portion of our conversation.

Michael - as I have recommended in the past find yourself a decent book on
music theory

Chris

On Thu, Apr 14, 2011 at 3:26 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
> >
> > Gene,
> >
> > A tritone is a diminished fifth or augmented. Fourth depending on contex
> which deterimines the enharmonic spelling.
>
> I was talking about the traditional definition, which does not recognize
> enharmonics. The tritone in Western music goes back to the Middle Ages,
> where (according to the theorist Jacobus) the 3-limit tritone was 729/512,
> an augmented fourth, and the "semitritone" 1024/512, a diminished fifth.
> Only the augmented fourth consisted of three tones, and so was actually a
> tri tone, and that continued to be true throughout the Renaissance. Who
> first used "tritone" for an augmented fifth I don't know.
>
>
> > The interval in 12edo is the same and resolves differently again
> depending on context.
>
> A fact which doesn't much interest me.
>
>
> > it was expedient for me to use the name tritone and I did not intend to
> invoke the definition you quoted.
>
> When you say something doesn't have a tritone, it's not exactly clear what
> is meant. Traditionally, once again, the tritone arose inside a diatonic
> scale, so if you say 22edo has a tritone, which scale and which interval do
> you mean?
>
>
>

Ok,

Now to address this:

"Thanks for sending the chromosounds renderings. I think you did a great
job, and want to know if I should put them on my chromosounds page or if you
had something else in mind. What's a JABB rendering?"

You are very welcome - the renderings are yours and do whatever you'd like.
I can give you the CD quality wav files too if you'd like. Also, I will
render more for you if you'd like. Thank you for being so patient seeing how
I forgot for a bit about the project.

COMB = concert and marching band
http://www.garritan.com/index.php?option=com_content&view=article&id=107&Itemid=159

JABB = Jazz and Big Band (listen to the examples on the page below)

http://www.garritan.com/index.php?option=com_content&view=article&id=144&Itemid=56

I've just scratched the surface of JABB and your piece is my first to use
COMB. All Garritan libraries are affordable, delivered by download, and
have native scala support.

It is hard to bet such a combination.

Chris

--- "cityoftheasleep" <igliashon@...> wrote:

> I always hear a leading tone that wants to resolve upward.

There's been a lot of this kind of stuff around here lately,
and Mike and I were talking about it offlist, so please let
me reiterate what I wrote to Mike:

* Nobody, not even you, cares how it sounds to you. *

I realize this can make composing difficult. But that is
precisely the challenge of xenharmonic music. Nobody can come
to these materials in a day, week, month, or even year and
unlock even a fraction of their potential. It took *hundreds*
of years to unlock the potential of a single system.

This is especially true for musicians -- and I think most
of us here probably had decent 12-ET chops before coming to
microtonality. So in addition to the problems faced by
medieval composers who tried to write like Debussy, we face
the additional hardship of having to *unlearn* the ingrained
patterns we've known since birth.

What does this mean? First, the notion of *keeping an open
mind* should be elevated to the status of mantra. Of course,
when making music we need to use our ears and our emotional
reactions. But we can reserve judgment and keep trying new
things even as we do so. And certainly we don't have to
write into a mailing list about how, 'No, sorry, it's
impossible, because I don't hear it that way, because I always
hear a half-step that wants to resolve to the nearest 12-ET
degree' or 'My psychoacoustic chunking periodicity detector
is tingling that this sounds like a "major third".' Because
saying things like that is counterproductive.

-Carl

Apologies for the crappy formatting, as my internet down. But Igs: let's
test it. Does D A D F# C G# -> G D F B G in 12-tet satisfy you? What about
in a tuning where the 7-limit tuning in the second chord is more accurate,
but the first remains detuned?

Then see if after the G7 it makes you happy to go to Cmaj. Then, if you
focus on the e in the C maj, does it make you happy to go to F5 power chord?
Finally, does it make you happy if you focus on the C in the F5 power chord
to move to the note C with no harmony afterward?

Sent from my iPhone

On Apr 14, 2011, at 3:50 PM, cityoftheasleep <igliashon@...>
wrote:

Nope. Don't buy it. In all these songs, they do treat a dom7 as the tonic,
but in every case I still hear it wanting to resolve cadentially. The
progressions that end on the dom7 tonics all feel unfinished to me. There's
nowhere in any of these where they hit a dom7 and I feel that "ah..." (sigh
of satisfaction) that that a V7-I cadence brings. Not that I think these
tracks sound "wrong" or anything, it's a whole different kind of musical
logic. My point is not that a 4:5:6:7 can't be used as a tonic chord (that's
patently false), just that you can't resolve to a 4:5:6:7 with the same drop
in tension as when resolving to a straight 4:5:6...unless perhaps you're
coming from an even higher-tension chord, maybe some kind of 9th or 11th
chord. But there is a tension that comes from that 5:7 tritone that's
undeniable...I always hear a leading tone that wants to resolve upward.

Try this as an experiment: take a chord progression that ends on a dom7
tonic from any of these songs, then tack on a major triad that's a fifth
below (or a fourth above) after the last chord and tell me what you think.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Apr 14, 2011 at 1:36 PM, Carl Lumma <carl@...> wrote:
> >
> > > C7 | C7 | C7 | C7
> > > F7 | F7 | C7 | C7
> > > G7 | F7 | C7 | C7
> > >
> > > -Mike
> >
> > Yeah, or that. :) -Carl
>
> Some more examples
>
> The Beatles - Get Back
> http://www.youtube.com/watch?v=pdBnNzQz67A
>
> Stevie Wonder - Uptight
> http://www.youtube.com/watch?v=wDbyOLzEyfk
>
> Marvin Gaye - Got To Give It Up, Part 1
> http://www.youtube.com/watch?v=wRcVQDELAd4
>
> Martha And The Vandellas - Dancing In The Streets
> http://www.youtube.com/watch?v=CdvITn5cAVc
>
> Jimi Hendrix - Manic Depression
> http://www.youtube.com/watch?v=QYdq0ABH3so
>
> Some jerk improvising on Youtube
> http://www.youtube.com/watch?v=mXX3-t_4jRU&t=2m49s <-- note how it
> "resolves" to something like C#dom9 omit 5 at 2:52, and then to B9
> omit5
>
> Little Richard - Lucille
> http://www.youtube.com/watch?v=z3-OaNevkfg
>
> James Brown - Sex Machine
> http://www.youtube.com/watch?v=GrFzB3CvU9M
>
> Red Hot Chili Peppers - Mellowship Slinky
> http://www.youtube.com/watch?v=UVNJtNUoUsY
>
> Tool - Reflection
> http://www.youtube.com/watch?v=CvFN1p6dzNk
>
> Radiohead - Bodysnatchers
> http://www.youtube.com/watch?v=YVDSdDoD4Sg
>
> Pearl Jam - Even Flow
> http://www.youtube.com/watch?v=eE_fr8Vgn_k
>
> Van Halen - Running with the Devil
> http://www.youtube.com/watch?v=73sKNUa4M-E
>
> Van Halen - Jamie's Cryin
> http://www.youtube.com/watch?v=pA07U_Gx0Bg
>
> Yes - Long Distance Runaround
> http://www.youtube.com/watch?v=XUzpX-KxNLg
>
> The Who - My Generation
> http://www.youtube.com/watch?v=594WLzzb3JI
>
> Claude Debussy - Prelude to the Afternoon of a Faun
> http://www.youtube.com/watch?v=9_7loz-HWUM <-- Bb7 at 0:27 doesn't
> sound unstable to me
>
> Claude Debussy - Feuilles Mortes
> http://www.youtube.com/watch?v=ixtZD3ybyT8 <-- after the initial
> stuff, it resolves to A9 at 0:24, which is a nice break from all of
> the diminished[12] type of stuff we had heard prior to this. Then, at
> 0:44, we hear a Gsus9 chord which sounds more like it wants to
> resolve. Finally, at 1:04, it resolves to Db7#9, which is a roughly
> 19-limit chord, finally then moving to Eb7#9, which is another
> 19-limit chord. These don't sound as "resolved," but give you a nice
> idea of what 19-limit harmony might one day sound like.
>
> Leroy Anderson - Blue Tango
> http://www.youtube.com/watch?v=oue8zZyrFic <-- flirts with dominant 7
> chords over nearly every chord of the song
>
> George Gershwin - Rhapsody in Blue
> http://www.youtube.com/watch?v=1U40xBSz6Dc <-- same as above
>
> Oscar Peterson - Oscar's Boogie
> http://www.youtube.com/watch?v=XhQjwPI6H0k
>
> Lee Morgan - The Sidewinder
> http://www.youtube.com/watch?v=yf1Eo-6sDIE
>
> That should include a little something for everyone, except for those
> who only like common practice music pre about 1900.
>
> -Mike
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> But there is a tension that comes from that 5:7 tritone that's undeniable...I always hear a leading tone that wants to resolve upward.

Zarlino heard a 7/5 (to put it into JI terms) as wanting to resolve up by an 8/7 to 8/5, and a 10/7 as wanting to descent by an 8/7 to 5/4. Was he wrong?

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > And yet, that isn't how they were treated in common practice in terms of resolution. Of
> > course, augmented sixth chords only occurred in certain contexts and that influenced
> > things.
>
> I don't get it...are you saying that since in Meantone a 4:7 is an augmented 6th, dom7 chords aren't really approximating 4:5:6:7's?

They are doing so very badly; what was doing a good job was an augmented sixth chord, the German sixth, which tended to move to a V7 directly or indirectly.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Gene,
>
> this is falling quickly into the abyss of absurdities. I prefaced my remark
> with "common practice" and I'm pretty sure you know more than enough music
> theory to know what I meant.

Actually, I really don't. Not trying to give you a hard time, but "common practice" usually includes the early modern period: Couperin would be a common practice composer, for instance. Or Schutz. Monteverdi is usually identified as the key transitional figure.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> You are very welcome - the renderings are yours and do whatever you'd like.
> I can give you the CD quality wav files too if you'd like. Also, I will
> render more for you if you'd like.

Thanks, that would be great--archives.org prefers you not use mp3s.

Thank you for being so patient seeing how
> I forgot for a bit about the project.

Thanks OK. The JABB rendition was aces.

. All Garritan libraries are affordable, delivered by download, and
> have native scala support.

Last time you said that someone urged me to ignore it, but it really does sound pretty good.

My renderings of your pieces did not require any more detail than you
already had. In fact I deleted some of the controller data to save myself
some work.
But - the online Garritan demos are the result of detailed work - however,
judging from your midi file you are no stranger to writing in detail and all
we are talking about to use Garritan to its full potential is to use midi
controller data.

Your chromosounds data (wav & mp3) will be here in about 5 minutes.

http://micro.soonlabel.com/gene_ward_smith/chromosounds/

Chris

On Thu, Apr 14, 2011 at 4:49 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > You are very welcome - the renderings are yours and do whatever you'd
> like.
> > I can give you the CD quality wav files too if you'd like. Also, I will
> > render more for you if you'd like.
>
> Thanks, that would be great--archives.org prefers you not use mp3s.
>
>
> Thank you for being so patient seeing how
> > I forgot for a bit about the project.
>
> Thanks OK. The JABB rendition was aces.
>
>
> . All Garritan libraries are affordable, delivered by download, and
> > have native scala support.
>
> Last time you said that someone urged me to ignore it, but it really does
> sound pretty good.
>
>
>

    This all begs the question....if 7/5 doesn't seem to work completely to you/Igs as a resolved chord...how about the other "tritone" of 10/7?  IE   a chord of 6:7:8:10?

Chris (to Gene)>"this is falling quickly into the abyss of absurdities. I prefaced  my
remark with "common practice" and I'm pretty sure you know more than
enough music theory to know what I meant."

>"Michael - as I have recommended in the past find yourself a decent book on music theory "

You lost me here.  This thread started through me on the basis of the many possible microtonal uses of 15EDO.  I also commented on one piece by Beethoven, "Moonlight Sonata" in 15EDO...saying that it sounded excellent. 

But how on earth does any of this relate to my needing to find a good book on theory? 
------------------------------------------
   Assuming you meant to respond to the thread on the tritone...I still don't get it. 

Apparently other people didn't either...they took tritone to mean 7/5.  And in Wikipedia it says both 7/5 and 10/7 are the Just forms of it -> http://en.wikipedia.org/wiki/Tritone. 
   Now...what on earth (perhaps) is this cryptic alternative definition of tritone you think I need a decent book on theory to learn that most everyone seems to be getting wrong?

Ok, then I will try to explain. PLEASE NOTE - Learning music theory worked
for me. If it doesn't work for you I'm ok with that. All I ask is that you
be ok with my preference too.
I don't like being called "eurocentric" or "academic elite" or
"disrespectful of folk traditions" simply because I found a way to gain
knowledge that worked for me. If this stuff is all crap to you - that is
fine by me. I don't write your music, you do, and you don't write my music
either.

In the college level theory class I took (76 - 78) the meantone meanings
were... discussed but pretty diluted in any practicality. In fact it gave
some people in the class a headache.

All of the following contain a tritone - the tritone in class was defined as
simply an interval that divides an octave in half.

http://en.wikipedia.org/wiki/Diminished_triad_chord

http://en.wikipedia.org/wiki/Diminished_seventh_chord

http://en.wikipedia.org/wiki/Dominant_seventh_chord

http://en.wikipedia.org/wiki/Augmented_sixth_chord

And while there are other notes around the tritone - written as diminished 5
or augmented 4th - the tritone is the common thread and the other notes
around it are color.

My theory teacher stated straight out that the tritone was considered the
"devil's interval" and that it was important because it was one of the
intervals that gave music motion and that we were going to learn all of the
ways composers learned to work this interval into their music in order to
give it motion, to modulate / change keys, and simply to rationalize
chromaticism.

The above sentences are why in the past when I heard Michael talk about
making a tuning that has no dissonance I have argued that the goal does not
make sense to me. Music is about creating tension and relaxation. Its one
of the things we learned when we analyzed music chord by chord and note by
note to reveal how it functioned - how composers solved compositional
problems. The rules we learned did not of course exist forever. Just like us
the composers back then were exploring / discovering. In context a bit was
discussed on how the transition from vocal music to instrumental music and
the collapse of the variety of meantone into 12 equal offer opportunity and
also lost nuance. But again - I'm sure due to headaches - we mostly
pretended 12 equal always existed.

That is the best I think I can do in email. Honestly any decent theory book
will cover this and explain it to some degree or another.

http://www.amazon.com/Harmony-Fifth-Walter-Piston/dp/0393954803

Schoenberg I think is a particularly good teacher.
http://www.amazon.com/Theory-Harmony-California-Library-Reprint/dp/0520049446/ref=sr_1_2?ie=UTF8&s=books&qid=1302815894&sr=1-2

Here are some of my text books - revised of course

http://www.amazon.com/Gradus-Integrated-Approach-Counterpoint-Analysis/dp/0393955494

http://www.amazon.com/Gradus-Integrated-Approach-Counterpoint-Analysis/dp/0393956261/ref=pd_bxgy_b_text_b

http://www.amazon.com/Music-Theory-Practice-Vol-Anthology/dp/0072950684

On Thu, Apr 14, 2011 at 4:46 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Gene,
> >
> > this is falling quickly into the abyss of absurdities. I prefaced my
> remark
> > with "common practice" and I'm pretty sure you know more than enough
> music
> > theory to know what I meant.
>
> Actually, I really don't. Not trying to give you a hard time, but "common
> practice" usually includes the early modern period: Couperin would be a
> common practice composer, for instance. Or Schutz. Monteverdi is usually
> identified as the key transitional figure.
>
>
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Apologies for the crappy formatting, as my internet down. But Igs: let's
> test it. Does D A D F# C G# -> G D F B G in 12-tet satisfy you? What about
> in a tuning where the 7-limit tuning in the second chord is more accurate,
> but the first remains detuned?
>
> Then see if after the G7 it makes you happy to go to Cmaj. Then, if you
> focus on the e in the C maj, does it make you happy to go to F5 power chord?
> Finally, does it make you happy if you focus on the C in the F5 power chord
> to move to the note C with no harmony afterward?

Tried this in 19-TET, since my 12-TET guitars are in storage. The Cmaj is the bottom of the resolution gravity-well, regardless of whether I voice the G chord GDFBG or GDEbBG (the latter has the better approximation of 7-limit harmony). On the other hand, if I drop the 7th from the G chord, it no longer feels like it wants to go to C. The added 11th in the D chord actually doesn't seem to help the G sound any more resolved. Actually, the added 11th in the D seems to make the resolution to G weaker, rather than stronger, because I hear the D as a sort of "ambiguous cloud" that was tense but didn't feel like it wanted to move in a specific direction. Interesting.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "cityoftheasleep" <igliashon@> wrote:
>
> > ...it seems that there is something psychoacoustically
> > tense about dom7's that causes them to want to resolve cadentially
> > (downward by a 3/2). Can anyone demonstrate a short chord
> > progression where you can resolve *to* a dom7 chord, rather than
> > *from* one?
>
> I don't hear otonal tetrads as tense in the least. Barbershop
> is loaded with functional progressions based on them.
>
> -Carl
>

Boy you know the way to a baritone's heart. I am a certified addict to the barbershop 4:5:6:7 chord. I automatically try to put every melody I hear to barbershop, and look for plugging in dominant 7ths and particularly German 6th's wherever I can justify it. So contrary to trying to get rid of tritones, I find it way up there with caffeine, alcohol, sugar and nicotine in its addictiveness. This could be why I've finding the newer symphonies written in the 20th century as being "diet classical music".

It does seem curious that a triad has not been described as wanting to resolve it's one 5-limit tone - the major 3rd - to an open 5th, 4th or octave. But the ear, upon hearing a dominant 7th, has come to expect a cadence to occur that resolves the 7th of the chord down (or in the case of the augmented 6th, up). I would expect that the ear becomes ambivalent upon hearing the dominant 7th simply because this set of notes has more than one viable harmonic justification. A strong tendency to resolve it down a fifth to a tonic can easily be based on hearing it as a 36:45:54:64 tuning found in the 5-limit just major scale. An ear that has been exposed to a lot of barbershop will probably find itself resolving it as an augmented 6th (128:160:192:225). You may note that both these tunings have in common the fact that it is the 7th of the chord (or augmented 6th) which is throwing the tuning way up into the stratosphere in the harmonic series (the triad is the 4:5:6 in all three of them), while the simple 4:5:6:7 does not.

The blues style of music that is totally content to play the dominant at the end of a song without resolving it could well have its basic in the hearing of a true septimal tuning.

Billy

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> There's been a lot of this kind of stuff around here lately,
> and Mike and I were talking about it offlist, so please let
> me reiterate what I wrote to Mike:
>
> * Nobody, not even you, cares how it sounds to you. *

What does that even mean? How do I not care how something sounds to me?

> I realize this can make composing difficult. But that is
> precisely the challenge of xenharmonic music. Nobody can come
> to these materials in a day, week, month, or even year and
> unlock even a fraction of their potential. It took *hundreds*
> of years to unlock the potential of a single system.

If anything seems counter-productive, it's precisely this sort of attitude. Are you saying that nothing that we've learned can be applied to microtonal systems?

> This is especially true for musicians -- and I think most
> of us here probably had decent 12-ET chops before coming to
> microtonality. So in addition to the problems faced by
> medieval composers who tried to write like Debussy, we face
> the additional hardship of having to *unlearn* the ingrained
> patterns we've known since birth.

Do we? I haven't yet felt the need to unlearn anything. Am I doing something wrong?

> What does this mean? First, the notion of *keeping an open
> mind* should be elevated to the status of mantra. Of course,
> when making music we need to use our ears and our emotional
> reactions. But we can reserve judgment and keep trying new
> things even as we do so. And certainly we don't have to
> write into a mailing list about how, 'No, sorry, it's
> impossible, because I don't hear it that way, because I always
> hear a half-step that wants to resolve to the nearest 12-ET
> degree' or 'My psychoacoustic chunking periodicity detector
> is tingling that this sounds like a "major third".' Because
> saying things like that is counterproductive.

We cannot expect the whole world, or even a few people, to "unlearn" a lifetime of pattern-recognition programming just so that they can enjoy our music properly. I'm all for keeping an open mind too, but there comes a point where you have to abandon a line of inquiry after it's repeatedly failed to satisfy one's goals.

I'm not hating on 4:5:6:7 or saying it's unmusical or that it's too tense or anything like that; I'm just saying that no matter how you gussy it up, it sounds like a dom7 chord, and it's going to sound that way to most listeners. Rather than being a "natural evolution" of tonality analogous to the addition of 5-limit harmony to Pythagorean music, it's just going to make everything sound generically "jazzy", which to me isn't all that remarkable.

Okay, maybe jazz *is* a natural evolution of tonality, and a system like 22-EDO that renders jazz chords closer to JI might be worthwhile to some people. But if that's really the case, the revolution is already at hand and doesn't really need microtonality to take it further--as you say, barbershop quartets have already been at it for almost a century, to say nothing of the rest of the jazz-influenced musical world.

I gave that approach a fair shake, I believe--the first several systems I explored (31-EDO, 22-EDO, and Catler's 12-tone Ultra Plus) were all supposed to demonstrate the "magical" properties of smoother 7-limit harmonies, and in fact quite a few of the other systems I've explored more recently (15, 16, and 20-EDO) all hit the 7th harmonic pretty well...but sorry, it's never sounded like anything more than a dom7 to me. If after almost eight years of work and exploration that prejudice hasn't budged, why should I expect anything different after another 8 years? Let alone anything different from other human beings who would listen to my music? To me, that line of inquiry seems dead as a door-nail.

I'll admit, 16's version of Lemba[6] (or whatever you want to call its 4L+2s scale) and its good 4:5:7 triads pushes a couple interesting buttons for me, but I'd be lying if I said it didn't feel remarkably like the whole-tone scale most of the time. If I have to unlearn my lifetime of perceptual biases for it not to sound that way, I don't see the point in it. For me, the point of microtonal music is to find stuff that turns my biases on their heads and freaks me out a bit in the process, but is just accessible enough to keep me coming back for more. I've found more success with that on many other avenues than I have by trying to make 7-limit tetrads the new "base building-block" of my chordal music.

-Igs

--- In tuning@yahoogroups.com, "Billy" <billygard@...> wrote:

> It does seem curious that a triad has not been described as wanting to resolve it's one 5-limit tone - the major 3rd - to an open 5th, 4th or octave.

That was actually done in the early Renaissance.

--- "cityoftheasleep" <igliashon@...> wrote:

> Tried this in 19-TET, since my 12-TET guitars are in storage.

Success! -Carl

--- "cityoftheasleep" <igliashon@...> wrote:

> I'm just saying that no matter how you gussy it up, it
> sounds like a dom7 chord,
[snip]
> Am I doing something wrong?

I'd say so, yes. A "dom7" chord is a figment of 12-ET musical
practice after about 1700 and really doesn't need to have anything
to do with xenharmonic music unless you want it to. -Carl

--- "Billy" <billygard@...> wrote:

> Boy you know the way to a baritone's heart. I am a certified
> addict to the barbershop 4:5:6:7 chord. I automatically try to
> put every melody I hear to barbershop, and look for plugging
> in dominant 7ths and particularly German 6th's wherever I can
> justify it. So contrary to trying to get rid of tritones, I
> find it way up there with caffeine, alcohol, sugar and
> nicotine in its addictiveness.

Nice to meet a fellow addict! I used to sing lead (occasionally
tenor) and always envied the baritones. Especially what
David Wright used to do with it -- some of the most exquisite
part writing I've heard anywhere, for sure.

-Carl

--- Chris Vaisvil <chrisvaisvil@...> wrote:

> Your chromosounds data (wav & mp3) will be here in about 5 minutes.
>
> http://micro.soonlabel.com/gene_ward_smith/chromosounds/

Thanks for doing this Chris! I think you're the third person
other than Gene to try rendering Gene's music, but this is the
first version I've heard that I like better than Gene's original.
I think the Jazz version is my favorite. You and GPO really
came through here, thanks again! This has always been one of
my favorite GWS pieces.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "cityoftheasleep" <igliashon@> wrote:
>
> > I'm just saying that no matter how you gussy it up, it
> > sounds like a dom7 chord,
> [snip]
> > Am I doing something wrong?
>
> I'd say so, yes. A "dom7" chord is a figment of 12-ET musical
> practice after about 1700 and really doesn't need to have anything
> to do with xenharmonic music unless you want it to. -Carl
>

I said it "sounds like", not "it is". Dominant 7ths are of course located specifically in a functional tonal framework based on a heptatonic scale generated by a series of reasonably-well approximated 3/2's...it wouldn't make sense to use the term "dominant 7th" to describe the tonic tetrad of a Pajara standard pentachordal major decatonic scale, of course. But the point is that the difference between a 12-TET dom7 and a 4:5:6:7 is pretty much negligible in terms of at least my own categorical perception, even after years of playing microtonal music. Thus the association between a 4:5:6:7 and the 12-ET-based functions of a dominant 7th is a difficult one to break. I'd honestly be surprised if other people have a drastically different view on the matter, such that the functional and/or generically "jazzy" connotations of the 12-ET dominant 7th chord don't overwhelmingly color perception of 4:5:6:7 chords.

I really don't get what you're suggesting. Do you think that if I somehow locked myself away from the musical cultural background and forced myself to play and compose in a system where I used 4:5:6:7's as the base consonance, I could get to a point where it no longer retains the 12-TET associations it currently has for me?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- Chris Vaisvil <chrisvaisvil@> wrote:
>
> > Your chromosounds data (wav & mp3) will be here in about 5 minutes.
> >
> > http://micro.soonlabel.com/gene_ward_smith/chromosounds/
>
> Thanks for doing this Chris! I think you're the third person
> other than Gene to try rendering Gene's music, but this is the
> first version I've heard that I like better than Gene's original.
> I think the Jazz version is my favorite. You and GPO really
> came through here, thanks again! This has always been one of
> my favorite GWS pieces.

I've updated the Chromosounds page:

http://www.archive.org/download/Chromosounds/GWS-GPO-Jazz-chromosounds.flac

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> But the point is that the difference between a 12-TET dom7 and a 4:5:6:7 is pretty much negligible in terms of at least my own categorical perception, even after years of playing microtonal music.

Listen again and I think you'll note that the seventh of Dom7 isn't even fully fused. It sticks way the hell out, so to speak. That's a whole other thing than just sonance, and puts it into a different perceptual category, I think. Of course, 4:5:6:7 sounds "jazzy", but I think it actually sounds *more* jazzy.

--- "cityoftheasleep" <igliashon@...> wrote:

> it wouldn't make sense to use the term "dominant 7th" to
> describe the tonic tetrad of a Pajara standard pentachordal
> major decatonic scale, of course. But the point is that the
> difference between a 12-TET dom7 and a 4:5:6:7 is pretty much
> negligible in terms of at least my own categorical perception,

Right! On Planet Pajara, they're saying the chord is no good
for a diatonic V7 because it sounds too stable. Who's right?

Of course you can use the shared categorical perception of
yourself and the audience as a starting point. And that's
probably what these guys
http://en.wikipedia.org/wiki/Burgundian_School
were doing with triads. That's how I hear it anyway. They use
the 3rds and 6ths for color but continually fall back on the
3-limit framework.

> even after years of playing microtonal music. Thus the
> association between a 4:5:6:7 and the 12-ET-based functions
> of a dominant 7th is a difficult one to break. I'd honestly
> be surprised if other people have a drastically different
> view on the matter, such that the functional and/or
> generically "jazzy" connotations of the 12-ET dominant 7th
> chord don't overwhelmingly color perception of 4:5:6:7 chords.

Speaking for myself, I went to barbershop concerts regularly
as a kid and I was instantly drawn to it. I never thought the
chords were tense - quite the opposite. When I was in college
I joined the JI network and got some tapes with 7-limit chords
in other contexts. I thought they sounded out-of-tune. Then
one day I was listening to barbershop and my ear did a 360
and suddenly recognized the 7-limit intervals in the music.
I'd gained the ability to listen analytically to barbershop.
After that the recordings from the JI network sounded great!
List regulars are tired of this story by now, and probably I
should stop telling it. I guess my barbershop experience did
give me a way of hearing 4:5:6:7 chords as basic consonances,
but I'm not claiming any kind of golden hearing. I have loads
of trouble finding melodies and progressions in xenharmonic
systems that sound 'natural' to me. Then I hear somebody like
you, Petr, Knowsur, Herman hit one out of the park in the same
system and I'm like, Oh, that's what it sounds like!

At barbershop boot camp somebody told me their chorus was
rehearsing with a conductor who had perfect pitch, for a
joint concert they were doing. Apparently the guy totally
freaked because he kept hearing that the chorus was out of
tune but couldn't reconcile it with the fact that it sounded
perfectly fine.

> I really don't get what you're suggesting. Do you think that
> if I somehow locked myself away from the musical cultural
> background and forced myself to play and compose in a system
> where I used 4:5:6:7's as the base consonance, I could get to
> a point where it no longer retains the 12-TET associations it
> currently has for me?

I'm saying we should work hard to avoid the assumption that
everything we hear is inherent in the intervals or chords,
and that others must hear it the same way. This was my general
point not aimed specifically at you. You said 7:5 has a
tension that's undeniable. I don't think it's inherently more
tense than any other dyad with n*d ~ 35. Try a raw listening
comparison and see if you agree. I think it sounds tense when
it reminds us of progressions where the its cousin's proximity
to 3:2 (and especially to the tonic 3:2) was used to create and
resolve tension.

-Carl

On Thu, Apr 14, 2011 at 4:58 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> My renderings of your pieces did not require any more detail than you already had. In fact I deleted some of the controller data to save myself some work.
> But - the online Garritan demos are the result of detailed work - however, judging from your midi file you are no stranger to writing in detail and all we are talking about to use Garritan to its full potential is to use midi controller data.
>
> Your chromosounds data (wav & mp3) will be here in about 5 minutes.
>
> http://micro.soonlabel.com/gene_ward_smith/chromosounds/

Chris: did you just pop in the MIDI file and let er rip? And you
managed to get rid of most of the MIDI junk data?

Is there any way you could post the MIDI file as well? I was trying to
come up with an EastWest render of this a long time ago, but never got
past the junk controller data. And after Gene posted recently that
he'd lost the original seq file in a computer crash, I'd lost all hope
about ever doing this again.

Thanks,
Mike

Somebody wanted examples, so I've added one:

http://x31eq.com/music/dingfei.ogg

If anybody can read a score in Tripod Notation, there's one
of those as well:

http://x31eq.com/music/dingfei.pdf

It's a work in progress. Worse than that, it's a work not
progressing, so I can't always remember what it's supposed
to sound like. But it does have some resolutions and,
according to the score, it's resolving onto pure seventh
chords (magic tempered).

The first is at bar 17, or 25s into the audio. There's a
sense of tension resolving onto the pure triad that follows
it. I hope I don't have to put down the 5-limit in order
to support the 7-limit. If you treat the new chord as a
tonic, the resolution would be IV-I.

Then there's a resolution at 32.5s (bar 22). If that isn't
final enough, it limps onto another at 37s (bar 25). Both
are pure sevenths.

The final chord is a pure 5-limit triad. And, yes, the
5-limit sounds good, doesn't it?

Oh, yes, and the main point of this piece is that it uses
both the pure 7-limit seventh chords and a 5-limit
rendering of a traditional dominant seventh (with 11-limit
implications). My surprise, on first listen, was how *bad*
and out of tune the extended 5-limit chord sounded.

Paul Erlich's "Decatonic Swing" is a good example of
7-limit harmony. I believe it's all seventh chords, and
they work. Even given the poor approximations of
Pajara/22, the harmonic logic makes sense.

Now to the debate:

"cityoftheasleep" <igliashon@...> wrote:
>
> I said it "sounds like", not "it is". Dominant 7ths are
> of course located specifically in a functional tonal
> framework based on a heptatonic scale generated by a
> series of reasonably-well approximated 3/2's...it
> wouldn't make sense to use the term "dominant 7th" to
> describe the tonic tetrad of a Pajara standard
> pentachordal major decatonic scale, of course. But the
> point is that the difference between a 12-TET dom7 and a
> 4:5:6:7 is pretty much negligible in terms of at least my
> own categorical perception, even after years of playing
> microtonal music. Thus the association between a 4:5:6:7
> and the 12-ET-based functions of a dominant 7th is a
> difficult one to break. I'd honestly be surprised if
> other people have a drastically different view on the
> matter, such that the functional and/or generically
> "jazzy" connotations of the 12-ET dominant 7th chord
> don't overwhelmingly color perception of 4:5:6:7 chords.

You're still saying you "would be" surprised when people
have already told you they have a different view. By now
you should have been surprised. I'll add myself to the
list. I don't hear "12-ET-based functions" when I hear a
4:5:6:7. I don't even know what a 12-ET-based function
would sound like. 4:5:6:7 sounds like a pure chord, and the
12-ET dominant seventh doesn't. I never hear the half-octave
"wanting to resolve" a particular way. I always thought
that was a convenient fiction harmony teachers use to
explain conventional chord sequences (which sound fine;
I'm not knocking them).

I can hear the 7 of 4:5:6:7 as being out of tune. So can
the 5 for that matter. I think it's because they're
outside the expected melodic framework. The solution is to
emphasize different melodic patterns. It may help to treat
the 7 as a dissonance when you use it first.

Another problem with 4:5:6:7 is that it sounds too pure and
fused. It doesn't bring an interesting new sonority to the
table. The solution there is to tie it in with scrunchier
chords that hold the 7.

I don't think functional considerations are leading me
anywhere. I don't think most listeners out there in the
big wide world are at all sensitive to the Common Practice
formula for treatment of dominant sevenths. A lot of us
are attuned to the liberal use of seventh chords in rock
and blues. They have a spicy feel and can you can use one
as the tonic. I don't find a 4:5:6:7 has the same feel at
all so I don't think it's altering my perceptions, other
than making be receptive to the use of the 7 as coloration.

> I really don't get what you're suggesting. Do you think
> that if I somehow locked myself away from the musical
> cultural background and forced myself to play and compose
> in a system where I used 4:5:6:7's as the base
> consonance, I could get to a point where it no longer
> retains the 12-TET associations it currently has for me?

I don't know how strong the associations are for you. I
have noticed that you don't focus on microtonal harmony.
Your Map of an Internal Landscape (that's you, right?) is
good microtonal music, but it doesn't have much harmony.
Or, at least, the harmony is kept in the background. Whereas
your 12-TET music uses conventional harmonic patterns. So
it sounds like you didn't find new patterns you liked in
the new systems. Something more recent has more harmony,
but it doesn't have the "wow factor", in harmonic terms,
that some of Gene's and George's music (and I hope some of
mine) does. And then you say you don't see the point of
close approximations to simple ratios, that they don't have
musical value for you. So, fine, if it doesn't work for
you, try something that does.

Graham

On Fri, Apr 15, 2011 at 1:36 AM, Carl Lumma <carl@...> wrote:
>
> Of course you can use the shared categorical perception of
> yourself and the audience as a starting point.

Hell yes you can! And then by using this curve

http://www.taiwanfirstnations.org/WundtCurve.jpg

you will surelv achieve victory.

> And that's
> probably what these guys
> http://en.wikipedia.org/wiki/Burgundian_School
> were doing with triads.

That's quite an all-star cast.

> I guess my barbershop experience did
> give me a way of hearing 4:5:6:7 chords as basic consonances,
> but I'm not claiming any kind of golden hearing.

I do sometimes think that you may have the best ears on the list, as
far as microtonal stuff is concerned. Either way, I still can't
believe we're having this discussion, because when I listen to this

http://www.youtube.com/watch?v=bQyWmaTSzNs

the last thing I'm thinking about is "god damn, these V7 chords need
to resolve to I." But I guess people hear things differently.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > There's been a lot of this kind of stuff around here lately,
> > and Mike and I were talking about it offlist, so please let
> > me reiterate what I wrote to Mike:
> >
> > * Nobody, not even you, cares how it sounds to you. *

How about if this were worded:

"Nobody, not even you, or I, or anyone else, cares how it sounds to you, or me, or anyone else?"

This would remove the (very understandable) immediate impression that the statement is designed to establish a hierarchy of perceptional value. Even worded such, the statement could very well be a feint intended to lay ground for the idea of a "scientific" perceptual "standard" being what should really be cared about- the "scientific" perception of course being the pet fantasy of the here oddly unspoken "I". That is, even the inclusion of "I" in the statement would not completely preclude Winternet chest-beating as the true motivation of this statement.

But let us ignore suspicions and blithely proceed as if the statement were made in good faith, and inludes by implication "I" and "anyone else", which it must in order to be consistent with the evocation of historical perspective which follows it.

Taken in this way, it is an excellent statement. Our conditioned perceptions simply cannot be not universal truths, or even terribly valuable indicators, about how musical motions and identities will be percieved in the long term.

Somewhere in storage I have a reproduction of a medieval woodcut illustrating the distinction between the music of devils and that of angels. The angels are playing plucked instruments, the shaggy (looks like Rob Zombie) devil a ... violin. The instrumentation is the reverse of that in contemporary conception- today it is the violin which is the symbol of "high culture" (f*cking monolingual communication, it's better as Hochkultur) and the guitars are in the hands of the "devils".

On the other hand, or hoof, it is the most odiferous of manure to ignore the value of the perceptions of the creators in the moment, and the most paralizing position, as far as making music, is to feel too strongly the weight of history past, present and future and not be able to say fukkit and just create. :-)

>

"Dominant" is a description of function, not of a reified sonority. V7 is a dominant 7, I7 a seventh chord.

Whether the tempering out of 36:35 is an act of timid dilution, or a celebration of human ability to reinterpret according to context, is an artistic decision that must be made by the individual creator.

But in order to make this entire conversation meaningful, we do need to establish whether 36:35 is being tempered out, physically or perceptually, or not. Otherwise we're just rubbing dickheads in the canebrake with less agility and awareness than that of theorists from centuries ago (see Tartini on this very subject).

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > And this is why I don't think the septimal otonal tetrad (4:5:6:7) is a viable analogue to the 5-limit triad as a harmonic basis for making tonal music. 4:5:6:7 is basically a Justly-tuned dominant 7th chord, and it seems that there is something psychoacoustically tense about dom7's that causes them to want to resolve cadentially (downward by a 3/2).
>
> And yet, that isn't how they were treated in common practice in terms of resolution. Of course, augmented sixth chords only occurred in certain contexts and that influenced things.
>

Passing the midi file is Gene's decision.

In Sonar there are at least 3 views to see midi controller data. I used
piano roll and deleted what didn't have a function in Garritan JABB. After
that the midi file played correctly with the exception that Garritan handles
velocity data a bit different.

Chris

On Fri, Apr 15, 2011 at 2:06 AM, Mike Battaglia <battaglia01@...m>wrote:

>
>
> On Thu, Apr 14, 2011 at 4:58 PM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> >
> > My renderings of your pieces did not require any more detail than you
> already had. In fact I deleted some of the controller data to save myself
> some work.
> > But - the online Garritan demos are the result of detailed work -
> however, judging from your midi file you are no stranger to writing in
> detail and all we are talking about to use Garritan to its full potential is
> to use midi controller data.
> >
> > Your chromosounds data (wav & mp3) will be here in about 5 minutes.
> >
> > http://micro.soonlabel.com/gene_ward_smith/chromosounds/
>
> Chris: did you just pop in the MIDI file and let er rip? And you
> managed to get rid of most of the MIDI junk data?
>
> Is there any way you could post the MIDI file as well? I was trying to
> come up with an EastWest render of this a long time ago, but never got
> past the junk controller data. And after Gene posted recently that
> he'd lost the original seq file in a computer crash, I'd lost all hope
> about ever doing this again.
>
> Thanks,
> Mike
>
>

>"Paul Erlich's "Decatonic Swing" is a good example of 7-limit harmony. I believe it's all seventh chords, and they work"

   Mathematically sound as it may be...that song IE the result sounds quite tense to me....though at least I can give it credit for having predictable tension rather than out-of-control variations in tension.  Just about anything from Igs though, IMVHO, sounds more balanced than that song...for example.

>"Your Map of an Internal Landscape (that's you, right?) is good microtonal music, but it doesn't have much harmony. Or, at least, the harmony is kept in the background."

  This goes back to a very old repeated view of mine...which is that "bad" scales have less chords and less harmonic possibilities.  "Map of an Internal Landscape" has chords, yes...but rather small ones and relatively few of them vs. your 12EDO music.  And agreed, Gene's music, Paul Erlich's music...does have that chordal depth...but often sounds a fair bit more unstable as a result (hence, IMVHO, why Igs is the most popular composer).  Predictably, my proposed solution to this issue is scales with many tall chords available...my chosen obsession for the last, what, 3 years or so.

  Which ultimately brings me back to "so if 12EDO is so perfect to so many people's hearing...what can we improve on from 12EDO that will allow us slack to let other things be 'worse' than in 12EDO and still maintain the same overall sense of balance?  And the two things that come to mind immediately are semitones (happily violating the Critical Band) and tritones (happily violating Harmonic Entropy).  Which is why I think solving the tritone problem can lead to a lot more harmonic flexibility in alternative scales and tunings.

--- On Thu, 4/14/11, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Much of common practice theory is about how to handle a tritone
To: tuning@yahoogroups.com
Date: Thursday, April 14, 2011, 11:06 PM

Somebody wanted examples, so I've added one:

http://x31eq.com/music/dingfei.ogg

If anybody can read a score in Tripod Notation, there's one

of those as well:

http://x31eq.com/music/dingfei.pdf

It's a work in progress. Worse than that, it's a work not

progressing, so I can't always remember what it's supposed

to sound like. But it does have some resolutions and,

according to the score, it's resolving onto pure seventh

chords (magic tempered).

The first is at bar 17, or 25s into the audio. There's a

sense of tension resolving onto the pure triad that follows

it. I hope I don't have to put down the 5-limit in order

to support the 7-limit. If you treat the new chord as a

tonic, the resolution would be IV-I.

Then there's a resolution at 32.5s (bar 22). If that isn't

final enough, it limps onto another at 37s (bar 25). Both

are pure sevenths.

The final chord is a pure 5-limit triad. And, yes, the

5-limit sounds good, doesn't it?

Oh, yes, and the main point of this piece is that it uses

both the pure 7-limit seventh chords and a 5-limit

rendering of a traditional dominant seventh (with 11-limit

implications). My surprise, on first listen, was how *bad*

and out of tune the extended 5-limit chord sounded.

Paul Erlich's "Decatonic Swing" is a good example of

7-limit harmony. I believe it's all seventh chords, and

they work. Even given the poor approximations of

Pajara/22, the harmonic logic makes sense.

Now to the debate:

"cityoftheasleep" <igliashon@...> wrote:

>

> I said it "sounds like", not "it is". Dominant 7ths are

> of course located specifically in a functional tonal

> framework based on a heptatonic scale generated by a

> series of reasonably-well approximated 3/2's...it

> wouldn't make sense to use the term "dominant 7th" to

> describe the tonic tetrad of a Pajara standard

> pentachordal major decatonic scale, of course. But the

> point is that the difference between a 12-TET dom7 and a

> 4:5:6:7 is pretty much negligible in terms of at least my

> own categorical perception, even after years of playing

> microtonal music. Thus the association between a 4:5:6:7

> and the 12-ET-based functions of a dominant 7th is a

> difficult one to break. I'd honestly be surprised if

> other people have a drastically different view on the

> matter, such that the functional and/or generically

> "jazzy" connotations of the 12-ET dominant 7th chord

> don't overwhelmingly color perception of 4:5:6:7 chords.

You're still saying you "would be" surprised when people

have already told you they have a different view. By now

you should have been surprised. I'll add myself to the

list. I don't hear "12-ET-based functions" when I hear a

4:5:6:7. I don't even know what a 12-ET-based function

would sound like. 4:5:6:7 sounds like a pure chord, and the

12-ET dominant seventh doesn't. I never hear the half-octave

"wanting to resolve" a particular way. I always thought

that was a convenient fiction harmony teachers use to

explain conventional chord sequences (which sound fine;

I'm not knocking them).

I can hear the 7 of 4:5:6:7 as being out of tune. So can

the 5 for that matter. I think it's because they're

outside the expected melodic framework. The solution is to

emphasize different melodic patterns. It may help to treat

the 7 as a dissonance when you use it first.

Another problem with 4:5:6:7 is that it sounds too pure and

fused. It doesn't bring an interesting new sonority to the

table. The solution there is to tie it in with scrunchier

chords that hold the 7.

I don't think functional considerations are leading me

anywhere. I don't think most listeners out there in the

big wide world are at all sensitive to the Common Practice

formula for treatment of dominant sevenths. A lot of us

are attuned to the liberal use of seventh chords in rock

and blues. They have a spicy feel and can you can use one

as the tonic. I don't find a 4:5:6:7 has the same feel at

all so I don't think it's altering my perceptions, other

than making be receptive to the use of the 7 as coloration.

> I really don't get what you're suggesting. Do you think

> that if I somehow locked myself away from the musical

> cultural background and forced myself to play and compose

> in a system where I used 4:5:6:7's as the base

> consonance, I could get to a point where it no longer

> retains the 12-TET associations it currently has for me?

I don't know how strong the associations are for you. I

have noticed that you don't focus on microtonal harmony.

Your Map of an Internal Landscape (that's you, right?) is

good microtonal music, but it doesn't have much harmony.

Or, at least, the harmony is kept in the background. Whereas

your 12-TET music uses conventional harmonic patterns. So

it sounds like you didn't find new patterns you liked in

the new systems. Something more recent has more harmony,

but it doesn't have the "wow factor", in harmonic terms,

that some of Gene's and George's music (and I hope some of

mine) does. And then you say you don't see the point of

close approximations to simple ratios, that they don't have

musical value for you. So, fine, if it doesn't work for

you, try something that does.

Graham

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Passing the midi file is Gene's decision.

Sure,it's OK.

Mike, the midi file is here:

http://micro.soonlabel.com/gene_ward_smith/chromosounds/GeneSmith_chromegpo2.mid

And - Carl - I'm glad you like the GPO'd version so well.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> Right! On Planet Pajara, they're saying the chord is no good
> for a diatonic V7 because it sounds too stable. Who's right?

Well, given that there is no evidence of the existence of a Planet Pajara....

> Speaking for myself, I went to barbershop concerts regularly
> as a kid and I was instantly drawn to it. I never thought the
> chords were tense - quite the opposite.

There's tense as in "this wants to move somewhere" and then there's tense as in "this induces a mild stress response" (a la some of Mike B.'s early listening tests). 4:5:6:7 is not what I would describe as a stress-inducing chord, it's just that it feels like it wants to move in a way that 4:5:6 doesn't, because of my associations between it and its nearest 12-TET counterpart. And also, I've tried out a bunch of progressions that are supposed to resolve to a 4:5:6:7, and for every one I've tried tacking on a 4:5:6 a 3/2 below the "tonic", and to me that latter chord sounds "even more" resolved every time. I'm not saying that ending on a 4:5:6:7 feels intolerably tense to me, like ending on an augmented chord would, just that dropping the 7 from it makes it sound more resolved. I would be surprised if anyone here felt that the 7 actually enhanced the feeling of resolution.

> I guess my barbershop experience did
> give me a way of hearing 4:5:6:7 chords as basic consonances,
> but I'm not claiming any kind of golden hearing.

The thing is, though, in barbershop they don't add the 7th to every chord, or even the majority of chords. It's there often enough to be characteristic of the style, but it's not the base unit of harmony.

> At barbershop boot camp somebody told me their chorus was
> rehearsing with a conductor who had perfect pitch, for a
> joint concert they were doing. Apparently the guy totally
> freaked because he kept hearing that the chorus was out of
> tune but couldn't reconcile it with the fact that it sounded
> perfectly fine.

I've always wondered how "perfect pitch" would interact with JI.

> I'm saying we should work hard to avoid the assumption that
> everything we hear is inherent in the intervals or chords,
> and that others must hear it the same way. This was my general
> point not aimed specifically at you.

First of all, I don't like to talk about intervals having properties that are somehow objective, which they could possess in absence of listeners. A musical interval isn't just a relationship between two tones, it's a relationship between those two tones and a listener. So when I talk about something "inherent" or "undeniable", I'm not talking universal...I'll be damned if I have any idea what constitutes harmonic tension to Indonesian or Middle Eastern musicians, for instance. The only assumptions I'm making are about people on this list and people who are likely to hear my music--which is to say, people who have been overwhelmingly acculturated to Western musical norms.

I don't see why it should be unreasonable to make assumptions about intervallic perception within this group. If I'm going to talk about music with other people, I have to assume that we have at least a modicum of shared perceptual experience, or else I might as well be talking to a tree for all the good it will do me. If people don't hear the way I do, they won't be able to tell me anything useful about the music I'm making (or wish to make).

> You said 7:5 has a
> tension that's undeniable. I don't think it's inherently more
> tense than any other dyad with n*d ~ 35. Try a raw listening
> comparison and see if you agree. I think it sounds tense when
> it reminds us of progressions where the its cousin's proximity
> to 3:2 (and especially to the tonic 3:2) was used to create and
> resolve tension.

I once spent a day indexing triads within the first 16 harmonics according to the "feeling" they gave me. 5:6:7 felt undeniably more tense to me than anything below it and many things above it. But anyway I've also done simpler dyadic listening tests. Dyads with n*d around 35 include 6/5, 10/3, 11/3, 7/5, 9/4, and 8/5. 7/5 and 8/5 feel considerably more tense than the others, and even in a vacuum surrounded by no other intervals, I hear both as wanting to resolve toward 3/2. 6/5 I do not hear as wanting to "move" very strongly at all; 9/4 might want to move down to a 2/1, but not very strongly. 11/3 feels tense in the "slightly stress-inducing" sense but doesn't give me a clear feeling of wanting to move one way or the other. If we kick up n*d a bit and let in 7/6, that's another one that feels stable; same with 9/5. And interestingly, I almost always hear a 4/3 as wanting to move down to a 5/4.

Note that I don't ascribe this to the intervals, but to my hearing of them. I won't deny that my acculturation undoubtedly explains this, but we're all acculturated to something, so why ignore that? Acculturation in ourselves and our listeners is just something we have to work with.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> I won't deny that my acculturation undoubtedly explains this, but we're all acculturated to something, so why ignore that?

Your acculturation undoubtedly explains how you think 11/3 should resolve?

On Friday, April 15, 2011, cityoftheasleep <igliashon@...> wrote:
>> Right! On Planet Pajara, they're saying the chord is no good
>> for a diatonic V7 because it sounds too stable. Who's right?
>
> Well, given that there is no evidence of the existence of a Planet Pajara....

You should keep in mind that 4:5:6:7 isn't really more concordant than
4:5:6 unless the notes have some kind of rolloff. Apply a 1/N^2
rolloff to that chord and it sounds a lot different. Not to say that I
think that 4:5:6:7 is particularly discordant, but there is some
psychoacoustic validity to what you're saying.

That is, a waveform with all harmonics present, equal volume, no
rolloff - an impulse train - will lead to a sound that is more
resonant than that of a sine wave, but not much "clearer" sounding.
The virtual pitch is stronger, but all of the harmonics are at equal
volume, so they poke out and you hardly hear it as "perfectly fused"
at all. The end result is the harshest virtual pitch you will have
ever heard in your life, a sawtooth wave on steroids. If you listen to
it, you'll recognize it - it's the same flavor as something like a
full 15-limit otonality, which I've noted you aren't a huge fan of.
Conversely, play a 15-limit otonality with the higher-limit notes
rolling off in volume, and you might enjoy it more.

This isn't to say that I think that 15-limit chords sound "bad," but
that they are simply more "commanding" than 5-limit chords, if no
rolloff is applied. They aren't very chilled out. Someday, I'd like to
be able to speak about this sort of thing by talking about epinephrine
responses in the central nervous system, but we aren't there yet.
Nonetheless, the observation itself is valid - that these higher-limit
chords can be, sometimes, discordant! - but are still "rooted," high
in tonalness, not inharmonic, etc.

That they have these characteristics is why I'm a fan of the notion
that higher-limit chords resolve to lower ones - especially if the
higher-limit chord is mistuned. The net effect is that of a
"commanding," somewhat tense, but still very "otonal" chord with a
clear virtual pitch resolving to a much less tense and also rooted
chord a 3/2 away - what could be more satisfying than that?

I note my example didn't work in 19-equal as well as it did in 12,
which may suggest that mistuning of the higher-limit chord "properly"
is really important. I'll work out some listening examples later. A
final note: play around with some 7 and 11-limit tetrads with the 7
and 11 lowered in volume - play around with the exact degree of
lowering - you might find you like them more.

-Mike

PS: perfect pitch in JI so far works... Not well. I basically have
relative pitch in JI like people do in 12, meaning they memorize a
single note's pitch chroma and get the rest via relative pitch from
that note. The same so far applies to me, except I have 12 reference
notes, which are the notes of 12-equal. A lot of the rest is relative.
I probably have all of 24-equal down. Tunings that don't utilize
unison vectors that 12 does are often fine, but ones that connect
things in ways that 12 doesn't sometimes mess me up. I'm getting a lot
better than I was, but still seem to be much behind Carl, who does not
have AP, so so much for that "advantage."

--
-Mike

Mike Battaglia <battaglia01@...> wrote:

> You should keep in mind that 4:5:6:7 isn't really more
> concordant than 4:5:6 unless the notes have some kind of
> rolloff. Apply a 1/N^2 rolloff to that chord and it
> sounds a lot different. Not to say that I think that
> 4:5:6:7 is particularly discordant, but there is some
> psychoacoustic validity to what you're saying.

It's worth saying . . . or maybe it isn't, but I'll say it
anyway . . . that 4:5:6:7 is more concordant than the
miserable excuse for a 4:5:6 that you get in 12-equal. If
acculturation were the issue I wouldn't think that.

Graham

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Your acculturation undoubtedly explains how you think 11/3 should resolve?
>

Yep, because I hear it as a major 7th an octave up.

-Igs

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > You should keep in mind that 4:5:6:7 isn't really more
> > concordant than 4:5:6 unless the notes have some kind of
> > rolloff. Apply a 1/N^2 rolloff to that chord and it
> > sounds a lot different. Not to say that I think that
> > 4:5:6:7 is particularly discordant, but there is some
> > psychoacoustic validity to what you're saying.
>
> It's worth saying . . . or maybe it isn't, but I'll say it
> anyway . . . that 4:5:6:7 is more concordant than the
> miserable excuse for a 4:5:6 that you get in 12-equal.

Alright, although that wasn't really the issue I was getting at. The point was that 4:5:6:7:8:9:10:11:12:13:14:15:16:17:18:19:... with all notes at equal volume is NOT more concordant than 4:5:6 with all notes at equal volume. On the other hand, the first chord IS more concordant if the notes have a 1/N or 1/N^2 rolloff applied. How much you have to mistune a just 4:5:6 to get it to be equally discordant with some other justly tuned chord isn't what I was getting at.

> If acculturation were the issue I wouldn't think that.

That Igs prefers 12-equal's major triad to a justly-tuned 4:5:6:7 just signifies that concordance is not the only thing determining someone's end-result preferences, which really do seem to have a cognitive or acculturative element to them. I hope it's possible to figure out what these learned features are, for the majority of existing Westerners, so we can pick tunings that excite those same features in interesting ways that people don't realize exist. If we can do that, we can hence find the tunings that are "just novel enough" to blow people's minds. Or perhaps it's a matter of working within a new feature space that is different from the one people have, but just similar enough to provide novelty that way. That is, we often talk about what music might sound like 200 years from now, but we don't live 200 years from now, and I wish I had a way to predict which tunings people will "get" as of 2011. But now I'm the one who's besides the point.

--- "cityoftheasleep" <igliashon@...> wrote:

> The thing is, though, in barbershop they don't add the 7th to
> every chord, or even the majority of chords.

They don't add it to the minor chords, but yes it is present
in a majority of the chords. -Carl

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> > You should keep in mind that 4:5:6:7 isn't really more
> > concordant than 4:5:6 unless the notes have some kind of
> > rolloff. Apply a 1/N^2 rolloff to that chord and it
> > sounds a lot different. Not to say that I think that
> > 4:5:6:7 is particularly discordant, but there is some
> > psychoacoustic validity to what you're saying.
>
> It's worth saying . . . or maybe it isn't, but I'll say it
> anyway . . . that 4:5:6:7 is more concordant than the
> miserable excuse for a 4:5:6 that you get in 12-equal. If
> acculturation were the issue I wouldn't think that.
>

Also worth mentioning that in JI, 4:5:6:7 isn't more
concordant than 4:5:6 no matter what the rolloff. Just as
4:5:6 isn't more concordant than 3:2. -C.

--- In tuning@yahoogroups.com, "battaglia01" <battaglia01@...> wrote:
>
> Alright, although that wasn't really the issue I was getting at.
> The point was that 4:5:6:7:8:9:10:11:12:13:14:15:16:17:18:19:...
> with all notes at equal volume is NOT more concordant than 4:5:6
> with all notes at equal volume.

Of course it isn't...

> On the other hand, the first chord IS more concordant if the
> notes have a 1/N or 1/N^2 rolloff applied.

Is not! :) -Carl

On Apr 15, 2011, at 2:38 PM, "Carl Lumma" <carl@...> wrote:

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> > You should keep in mind that 4:5:6:7 isn't really more
> > concordant than 4:5:6 unless the notes have some kind of
> > rolloff. Apply a 1/N^2 rolloff to that chord and it
> > sounds a lot different. Not to say that I think that
> > 4:5:6:7 is particularly discordant, but there is some
> > psychoacoustic validity to what you're saying.
>
> It's worth saying . . . or maybe it isn't, but I'll say it
> anyway . . . that 4:5:6:7 is more concordant than the
> miserable excuse for a 4:5:6 that you get in 12-equal. If
> acculturation were the issue I wouldn't think that.
>

Also worth mentioning that in JI, 4:5:6:7 isn't more
concordant than 4:5:6 no matter what the rolloff. Just as
4:5:6 isn't more concordant than 3:2. -C.

Do you think that a parabolic wave is more concordant than a sine wave?

Is a parabolic wave more or less concordant than an impulse train? How about
a sawtooth wave?

-Mike

>"That Igs prefers 12-equal's major triad to a justly-tuned 4:5:6:7 just
signifies that concordance is not the only thing determining someone's
end-result preferences"

A few things....
    4:5:6:7 may have more notes pointing to a virtual pitch...but it also has an extra note forming more critical band dissonance than anything in/near 4:5:6 forming the 7/6 dyad.

   There seems to be somewhat of a character issue here: 7-limit dyads, to my ear, clearly seem to have a tenser mood than many other dyads: concordant, but tense.  5:7:8 and 5:7:9 appear to have the same issue with tensity.

  Far as concordance vs. resolve/tensity...try the 9-limit 14/9 and 16/9 compared to 7/4...for example.    Note this may be due to the fact 9 is divisible by 3 (and same goes with the 6 in 11/6...for example).  7 does sound in tune to me...but it also sounds like "controlled dissonance/tensity".  Now try 11/7 vs. 8/5...same sort of deal, only the 11/7 actually sounds less tense (in general, it seems to me x/7 ratios actually sound less tense than 7/x ratios).  This kind of stuff freaks me out a bit because my ears are telling me the polar opposite of what most psychoacoustics-related theories say should happen. 

--- Mike Battaglia <battaglia01@...> wrote:

> Also worth mentioning that in JI, 4:5:6:7 isn't more
> concordant than 4:5:6 no matter what the rolloff. Just as
> 4:5:6 isn't more concordant than 3:2. -C.
>
> Do you think that a parabolic wave is more concordant than
> a sine wave?
>
> Is a parabolic wave more or less concordant than an impulse
> train? How about a sawtooth wave?

I don't know, nor do I see the relevance of these questions
here. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@> wrote:
>
> > Also worth mentioning that in JI, 4:5:6:7 isn't more
> > concordant than 4:5:6 no matter what the rolloff. Just as
> > 4:5:6 isn't more concordant than 3:2. -C.
> >
> > Do you think that a parabolic wave is more concordant than
> > a sine wave?
> >
> > Is a parabolic wave more or less concordant than an impulse
> > train? How about a sawtooth wave?
>
> I don't know, nor do I see the relevance of these questions
> here. -Carl

You have said in the past that you do. They are relevant because the answers tell us things about the kind of spectrum that we tend to perceive as being maximally concordant.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@> wrote:
>
> > Also worth mentioning that in JI, 4:5:6:7 isn't more
> > concordant than 4:5:6 no matter what the rolloff. Just as
> > 4:5:6 isn't more concordant than 3:2. -C.
> >
> > Do you think that a parabolic wave is more concordant than
> > a sine wave?
> >
> > Is a parabolic wave more or less concordant than an impulse
> > train? How about a sawtooth wave?
>
> I don't know, nor do I see the relevance of these questions
> here. -Carl

They are all less concordant than a Jacobi theta function wave, and no, I don't see the relevance of my answer.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> It's a work in progress. Worse than that, it's a work not
> progressing, so I can't always remember what it's supposed
> to sound like. But it does have some resolutions and,
> according to the score, it's resolving onto pure seventh
> chords (magic tempered).
>
> The first is at bar 17, or 25s into the audio. There's a
> sense of tension resolving onto the pure triad that follows
> it. I hope I don't have to put down the 5-limit in order
> to support the 7-limit. If you treat the new chord as a
> tonic, the resolution would be IV-I.
>
> Then there's a resolution at 32.5s (bar 22). If that isn't
> final enough, it limps onto another at 37s (bar 25). Both
> are pure sevenths.

Okay, I'm going to eat some of my words here and say that I don't hear an unfinished cadence here. I don't know if it sounds "resolved", but I don't hear the same movement wanting to happen as I usually do.

> The final chord is a pure 5-limit triad. And, yes, the
> 5-limit sounds good, doesn't it?

Yep.

> Oh, yes, and the main point of this piece is that it uses
> both the pure 7-limit seventh chords and a 5-limit
> rendering of a traditional dominant seventh (with 11-limit
> implications). My surprise, on first listen, was how *bad*
> and out of tune the extended 5-limit chord sounded.

Indeed, tuning a 5-limit dominant 7th tends to sound horrible. In that regard, 12-TET's error/ambiguity actually seems to work in its favor, since in 19 the diatonic dominant 7th sounds atrocious compared to the augmented 6th.

> Paul Erlich's "Decatonic Swing" is a good example of
> 7-limit harmony. I believe it's all seventh chords, and
> they work. Even given the poor approximations of
> Pajara/22, the harmonic logic makes sense.

I'm not saying 7-limit harmony doesn't "work". I'm saying it doesn't work analogously to 5-limit harmony.

> You're still saying you "would be" surprised when people
> have already told you they have a different view.

No, they really haven't. Slightly different views have been expressed, but no one seems to hear a 4:5:6:7 as being entirely unlike a dominant 7th.

> By now
> you should have been surprised. I'll add myself to the
> list. I don't hear "12-ET-based functions" when I hear a
> 4:5:6:7. I don't even know what a 12-ET-based function
> would sound like. 4:5:6:7 sounds like a pure chord, and the
> 12-ET dominant seventh doesn't. I never hear the half-octave
> "wanting to resolve" a particular way. I always thought
> that was a convenient fiction harmony teachers use to
> explain conventional chord sequences (which sound fine;
> I'm not knocking them).

Well, color me surprised by your views.

> I can hear the 7 of 4:5:6:7 as being out of tune. So can
> the 5 for that matter. I think it's because they're
> outside the expected melodic framework. The solution is to
> emphasize different melodic patterns. It may help to treat
> the 7 as a dissonance when you use it first.

Wouldn't that be defeating the purpose of using 4:5:6:7 as a base harmonic unit analogous to a 4:5:6?

> Another problem with 4:5:6:7 is that it sounds too pure and
> fused. It doesn't bring an interesting new sonority to the
> table. The solution there is to tie it in with scrunchier
> chords that hold the 7.

That's also kind of beside the point I was trying to make.

> I don't think functional considerations are leading me
> anywhere. I don't think most listeners out there in the
> big wide world are at all sensitive to the Common Practice
> formula for treatment of dominant sevenths.

Really? You don't hear a G7 progressing to a C major (in 12-ET or any other meantone or pythagorean tuning) as being a strong, natural, resolved progression? You don't think most people hear it that way? The "rules" of common practice are totally arbitrary and not at all based in some fundamental aspect of hearing?

> A lot of us
> are attuned to the liberal use of seventh chords in rock
> and blues. They have a spicy feel and can you can use one
> as the tonic. I don't find a 4:5:6:7 has the same feel at
> all so I don't think it's altering my perceptions, other
> than making be receptive to the use of the 7 as coloration.

Jon Catler would disagree with you, and so (I would suspect) harmonic entropy. The canonical line I've always heard from people in the tuning community is 12-TET's dominant 7th chords are just out-of-tune septimal otonalities. I'll admit a reasonably-pure 4:5:6:7 lacks the spiciness of 12-TET, but Catler sure rocks them pretty hard in his own blues and it seems to work.

> I don't know how strong the associations are for you. I
> have noticed that you don't focus on microtonal harmony.

That's not entirely true. Just because I don't focus on integrating extended JI (or temperaments thereof) doesn't mean I don't focus on harmony. Quite the contrary, the coloration of different (and extreme) mistunings of standard 5-limit chords is pretty much an integral feature of my music.

> Your Map of an Internal Landscape (that's you, right?) is
> good microtonal music, but it doesn't have much harmony.

It's got as much harmony as most music in the same genre, i.e. rock or pop. Almost every single track has at least triadic harmony happening, except for the tracks in 11, 23, and 28 (because at the time I was a bit more conservative with using wonky 3-limit approximations). But indeed I paid more attention to melodies and root movements, since that seemed like a better starting-place for exploration. Getting some basics down first seemed a more sensible move than trying to go whole-hog for extended otonalities (which I generally dislike, even when Just).

> Or, at least, the harmony is kept in the background. Whereas
> your 12-TET music uses conventional harmonic patterns. So
> it sounds like you didn't find new patterns you liked in
> the new systems. Something more recent has more harmony,
> but it doesn't have the "wow factor", in harmonic terms,
> that some of Gene's and George's music (and I hope some of
> mine) does.

Gene's music gets its wow factor for me mainly because he's juggling so many notes, and George's I really haven't heard any of except for his 11-EDO piece (which was awesome). Your work reminds me a lot of Gene's, in that both have some really funky alien progressions that definitely require me to work against my "programming" (though I rarely succeed). To be frank, though, I think that bringing in totally unusual harmonies as well as very unusual and complex scales, and doing very intricate and complex things with these harmonies and scales, is an approach that it's a bit too ahead of its time for me. It's hard for me to make it through an entire piece by either of you because I feel like there's nothing for me to latch on to. Neither of you write particularly rhythmically-oriented music, either, so there isn't even that as a "safety-net". But hey, to each his own. The both of you come from very different musical backgrounds than I do and have a very different set of goals. But anyway the point is that my "lack of focus" on extended harmony probably makes more sense if you take into account my background and the "compositional problems" I turned to microtonality to solve.

> And then you say you don't see the point of
> close approximations to simple ratios, that they don't have
> musical value for you. So, fine, if it doesn't work for
> you, try something that does.

I don't recall saying anything quite so drastic, but it's true that accuracy is pretty far down my list of priorities. Mostly because it seems to take care of itself well enough, insofar as no scale is completely devoid of some form of consonance.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> > The thing is, though, in barbershop they don't add the 7th to
> > every chord, or even the majority of chords.
>
> They don't add it to the minor chords, but yes it is present
> in a majority of the chords. -Carl

Really? Have you done a statistical analysis?

-Igs

On Fri, Apr 15, 2011 at 3:58 PM, genewardsmith
<genewardsmith@...> wrote:
>
> They are all less concordant than a Jacobi theta function wave, and no, I don't see the relevance of my answer.

It's relevant because while we like to pretend that "chords" are made
up of "notes" of various "timbres," those notes and their timbres
themselves are made up of sine waves, which are ultimately the basis
for everything that we're doing here. 1:2:3:4:5:6:7:8:9:10:... played
with sine waves of equal volume, is an impulse train, which looks like
the derivative of a sawtooth wave. 1:2:3:4:5:6:7:8:9:10:... envisioned
as a "chord" being played with "notes" of timbres that are not sine
waves, e.g. as a chord being played with sawtooths, leads to an even
harsher result, as you end up with the impulse train with all of its
harmonics added to itself, which gives you a negative rolloff. Hence
that "chord" will exhibit even harsher behavior than what I'm talking
about.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> The canonical line I've always heard from people in the tuning >community is 12-TET's dominant 7th chords are just out-of-tune >septimal otonalities.

Does anyone know if this really is the canonical line?

Statistical analysis has been done, I don't know how formally.

As you can analize by simply listening, seventh chords are the signature sound of barbershop

The relevant quote from this book

http://books.google.com/books?id=4N6Q7dYV2FoC&dq=isbn:0195116720&hl=sl&ei=HAOpTf3vIo_FswbMkNWZBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCcQ6AEwAA

on Wikipedia gives "35 to 60 percent". "About half" would be my guess from remembered listening experience, so that sounds right on to me. Considering how they tend to really lean into those seventh chords, "most" isn't really an exaggeration.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > > The thing is, though, in barbershop they don't add the 7th to
> > > every chord, or even the majority of chords.
> >
> > They don't add it to the minor chords, but yes it is present
> > in a majority of the chords. -Carl
>
> Really? Have you done a statistical analysis?
>
> -Igs
>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > And yet, that isn't how they were treated in common practice in terms of resolution. Of
> > > course, augmented sixth chords only occurred in certain contexts and that influenced
> > > things.
> >
> > I don't get it...are you saying that since in Meantone a 4:7 is an augmented 6th, dom7 chords aren't really approximating 4:5:6:7's?
>
> They are doing so very badly; what was doing a good job was an augmented sixth chord, the German sixth, which tended to move to a V7 directly or indirectly.
>

The minor seventh and aug. sixth were distinguished, the minor seventh NOT approximating the harmonic seventh. Tartini, Kirnberger and others advocated the seventh partial in the 18th century, not in the manner of simply swapping out one fixed ratio for another, but as an augmented sixth as Gene described. Very conveniently, quarter-comma meantone, which was and still is the tuning nearest to the heart of "common practice" has an augmented sixth which is an excellent approximation of 7:4.

This supports the position Igs is taking, by the way.

More accurately, the historical advocacy of the harmonic seventh as an augmented sixth supports Igs general position of considering 4:5:6:7 chords unresolved, not his position that they are "dominant" in nature, which is simply wrong in meantone (aug.6s don't resolve to I) and clearly not a universal perception (barbershop being the clearest example).

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > > And yet, that isn't how they were treated in common practice in terms of resolution. Of
> > > > course, augmented sixth chords only occurred in certain contexts and that influenced
> > > > things.
> > >
> > > I don't get it...are you saying that since in Meantone a 4:7 is an augmented 6th, dom7 chords aren't really approximating 4:5:6:7's?
> >
> > They are doing so very badly; what was doing a good job was an augmented sixth chord, the German sixth, which tended to move to a V7 directly or indirectly.
> >
>
> The minor seventh and aug. sixth were distinguished, the minor seventh NOT approximating the harmonic seventh. Tartini, Kirnberger and others advocated the seventh partial in the 18th century, not in the manner of simply swapping out one fixed ratio for another, but as an augmented sixth as Gene described. Very conveniently, quarter-comma meantone, which was and still is the tuning nearest to the heart of "common practice" has an augmented sixth which is an excellent approximation of 7:4.
>
> This supports the position Igs is taking, by the way.
>

The question is, when barbershop quartets sing a 4:5:6:7 (the characteristic barbershop 7th), what chord are they singing according to the notation? I'd be willing to bet good money that if you ask a barbershop quartet to sing you G-B-D-F, they'll sing you a 4:5:6:7. If that is in fact the case, that suggests to me that given freedom of intonation, people tune a dominant 7th as a 4:5:6:7, rather than anything more harmonically complex, which seems to support the canonical line coming out of the JI network.

But all of this is beside the point I was originally trying to make. My whole issue of a septimal otonality sounding like a dominant 7th chord was supposed to be nothing more than an illustration of my disagreement with the idea that music based on septimal otonalities is the logical evolution of 5-limit music. Basically, I think the 7-limit is already implied in a lot of 5-limit music in the form of the dominant 7th (or augmented 6th, whatever, it doesn't matter), so if we look at the places 7 is implied, it sort of already has a functionality relative to the standard 5-limit palette. Regardless of whether we're talking classical functionality or jazz functionality or barbershop functionality, hearing a 7-limit otonality is almost certainly going to evoke those well-established associations in listeners that have them.

Unless, of course, that otonality is located firmly in a functionality that isn't really analogous to 5-limit meantone functionality. But in order to take the 7-limit to a place where people stop associating it with its established implications in a meantone or pythagorean system, we're almost certainly going to have to produce a tonal system that's going to be beyond comprehension to most listeners. Mostly because any scale that's going to produce a multitude of decently-tuned 4:5:6:7 chords, without being related to something familiar like meantone or diminished, is going to be absurdly complex compared to meantone and/or 12-TET, thus causing people accustomed to 12-TET to scratch their heads and flip the channel. If some of you don't care about that, fine, but that's beside the point.

It's just like how most listeners don't give a damn whether they hear meantone 5-limit 3rd or a 3-limit Pythagorean one. In any case, whatever evolutionary chutzpah a 7-limit-based tonal system might possess, it will almost certainly come from the rise in scalar complexity and the unusual/complex "byproduct" intervals it produces, rather than any amazing novelty of the 7-limit harmonies. This is patently obvious in Graham's and Gene's music, which would sound just as insane and forward-thinking with the 7ths dropped as otherwise, because those two use such bizarre and un-meantone-like scales. This is also why music in Pajara temperament universally fails to freak people out--you can play the same shit in 12 and it'll just sound a bit more out-of-tune, but still get the same point across. So what's the big to-do about the 7th harmonic?

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Statistical analysis has been done, I don't know how formally.
>
> As you can analize by simply listening, seventh chords are the signature sound of barbershop
>
> The relevant quote from this book
>
> http://books.google.com/books?id=4N6Q7dYV2FoC&dq=isbn:0195116720&hl=sl&ei=HAOpTf3vIo_FswbMkNWZBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCcQ6AEwAA
>
> on Wikipedia gives "35 to 60 percent". "About half" would be my guess from remembered listening experience, so that sounds right on to me. Considering how they tend to really lean into those seventh chords, "most" isn't really an exaggeration.
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > > The thing is, though, in barbershop they don't add the 7th to
> > > > every chord, or even the majority of chords.
> > >
> > > They don't add it to the minor chords, but yes it is present
> > > in a majority of the chords. -Carl
> >
> > Really? Have you done a statistical analysis?
> >
> > -Igs
> >
>

--- "battaglia01" <battaglia01@...> wrote:

>>>> Also worth mentioning that in JI, 4:5:6:7 isn't more
>>>> concordant than 4:5:6 no matter what the rolloff. Just as
>>>> 4:5:6 isn't more concordant than 3:2. -C.
>>>
>>> Do you think that a parabolic wave is more concordant than
>>> a sine wave?
>>> Is a parabolic wave more or less concordant than an impulse
>>> train? How about a sawtooth wave?
>>
>> I don't know, nor do I see the relevance of these questions
>> here. -Carl
>
> You have said in the past that you do.

Where?

> They are relevant because the answers tell us things about
> the kind of spectrum that we tend to perceive as being
> maximally concordant.

A chord is not a waveform. It's an abstraction represnting
musical sounds which may come from different sources / vary
in a lot of ways. One of them is phase, which changes the
wave shape more than it does the sound. But even in a
lab-type setting, rolling off chord fundamentals at 6dB/oct
does not (for example) produce a sawtooth, since amplitudes
of coinciding partials add. So if you want to draw a
comparison here you'll need to be more specific.

-Carl

--- "cityoftheasleep" <igliashon@...> wrote:
>
> > > The thing is, though, in barbershop they don't add the 7th to
> > > every chord, or even the majority of chords.
> >
> > They don't add it to the minor chords, but yes it is present
> > in a majority of the chords. -Carl
>
> Really? Have you done a statistical analysis?
>
> -Igs

No, but I have done some barbershop arranging. Check out
Aaron Wolf's arrangements, which he performed in Melodyne
in JI, for some concrete examples. -Carl

--- "lobawad" <lobawad@...> wrote:

> > The canonical line I've always heard from people in the tuning
> > community is 12-TET's dominant 7th chords are just out-of-tune
> > septimal otonalities.
>
> Does anyone know if this really is the canonical line?

The old thread on this had monz making several versions of
the dominant cadence in JI. Opinions on 4:5:6:7 were mixed
but the general consensus seemed to be that strict JI chords
like 1/1-5/4-3/2-16/9 worked better. I tried but failed to
find monz's page on this just now. -Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Mostly because any scale that's going to produce a multitude of decently-tuned 4:5:6:7 chords, without being related to something familiar like meantone or diminished, is going to be absurdly complex compared to meantone and/or 12-TET, thus causing people accustomed to 12-TET to scratch their heads and flip the channel. If some of you don't care about that, fine, but that's beside the point.

The complexity of an otonal tetrad in meantone is 10. To this we may compare its complexity in pajara, which is 6, in augene, which is 9, in myna, which is 10, orwell, which is 11, in magic and valentine, which is 12, in miracle and sensi, which is 13. Hence this claim is baloney; just because you don't use these systems doesn't mean they don't exist. Moreover, going up a rank to rank three adds further 7-limit possibilities, and there's always JI.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> The old thread on this had monz making several versions of
> the dominant cadence in JI. Opinions on 4:5:6:7 were mixed
> but the general consensus seemed to be that strict JI chords
> like 1/1-5/4-3/2-16/9 worked better.

As a consonance or in terms of functional harmony?

--- "genewardsmith" <genewardsmith@...>

> The complexity of an otonal tetrad in meantone is 10. To this we
> may compare its complexity in pajara, which is 6, in augene, which
> is 9, in myna, which is 10, orwell, which is 11, in magic and
> valentine, which is 12, in miracle and sensi, which is 13. Hence
> this claim is baloney; just because you don't use these systems
> doesn't mean they don't exist.

Maybe Igs meant that these numbers are high compared to triads
in meantone. -Carl

--- "genewardsmith" <genewardsmith@...> wrote:

> > The old thread on this had monz making several versions of
> > the dominant cadence in JI. Opinions on 4:5:6:7 were mixed
> > but the general consensus seemed to be that strict JI chords
> > like 1/1-5/4-3/2-16/9 worked better.
>
> As a consonance or in terms of functional harmony?

The latter. 4:5:6:7 was deemed more relaxed than ideal for
creating tension in the cadence. Igs may have been thinking
of the general consensus that the dom7 chord in 12 (and
36:45:54:64 for that matter) approximates 4:5:6:7 in the
virtual pitch sense.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "genewardsmith" <genewardsmith@>
>
> > The complexity of an otonal tetrad in meantone is 10. To this we
> > may compare its complexity in pajara, which is 6, in augene, which
> > is 9, in myna, which is 10, orwell, which is 11, in magic and
> > valentine, which is 12, in miracle and sensi, which is 13. Hence
> > this claim is baloney; just because you don't use these systems
> > doesn't mean they don't exist.
>
> Maybe Igs meant that these numbers are high compared to triads
> in meantone. -Carl

That's not what he said, but perhaps. Note, however, that while the complexity of a 5-limit triad is 4, the complexity of a 1-6/5-10/7 triad is 6, of a 1-7/6-7/5 or 1-6/5-7/5 triad is 9, and of a 1-7/6-3/2 or 1-9/7-3/2 triad is also 9. In myna, 1-6/5-10/7 has a complexity of 2, 1-7/6-7/5 a complexity of 3, 1-7/6-3/2 a complexity of 13 and 1-5/4-3/2 a complexity of 10. Myna and meantone are generally comparable in complexity, but differ in the details.

--- "lobawad" <lobawad@...> wrote:

> Considering how they tend to really lean into those seventh
> chords, "most" isn't really an exaggeration.

Good choice of words - they lean in figuratively and literally!

Couldn't find an ideal example on youtube, but this will do
http://www.youtube.com/watch?v=u7mGjSZpdpk&#t=4m20s

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> The old thread on this had monz making several versions of
> the dominant cadence in JI. Opinions on 4:5:6:7 were mixed
> but the general consensus seemed to be that strict JI chords
> like 1/1-5/4-3/2-16/9 worked better. I tried but failed to
> find monz's page on this just now. -Carl

There is also this:

http://nowitzky.hostwebs.com/justint/dom7.htm

Kalle

On Sat, Apr 16, 2011 at 1:42 AM, Carl Lumma <carl@...> wrote:
> >
> > You have said in the past that you do.
>
> Where?

Er, I thought you did. I was talking about this there:

/tuning/topicId_85488.html#85555

I then responded with "what about parabolic waves, which are 1/N^2
rolloff, all harmonics present," and you also said that that'd be
better than a sawtooth. Maybe at the time you were just talking about
timbres that most closely approximate the human voice, but I thought
the greater point was that timbres with a 1/N^2 rolloff are generally
closer to a more "perfectly concordant sound" than those with a 1/N
rolloff. I've been talking about using parabolic waves as "ideal,"
archetype waveforms for the cross-correlation "filterbank" for like
1-2 years now, and you were always onboard.

Anyway, the point is - even if you disagree, go listen to those "buzz
wave" examples again from the periodicity buzz tests. Those are
impulse trains, which are differentiated sawtooths. All harmonics
present, equal volume. This means the harmonics stick out and don't
"fuse" as nicely as if they were rolling off. This also means that the
resulting waveform sounds like you're being stabbed in the ear with a
rusty knife. On the other hand, sines don't sound like this, but then
they don't produce the "clearest" sounding pitch, either. Thus the
ideal rolloff is somewhere between just one sine wave, and all
harmonics equal.

> > They are relevant because the answers tell us things about
> > the kind of spectrum that we tend to perceive as being
> > maximally concordant.
>
> A chord is not a waveform. It's an abstraction represnting
> musical sounds which may come from different sources / vary
> in a lot of ways. One of them is phase, which changes the
> wave shape more than it does the sound.

OK, and all of that applies to timbre as well. We are assuming that
for any of this to matter at all, there exists a central pitch
processor that is attempting to fuse all of this mess into a single VF
at all times, regardless of where the sources are coming from. This
applies even if instead of a chord, we're talking about a timbre, in
which harmonics are being played to alternating ears with different
phases - a VF will still be produced. Thus, with a chord, even if the
sources in real life exhibit phase irregularities, differences in
inter-aural spatialization cues, F0 estimation will be taking place
regardless. If it wasn't, then there'd be no point in us talking
meaningfully about "4:5:6" to begin with.

As for phase, 100% phase synchronicity between harmonics rarely occurs
in real life. It certainly doesn't occur in a reverberant hall, where
the sound of reverb is actually caused by making random adjustments to
the phase of each sine. Nonetheless, that doesn't interfere with F0
estimation. Sometimes it really does, as in the case of the
periodicity buzz examples with impulse trains of varying phases, so I
may have to concede your point a little bit. But that behavior didn't
really occur until you had like 30+ harmonics involved, and when there
were a huge amount of fully unresolved upper harmonics at equal
volume, so if we're sticking to discussing 7-15 limit otonalities in
which the harmonics are mostly resolved, it wouldn't be as relevant.

For the moment, I'm isolating the analysis to a chord that is produced
by one sound source - a speaker, since that's the main thing that most
of us have listened to any of this stuff on.

> But even in a
> lab-type setting, rolling off chord fundamentals at 6dB/oct
> does not (for example) produce a sawtooth, since amplitudes
> of coinciding partials add. So if you want to draw a
> comparison here you'll need to be more specific.

Right, and as I told Gene, I'm being generous - a 1:2:3:4:5:6:7:8:...
timbre is a "chord" where all of the "notes" have sine wave timbres.
If you actually wanted to play a 1:2:3:4:5:6:7:8:... chord with
sawtooth waves, that would be even harsher, as you'd end up with a
negative rolloff where upper harmonics are louder in volume than lower
ones. A 1:2:3:4:5:6:7:8:... chord where each successive note and its
harmonics are placed at an 1/N rolloff would yield some kind of
interesting "prime-sieving" rolloff where primes have a lower
amplitude than everything else. We can start to understand and predict
the concordance of complex spectra such as these by first considering
the concordance of simpler spectra.

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> The complexity of an otonal tetrad in meantone is 10. To this we may compare its
> complexity in pajara, which is 6, in augene, which is 9, in myna, which is 10, orwell,
> which is 11, in magic and valentine, which is 12, in miracle and sensi, which is 13. Hence
> this claim is baloney; just because you don't use these systems doesn't mean they don't
> exist.
>
> Moreover, going up a rank to rank three adds further 7-limit possibilities, and there's
> always JI.

I think you misunderstood. I know meantone is not the simplest system in terms of producing septimal otonal tetrads (and in any case, it's probably more reasonable to talk about 12-TET as a dominant temperament rather than a meantone, based on psychoacoustic considerations of how 12-TET music is likely "heard", so dominant is really the benchmark for comparison).

I'm not trying to say that septimal harmony sucks or isn't useful or anything of the sort. Septimal harmony is wonderful and I like it very much, but I think it's implied strongly enough in 12-TET that any temperament related to 12-TET is going to evoke 12-TET-like associations such that people coming to microtonality looking for something that sounds very untwelvish (like me) are going to roll their eyes and say "that just sounds like [insert familiar genre of music here]" (For the record, when I say related to 12-TET, I mean pretty much any temperament that produces a proper or nearly-proper 12-note MOS scale, because every single one of those will be to some degree supported in 12-TET). I'm not against these temperaments or anything, and I know if you optimize them and carry them out to much larger MOS's they get really xenharmonic.

However, if you look at your above list, and reduce to the non-12-supported temperaments, the lowest complexity is no better than meantone, meaning you need a 10-note MOS to get ONE septimal otonality. That's pretty dang high compared to triads in meantone, we're looking at scales of at least 13 or 14 notes. So my point stands that to get to 7-limit harmony in a way analogous to meantone, we either have to use systems already supported in 12-TET or else systems of much higher complexity. Which is fine if that solves your particular set of compositional problems, but I don't see how it supports anyone's claim of septimal otonal tetrads being a viable "analog" or "evolutionary replacement" for 5-limit triads. Of course, I haven't seen anyone making that claim here in recent years, but it's pretty well enshrined in Paul's 22-tone paper, and I get the feeling that it's pretty well taken as granted by a lot of the "old guard" here.

I get the sense that the attitude that informs the creation of most scales around here is an attitude of "scales that well-approximate or at least imply higher-limit JI are the best thing to look for" without any regard to other properties the scales might have and a sort of resolute ignorance of how higher-limit JI is already implied in something as simple and familiar as 12-TET. And that's fine, of course, if it's solving compositional problems for people, but I've long felt there are lots of interesting things about scales that get totally ignored in this approach.

Many people here look at the scales I use and they only see "error" and think that "these scales are not any good for harmonic music". Not that I'm the only one to use them; plenty of others have as well (Herman Miller, J.L. Smith, Cameron, Ozan, George Secor, and Chris V. all come to mind as having used scales like 11, 13, 15, and 17-EDO), and generally speaking we all get positive responses to our music. I don't think JI considerations satisfactorily explain why music works in these scales, and I think it's kind of insane that people aren't interested in exploring what *does* make them work.

End rant.

-Igs

I agree with Igs' rant. I thought part of the fun was to discover the
"new" rules (though I've yet to systematize what I'm doing) instead of
relating to 12 tone common practice.

Chris

On Sat, Apr 16, 2011 at 12:43 PM, cityoftheasleep
<igliashon@...> wrote:
>
>
>
> Many people here look at the scales I use and they only see "error" and think that "these scales are not any good for harmonic music". Not that I'm the only one to use them; plenty of others have as well (Herman Miller, J.L. Smith, Cameron, Ozan, George Secor, and Chris V. all come to mind as having used scales like 11, 13, 15, and 17-EDO), and generally speaking we all get positive responses to our music. I don't think JI considerations satisfactorily explain why music works in these scales, and I think it's kind of insane that people aren't interested in exploring what *does* make them work.
>
> End rant.
>
> -Igs

Well put.

Sent from my iPhone

On Apr 16, 2011, at 12:43 PM, "cityoftheasleep" <igliashon@...>
wrote:

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> The complexity of an otonal tetrad in meantone is 10. To this we may
compare its
> complexity in pajara, which is 6, in augene, which is 9, in myna, which is
10, orwell,
> which is 11, in magic and valentine, which is 12, in miracle and sensi,
which is 13. Hence
> this claim is baloney; just because you don't use these systems doesn't
mean they don't
> exist.
>
> Moreover, going up a rank to rank three adds further 7-limit
possibilities, and there's
> always JI.

I think you misunderstood. I know meantone is not the simplest system in
terms of producing septimal otonal tetrads (and in any case, it's probably
more reasonable to talk about 12-TET as a dominant temperament rather than a
meantone, based on psychoacoustic considerations of how 12-TET music is
likely "heard", so dominant is really the benchmark for comparison).

I'm not trying to say that septimal harmony sucks or isn't useful or
anything of the sort. Septimal harmony is wonderful and I like it very much,
but I think it's implied strongly enough in 12-TET that any temperament
related to 12-TET is going to evoke 12-TET-like associations such that
people coming to microtonality looking for something that sounds very
untwelvish (like me) are going to roll their eyes and say "that just sounds
like [insert familiar genre of music here]" (For the record, when I say
related to 12-TET, I mean pretty much any temperament that produces a proper
or nearly-proper 12-note MOS scale, because every single one of those will
be to some degree supported in 12-TET). I'm not against these temperaments
or anything, and I know if you optimize them and carry them out to much
larger MOS's they get really xenharmonic.

However, if you look at your above list, and reduce to the non-12-supported
temperaments, the lowest complexity is no better than meantone, meaning you
need a 10-note MOS to get ONE septimal otonality. That's pretty dang high
compared to triads in meantone, we're looking at scales of at least 13 or 14
notes. So my point stands that to get to 7-limit harmony in a way analogous
to meantone, we either have to use systems already supported in 12-TET or
else systems of much higher complexity. Which is fine if that solves your
particular set of compositional problems, but I don't see how it supports
anyone's claim of septimal otonal tetrads being a viable "analog" or
"evolutionary replacement" for 5-limit triads. Of course, I haven't seen
anyone making that claim here in recent years, but it's pretty well
enshrined in Paul's 22-tone paper, and I get the feeling that it's pretty
well taken as granted by a lot of the "old guard" here.

I get the sense that the attitude that informs the creation of most scales
around here is an attitude of "scales that well-approximate or at least
imply higher-limit JI are the best thing to look for" without any regard to
other properties the scales might have and a sort of resolute ignorance of
how higher-limit JI is already implied in something as simple and familiar
as 12-TET. And that's fine, of course, if it's solving compositional
problems for people, but I've long felt there are lots of interesting things
about scales that get totally ignored in this approach.

Many people here look at the scales I use and they only see "error" and
think that "these scales are not any good for harmonic music". Not that I'm
the only one to use them; plenty of others have as well (Herman Miller, J.L.
Smith, Cameron, Ozan, George Secor, and Chris V. all come to mind as having
used scales like 11, 13, 15, and 17-EDO), and generally speaking we all get
positive responses to our music. I don't think JI considerations
satisfactorily explain why music works in these scales, and I think it's
kind of insane that people aren't interested in exploring what *does* make
them work.

End rant.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

(For the record, when I say related to 12-TET, I mean pretty much any temperament that produces a proper or nearly-proper 12-note MOS scale, because every single one of those will be to some degree supported in 12-TET). I'm not against these temperaments or anything, and I know if you optimize them and carry them out to much larger MOS's they get really xenharmonic.

If 12 note near-proper scales are the problem, then avoid them. If you look on the Chromatic pairs page, for myna you'll find 7, 11 and 15 note scales; for magic 7, 10, 13, and 15; for sensi 5, 8, 11 and 19; for orwell 9 and 13. Somehow I am failing to find this plague of 12-note proper scales you complain of here. A more reasonable complaint would be that there are too many improper scales, but if you are seeking to escape the usual that should not worry you.

Admittedly, I did give a whole slew of 12-note proper hobbit scales recently, under the dulusive belief that this is what people wanted. You can ignore them if you don't want them.

> However, if you look at your above list, and reduce to the non-12-supported temperaments, the lowest complexity is no better than meantone, meaning you need a 10-note MOS to get ONE septimal otonality. That's pretty dang high compared to triads in meantone, we're looking at scales of at least 13 or 14 notes.

You are arguing out of both sides of your mouth. On the one hand, you want to get away from same-old-same-old. On the other, you complain of a dearth of 5-limit triads. Myna has fewer of those than meantone, but more of other kinds of triads. One would have thought you would approve.

> So my point stands that to get to 7-limit harmony in a way analogous to meantone, we either have to use systems already supported in 12-TET or else systems of much higher complexity.

And your point remains baloney.

> Many people here look at the scales I use and they only see "error" and think that "these scales are not any good for harmonic music". Not that I'm the only one to use them; plenty of others have as well (Herman Miller, J.L. Smith, Cameron, Ozan, George Secor, and Chris V. all come to mind as having used scales like 11, 13, 15, and 17-EDO), and generally speaking we all get positive responses to our music.

Did it occur to you that people don't like to give reviews like "your harmony made me puke?"

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I agree with Igs' rant. I thought part of the fun was to discover the
> "new" rules (though I've yet to systematize what I'm doing) instead of
> relating to 12 tone common practice.

You think I am relating everything to 12 notes in common practice and Igs doing something else?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Well put.

Uh huh. We can only get 5-limit triads and a pukey sort of 7-limit in 12 notes of dominant, so we must inflict 14edo on people whether they like it or not, and for the record I do not. But of course, pajara does much better in the 7-limit than dominant, and keemun has vastly better 5-limit triads. But who died and made dominant king, anyway? Why, to be xenharmonic, do we either need to focus on 5-limit triads or say "screw it" and deep-six the whole regular temperament paradigm to the detriment of what the music we make actually ends up sounding like?

I'm for live and let live in xentonality. To each his own. But do NOT try to claim I should be using scales which make me puke if I want to be truly xenharmonic. I am not interested. And don't claim everyone loves the result of using any random system that comes to along just because of a lack of negative reviews.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> Uh huh. We can only get 5-limit triads and a pukey sort of 7-limit in 12 notes of dominant, so we must inflict 14edo on people whether they like it or not, and for the record I do not. But of course, pajara does much better in the 7-limit than dominant, and keemun has vastly better 5-limit triads. But who died and made dominant king, anyway? Why, to be xenharmonic, do we either need to focus on 5-limit triads or say "screw it" and deep-six the whole regular temperament paradigm to the detriment of what the music we make actually ends up sounding like?

Who said anything about deep sixing regular temperament? The takeaway point from Igs' post was that Pajara, while an excellent system, doesn't sound particularly xenharmonic. At least it doesn't to me. I find it theoretically interesting, but I think a large part of the "Pajara sound" was already discovered in jazz, so it doesn't sound that out there to me. It can lead to some interesting harmonic ideas, but compared to Blackwood or Machine it sounds much less novel.

On the other hand, father temperament does sound new and different, but harmonically... takes some getting used to. The point is that the first statement about Pajara is significant. In many cases, 5-limit systems with "new puns" will sound more xenharmonic than 7-limit systems forming proper MOS's at 12, at least to me. Perhaps you hear it differently. But I'd be surprised if you disagree.

> I'm for live and let live in xentonality. To each his own. But do NOT try to claim I should be using scales which make me puke if I want to be truly xenharmonic. I am not interested. And don't claim everyone loves the result of using any random system that comes to along just because of a lack of negative reviews.

I don't think Igs was claiming that.

-Mike

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I agree with Igs' rant. I thought part of the fun was to
> discover the "new" rules (though I've yet to systematize what
> I'm doing) instead of relating to 12 tone common practice.
>
> Chris

Er, I thought that was my point, with Igs arguing against it!
-Carl

--- In tuning@yahoogroups.com, "battaglia01" <battaglia01@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:

> Who said anything about deep sixing regular temperament?

That seemed to me what Igs was saying.

The takeaway point from Igs' post was that Pajara, while an excellent system, doesn't sound particularly xenharmonic. At least it doesn't to me.

Before I ever heard a note of either 19 or 22, I expected them to sound familiar in certain ways--19 because it shared 81/80 with 12, and 22 because it shared 64/63. And I was not disappointed. In those days, that did not prevent them from sounding, to my ears which had never heard such things, new and exciting. I worked with 19, with 22, and with 7-limit JI and to me it was a new world. Perhaps we are a little jaded.

As for the linear temperaments of fairly low complexity I've been discussing, 12 shares 99/98, 176/175 and 225/224 with orwell; 126/125 with myna and sensi; 100/99 and 225/224 with magic. It's bound to share something with a rank two 7 limit temperament because it can't increase the rank to four, although what it shares might be pretty remote from the realities of either.

> In many cases, 5-limit systems with "new puns" will sound more xenharmonic than 7-limit systems forming proper MOS's at 12, at least to me. Perhaps you hear it differently. But I'd be surprised if you disagree.

Except Igs is dismissing all these temperaments I mentioned above which don't form proper MOS at 12.

No, not at all. And in fact I thought Igs, and I certainly am speaking in
generalities. There is a lot of talk along the lines of rationalizing
tunings in terms of JI and that seems to be related to 12 equal practice.

Perhaps it is just a perception because, after all, 12 tone practice IS our
common language. And the next common language are JI fractions and harmonic
series.

I think as a side project, when I'm done with my serial piece in JI I will
try to figure out some non-meantone related chord progressions in one of the
following tunings - 17, 19 (I hope to get my 19 edo guitar Monday) or 12th
root of Phi (I found an electric guitar last night at guitar center for
$30!! And it played good - its worth that in parts alone - I am going to rip
out the frets, fill in the slots with plastic wood, and try super gluing
wire to the fretboard in a 12th root of Phi layout. All I got to lose is a
bit of time.) My 18 edo acoustic - I decided that actually I'm going to
copy one of Dante Rosati's harmonic series layouts. I've not decided which
yet. And I'll probably switch that guitar to nylon strings too. The 22 edo
stick guitar is progressing but slower as I'm trying to do a decent job of
it and I might have a swappable fret board system going. That would be quite
useful

Don't ask me why I blurted all of that out....

And - it was funny - the guy I buy from at guitar center and I had a laugh -
we plugged the $30 guitar into a $1,200 Mesa Boogie amp. It actually sounded
pretty good.

Chris

On Sat, Apr 16, 2011 at 4:11 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > I agree with Igs' rant. I thought part of the fun was to discover the
> > "new" rules (though I've yet to systematize what I'm doing) instead of
> > relating to 12 tone common practice.
>
> You think I am relating everything to 12 notes in common practice and Igs
> doing something else?
>
>
>

entirely possible I'm confused.

I think I should be working out chord progressions in tunings other than 12
equal that do not imitate 12 equal chord progressions. That is what I meant.

Chris

On Sat, Apr 16, 2011 at 5:52 PM, Carl Lumma <carl@...> wrote:

>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > I agree with Igs' rant. I thought part of the fun was to
> > discover the "new" rules (though I've yet to systematize what
> > I'm doing) instead of relating to 12 tone common practice.
> >
> > Chris
>
> Er, I thought that was my point, with Igs arguing against it!
> -Carl
>

--- Mike Battaglia <battaglia01@...> wrote:

> Er, I thought you did. I was talking about this there:
> /tuning/topicId_85488.html#85555
> I then responded with "what about parabolic waves, which are
> 1/N^2 rolloff, all harmonics present," and you also said that
> that'd be better than a sawtooth. Maybe at the time you were
> just talking about timbres that most closely approximate the
> human voice, but I thought the greater point was that timbres
> with a 1/N^2 rolloff are generally closer to a more "perfectly
> concordant sound" than those with a 1/N rolloff.

Yes, and we talked about the discordance of timbres, such as
sawtooth waves, maybe around that time. However there is a
difference between timbres and chords of timbres. As a rule,
adding notes to any rooted chord should not decrease its
discordance. This rule is entirely consistent with the notion
that timbres having 12db/oct rolloff are more concordant than
those having 6db/oct rolloff.

> We are assuming that for any of this to matter at all, there
> exists a central pitch processor that is attempting to fuse
> all of this mess into a single VF at all times, regardless
> of where the sources are coming from. This applies even if
> instead of a chord, we're talking about a timbre,

If you want to compare chords and timbres you should compute
the spectra of the chords assuming some timbre. That has the
obvious drawback of having to pick a timbre -- a choice that's
averaged away in the "chord" abstraction. The other drawback
is that processing may be hierarchical to some degree,
especially if the individual tones are separated by spatial or
timing cues (also averaged away in the "chord" abstraction).
However it might still be interesting. Comparing the spectra
of chord fundamentals (i.e. picking sine tones for the timbre)
is what I thought you were doing when I first replied here.
It's something, but it's not a typical musical situation.

> sources in real life exhibit phase irregularities, differences
> in inter-aural spatialization cues, F0 estimation will be
> taking place regardless. If it wasn't, then there'd be no
> point in us talking meaningfully about "4:5:6" to begin with.

I only brought up phase because it doesn't seem to matter much
in practice (though it doesn't seem to be entirely inaudible
either) yet it matters a lot to waveform. So referring to
timbres by waveform may not be a good idea.

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> No, not at all. And in fact I thought Igs, and I certainly am speaking in
> generalities. There is a lot of talk along the lines of rationalizing
> tunings in terms of JI and that seems to be related to 12 equal practice.

I don't think there is any strong connection between 12edo and regular mappings in general. If anything, it goes the other way--there is a school of thought, very common among those who come out of an academic theory environment, to downplay approximations to JI, perhaps because beyond the 3-limit 12edo doesn't do a very good job, and yet it became the central fact of tuning. There are 72edo composers who seem embarrassed by the fact that 72edo does such a good job of approximating ratios, for one curious example of this phenomenon. At one time, there was even a political dimension for some people, where equal temperament and a/pan/tonal music was valorized for its Marxist adherence to equality for all. So no, I don't think 12 has been very friendly at all to the development of the paradigm, quite the reverse.

> Perhaps it is just a perception because, after all, 12 tone practice IS our
> common language. And the next common language are JI fractions and harmonic
> series.

It's really not my common language. I tend to think in meantone terms about common practice music.

> My 18 edo acoustic - I decided that actually I'm going to
> copy one of Dante Rosati's harmonic series layouts.

18 has possibilities; I'll be interested to hear what you make of them.

--- Chris Vaisvil <chrisvaisvil@...> wrote:
>
> entirely possible I'm confused.

The discussion may have branched too since my last check in.

Igs seemed to characterize the 4:5:6:7 chord in terms of
common practice harmony and its "dominant 7th", and I said
that's a pitfall of xenharmonic music we should strive
to overcome. He replied that he can't see how to escape
cultural conditioning, and instead intends to springboard
off it, along with his audience. I acknowledged that's a
valid approach, but it tends to raise my hackles when
people make snap judgments about xenharmonic resources on
this list, where "snap" is defined as anything shorter than
200 years. That's why I almost never describe chords as
sounding like a "major third" or "dominant 7th". Such
descriptions are of the diatonic realm.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> I acknowledged that's a
> valid approach, but it tends to raise my hackles when
> people make snap judgments about xenharmonic resources on
> this list, where "snap" is defined as anything shorter than
> 200 years.

I thought it was absurd to bemoan the lack of rank two temperaments of modest complexity and xenharmonic character which could be used in place of meantone when I've spent weeks now massively demonstrating precisely the opposite point here:

http://xenharmonic.wikispaces.com/Chromatic+pairs

If people don't want to use these resources (and so far, I've not seen a lot of customers in that store) that's fine, but please don't say they don't exist.

Gene said:

> It's really not my common language. I tend to think in meantone terms about common practice music.

Ok, noted.

> My 18 edo acoustic - I decided that actually I'm going to
> copy one of Dante Rosati's harmonic series layouts.

Gene: 18 has possibilities; I'll be interested to hear what you make of them.

Well, I've given up on my 18 guitar because I didn't find it different
enough from 17. So I'm going to copy one of Dante's ideas. I figure
he is a good guy to copy. And I like the music he wrote with them.

Chris

Ah, ok - well, like I said, I should get to characterizing some xenharmonic
progressions and mixed xen and 12-ish progressions.
Progress should be faster for us since we have the trial and error in 12 as
a guide.

Chris

On Sat, Apr 16, 2011 at 6:32 PM, Carl Lumma <carl@...> wrote:

>
>
> --- Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > entirely possible I'm confused.
>
> The discussion may have branched too since my last check in.
>
> Igs seemed to characterize the 4:5:6:7 chord in terms of
> common practice harmony and its "dominant 7th", and I said
> that's a pitfall of xenharmonic music we should strive
> to overcome. He replied that he can't see how to escape
> cultural conditioning, and instead intends to springboard
> off it, along with his audience. I acknowledged that's a
> valid approach, but it tends to raise my hackles when
> people make snap judgments about xenharmonic resources on
> this list, where "snap" is defined as anything shorter than
> 200 years. That's why I almost never describe chords as
> sounding like a "major third" or "dominant 7th". Such
> descriptions are of the diatonic realm.
>
> -Carl
>
>
>

>"I acknowledged that's a valid approach, but it tends to raise my hackles when

people make snap judgments about xenharmonic resources on this list, where "snap" is defined as anything shorter than 200 years. That's why I almost never describe chords as

sounding like a "major third" or "dominant 7th". Such descriptions are of the diatonic realm."

   Right, but so (largely) are those of so-called leading theories such as Harmonic Entropy.  Not to say those theories are bad, they work great for anything 5-limit or less...but they are increasingly tending toward "newer" standard Western tuning (later mean-tone or 5-limit-like JI), whether you like it or not.

  If we don't want to simply reenforce "can't see how to escape cultural conditioning" diatonic logic it seems we have two obvious choices: stick to theories of the far past and often of "far" cultures like Middle Eastern music or try to bring about something very much new.

  We have an advantage in that 12EDO already has a lot of 9-limit in it and a tad of implied 7-limit (in the tri-tone, though that's generally viewed as a dissonant/borderline area often only used in advanced genres like jazz).

  The mystery seems to lie in getting the 7-limit to be used as resolve points in harmony, rather than only their traditional common practice theory role as dissonances.  That...and to bring in the 11-limit (for "tolerable dissonance" if not also to occasionally double as resolve points in music)...and it seems clear none of the answers are going to sound as clear-cut and elegant as 5-limit ones (agreed with HE, on the whole): and the trick seems to be making them "not much worse/still quite usable".
--------------------------------------------------------------------------------------------------------
   On the other hand...both 5-limit and 9-limit seem largely engrained in Western culture from 12EDO...and the most likely "marketable" solutions are going to use at least them and likely also some of the resolve/tension patterns in chord progressions borrowed from 12EDO (Blackwood anyone?)   Igs was right: people like to shift roots of chords down by 5ths and sometimes 4th and 3rds to achieve resolve: this seems to be perhaps a side effect of those ratios being so prominent in meantone and 12EDO. 

   There are also weird artifacts of 12EDO-ism in my own mind...like that 16/9 sounds more normal to me than 7/4 despite 7/4 being so much lower limit/Tenney Height/etc. or that the "square root of 2" tritone doesn't sound half as bad as its rational value implies or that the high limit 15/8 doesn't sound much worse to me than 11/6 and actually sounds better in some chords and even 19/10 doesn't sound too bad (note 12EDO's major 7th is smack in between 19/10 and 15/8).. 

   It's not that I want it to be that way but, rather, that simply appears to be what it is.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Except Igs is dismissing all these temperaments I mentioned above which don't form proper > MOS at 12.

For the record: it's not the scales and tunings that result from these temperaments that I'm dismissing. Orwell, Miracle, and Myna (to say the least) both lead to exceptionally xenharmonic scales, especially if one uses the smaller MOS's...but those smaller MOS's don't actually support the harmony those temperaments were designed for, i.e abundant septimal otonal tetrads. Orwell[9], Miracle[10], and Myna[7] are all totally lacking in 4:5:6:7 tetrads, and tend to force one's hand in all sorts of new weird directions, and I love them for that. I've gotten plenty of mileage out of scales produced under the regular mapping paradigm by using them for things they weren't necessarily designed for. But if you want to use those scales to fulfill the purpose of abundant septimal otonal (and utonal) tetradic harmony, that's where the scales start bordering on obnoxiously complex and I start tuning out.

-Igs

>"Why, to be xenharmonic, do we either need to focus on 5-limit triads or
say "screw it" and deep-six the whole regular temperament paradigm to
the detriment of what the music we make actually ends up sounding like?"

   Agreed: I usually find a balance of 70% 12EDO-like ratios, 30% other types works pretty well.  And even if you, say, have a chord like 1/1 11/9 22/15 which is more like 70% "xenharmonic"...people can hear the 6/5 (between 22/15 and 11/9) in there and some overall resemblance to major and minor triads.

   Personal experience: most of the easier to compose in scales I've made, at least from my experience, have at least 65% of the dyads in mathematically in common with 12EDO.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> >
> > I agree with Igs' rant. I thought part of the fun was to
> > discover the "new" rules (though I've yet to systematize what
> > I'm doing) instead of relating to 12 tone common practice.
> >
> > Chris
>
> Er, I thought that was my point, with Igs arguing against it!
> -Carl

The difference in opinion we seem to have, Carl, is in regards to how free we are to define new rules, and whether in fact they can be defined creatively and arbitrarily or whether they must be "discovered". (I tend to suspect the latter is the case).

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

>Orwell, Miracle, and Myna (to say the least) both lead to exceptionally xenharmonic scales, especially if one uses the smaller MOS's...but those smaller MOS's don't actually support the harmony those temperaments were designed for, i.e abundant septimal otonal tetrads.

Using that logic, Meantone[7] is no good because it has only one 7-limit interval.

> Orwell[9], Miracle[10], and Myna[7] are all totally lacking in 4:5:6:7 tetrads, and tend to force one's hand in all sorts of new weird directions, and I love them for that. I've gotten plenty of mileage out of scales produced under the regular mapping paradigm by using them for things they weren't necessarily designed for.

Glad to hear that, and would be interested to hear the results.

> But if you want to use those scales to fulfill the purpose of abundant septimal otonal (and utonal) tetradic harmony, that's where the scales start bordering on obnoxiously complex and I start tuning out.

They flake out in exactly the same way meantone flakes out.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> The difference in opinion we seem to have, Carl, is in regards
> to how free we are to define new rules, and whether in fact
> they can be defined creatively and arbitrarily or whether they
> must be "discovered". (I tend to suspect the latter is the case).

Nope, I agree they must be discovered. Calling a 4:5:6:7
a "dominant 7th" chord is what I objected to. -Carl

--- "Kalle Aho" <kalleaho@...> wrote:

> > The old thread on this had monz making several versions of
> > the dominant cadence in JI. Opinions on 4:5:6:7 were mixed
> > but the general consensus seemed to be that strict JI chords
> > like 1/1-5/4-3/2-16/9 worked better. I tried but failed to
> > find monz's page on this just now. -Carl
>
> There is also this:
> http://nowitzky.hostwebs.com/justint/dom7.htm

Thanks Kalle, I'd forgotten about it. What a classic page.

To me the version with 9/5 is the worst (has a sour quality),
followed by 12-ET, then 4:5:6:7, and I agree with Mark that the
version with 16/9 is best for this cadence.

What does anybody else think?

-Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> If 12 note near-proper scales are the problem, then avoid them. If you look on the
> Chromatic pairs page, for myna you'll find 7, 11 and 15 note scales; for magic 7, 10, 13, > and 15; for sensi 5, 8, 11 and 19; for orwell 9 and 13.

And how many of these scales of <11 notes would actually be useful for abundant septimal tetradic harmonies? I love almost all of them--Myna[7], Sensi[8], and Orwell[9], and to an extend Magic [10] (though not so much Magic [7] because its humongous impropriety makes it melodically absurd), but for reasons entirely unrelated to septimal tetradic harmony.

I might question whether any of the scales up there that I like should actually be considered manifestations of those temperaments, since they're too poor in septimal otonal tetrads (the harmonic unit they were designed to produce optimally) to make music based on such harmonies. But that's another discussion.

> Somehow I am failing to find this > plague of 12-note proper scales you complain of
> here. A more reasonable complaint
> would be that there are too many improper scales, but if you are seeking to escape the
> usual that should not worry you.

I've ranted too much and obscured my own point. Let me try again to clear up what I'm all hot and bothered about. There's a narrow field of "pleasant and rewarding novelty" between the realm of the "too familiar" and the "alien/unintelligible". Most of the microtonal systems I don't like fall within the "too familiar", but ironically many of the "alien/unintelligible" have been discovered by looking for systems based on an all-too-familiar harmonic unit: the septimal tetrad. For the record, so have many systems that I'd call "pleasantly novel"--such as the ones you mentioned above--but they get their novelty for reasons unrelated to the motivations that led to their discovery.

All I'm saying that most high-accuracy temperaments that give abundant septimal otonal tetrads produce scales that are either a) too familiar or b) too outlandish (too improper, too large, etc.) to be intelligible to me (let alone a naive listener). Call me Goldilocks, because I'm looking for things that are "just right"--novel-sounding, yet intelligible; enough familiarity to have appeal, but with enough of a twist to inspire a bit of a Keanu Reeves "woah" moment. Most of the scales that provide this tend come from either 5-limit temperaments, subgroup temperaments, or (dare I say) exotemperaments.

> Admittedly, I did give a whole slew of 12-note proper hobbit scales recently, under the > dulusive belief that this is what people wanted. You can ignore them if you don't want
> them.

Not being MOS's, I'd say your hobbits definitely go well outside of the familiar, but I haven't really spent enough time with them to form an opinion. Mostly what I'm talking about are the 7-to-13-limit rank 2 temperaments.

> You are arguing out of both sides of your mouth. On the one hand, you want to get away > from same-old-same-old. On the other, you complain of a dearth of 5-limit triads.

What I've said from the beginning is that I do believe 4:5:6:7 can escape the "pull" of meantone/12-TET functionality if you can put it in a scale that's far enough removed from 12-TET structures. The trouble is that any such scale is going to be of much higher complexity or much greater impropriety...or greater error. Blackwood (or Blacksmith if we're using Middle Path names) is a great example of a scale totally divorced from 12-TET, rich in septimal otonal tetrads, and exquisitely simple in structure, and I love it dearly and suspect you would too if the fifths were in-tune.

To clarify, what I consider "familiar" has less to do with harmony and more to do with scale structure, since 5-limit temperaments like Porcupine and Negripent have familiar harmonic units but sound anything but familiar as soon as the chords start moving.

> Did it occur to you that people don't like to give reviews like "your harmony made me
> puke?"

If my harmony could literally caused vomiting in someone, I would be amazed and overcome with pride. Quite the accomplishment it would be for my music to produce such a strong visceral response! In all seriousness, though--if people find what I write unlistenable or unpleasant on account of the harmony, I would prefer to hear about it than not. However, I really would be surprised to learn that the many people who have heaped praise on the various "out-of-tune" works produced by various list members were just "being nice" and actually found the works quite objectionable on account of the harmonies.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Nope, I agree they must be discovered. Calling a 4:5:6:7
> a "dominant 7th" chord is what I objected to. -Carl

I never said a 4:5:6:7 "is" a dominant 7th, though I did say the reverse and it's easy to see how that would be confusing. 4:5:6:7 simply has a tendency to evoke similar associations to the dominant 7th unless it's radically recontextualized. To effectively accomplish that probably requires using generous amounts of additional xenharmonic intervals, as Graham and Gene are known to do, which suggests that one is not using the 4:5:6:7 as the base harmonic unit.

-Igs

> On the other hand...both 5-limit and 9-limit seem largely engrained
> in Western culture from 12EDO...

I'm not convinced that 12 EDO (as it became used in the late 19th / early 20th century) or 12-tET (as it started in the decades before that) should really be thought of as a prime-limit system. It looks like its roots were historical and practical as much as (or more than?) mathematical. We're used to hearing a 200-cent whole step; who cares what the prime number limits are?

Put another way: If a 996-cent 16/9 sounds more normal than a 7/4, then either the Tenney Height model isn't right in general, or the force of attraction of these traditional tones is stronger -- and therefore even more relevant -- than the Tenney Height. If it's the former, then comparing 12-EDO steps to lowish-Tenney-height JI intervals is mostly irrelevant; if it's the latter, then there's something about 12 EDO itself that's more important than the ratios that it's close to.

I'm not saying that prime-limit ratios are irrelevant, but what if structure is just as important? There appear to be times when JI composers focus almost exclusively on the ratios involved, and mostly ignore, say, the fact that there are different sizes of scale steps; maybe there are times when step sizes are paramount and looking at ratios is mostly worthless.

> There are also weird artifacts of 12EDO-ism in my own mind...like that
> 16/9 sounds more normal to me than 7/4 despite 7/4 being so much lower
> limit/Tenney Height/etc. or that the "square root of 2" tritone doesn't
> sound half as bad as its rational value implies or [snip]

Musically speaking -- as opposed to listening to dyads or scales outside of a larger musical context -- 12 EDO never seems to sound wrong. When I play around with scales, a 12 EDO piece of music has the potential to sound "wrong" or "out of tune" when rendered in a non-12 tuning, even if it's just Prinz or a Werckmeister temperament. When I pick a non-12 piece -- whether it's common-practice music from before the dominance of 12 EDO or one of my own attempts at composing outside of 12 EDO -- and render it with 12 EDO, it never sounds out of tune. Ugly, boring, inelegant, sure, but not "out of tune".

The question is, should I care?

I don't really think so. Those are tones I'm used to, as is most of the rest of the culture I'm in.

It would be like caring about how common split-rail fencing is; I don't need to put one around my own house, but if I put a do something really interesting and unusual with my landscaping -- like planting specially pruned fruit trees at the edge of my yard, each having two branches going out from each side, trained to be level with the ground, and almost touching the tree next to it -- then I shouldn't be surprised if people see it as similar to a split-rail fence. If anything, that familiarity becomes a new dimension to play with.

Regards,
Jake

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Using that logic, Meantone[7] is no good because it has only one 7-limit interval.

Correct. No one's going to use Meantone[7] for music where 4:5:6:7 is supposed to be the "basic" or "atomic" consonance. Meantone[12], maybe, or whatever temperament you think all those crazy jazz cats are implying in 12-TET.

> Glad to hear that, and would be interested to hear the results.

I've already published two or three songs in Orwell[9]. My next-next album (I'm always a step or two ahead of myself) is going to feature entirely my favorite temperaments, subgroup temperaments, and exotemperaments, including Godzilla[9], Negri[10], Myna[7], Beatles[7] (which might more sensibly be called Dicot at that level), maybe a piece in Sensi[8] (which sounds an awful lot like Father at that level), some subgroup stuff in 16-EDO that's not really named but which loosely resemble Cynder and Lemba, as well as some obligatory Mavila[7]. Maybe some Magic[10] stuff if I can figure out how to deal with that scale on guitar. Basically it's going to be a prog-rock album playing 19-EDO and 16-EDO off of each other. Then after that I have plans for an album about the deep sea that uses 20 and 23-EDO, which are both what I consider "watery" tunings.

Really, I didn't mean to come off like I was knocking the regular mapping paradigm. Just because I don't like a lot of the scales that come out of some of the more complex temperaments doesn't mean I don't like the paradigm itself.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> To me the version with 9/5 is the worst (has a sour quality),
> followed by 12-ET, then 4:5:6:7, and I agree with Mark that the
> version with 16/9 is best for this cadence.
>
> What does anybody else think?

I thought the JI tetrad sounded the most different from the rest, that the 16/9 chord sounded the most like a dominant 7th (kind of surprising, given that 12edo was in the mix) and that the 9/5 chord was interesting and not awful sounding, but not as good as a dominant 7th.

On 16 April 2011 20:43, cityoftheasleep <igliashon@...> wrote:

> Many people here look at the scales I use and they only see "error" and think that "these scales are not any good for harmonic music".  Not that I'm the only one to use them; plenty of others have as well (Herman Miller, J.L. Smith, Cameron, Ozan, George Secor, and Chris V. all come to mind as having used scales like 11, 13, 15, and 17-EDO), and generally speaking we all get positive responses to our music.  I don't think JI considerations satisfactorily explain why music works in these scales, and I think it's kind of insane that people aren't interested in exploring what *does* make them work.

I'll embody at least part of that straw man, in that I believe that a
high error is bad for harmonic music. Your music, as I said before
(and I listened again last night) generally works because the
harmony's sidelined. It shows that you can get away with bad harmony,
but not that any of these scales give good harmony.

11 and 13 do approximate simple ratios. The only problem is that the
simple ratios they approximate don't the constitute 5-limit. That's
well known in these parts. Do you have examples to show good harmony
that ignores these approximations?

Of course, you can make good music in any equal temperament. That's
well established. And any equal temperament will have an
approximation to some ratios. The question is whether you'd get
better harmony with lower errors.

15-equal has a middling poor approximation to the 5-limit. Not as
good as 12, but not that much worse. With a 7 cent target error,
these ETs come out as optimal:

12, 7, 19, 15, 3, 5, 22, 10, 24, 4

http://x31eq.com/cgi-bin/pregular.cgi?limit=5&error=7

If 7 has too few notes and 19 too many (or is too boringly consonant
and diatonically familiar) it's entirely to be expected that 15 would
come up as an alternative to 12 if you wanted to avoid high errors.
It'll give harmony that you can get away with, but not good, pure
harmonies.

Including George Secor and 17 is a bit rich. He explained (with Margo
Schulter) the considerations that led to 17 notes and you could
discuss them if you like. Part of that is minimizing error. And his
17 note well temperament is specifically designed to minimize error.
That's likely where the good harmony came from. (He did something
with 11 as well, maybe you're thinking of that, but it isn't as good.)

Graham

--- "cityoftheasleep" <igliashon@...> wrote:

> I never said a 4:5:6:7 "is" a dominant 7th, though I did say
> the reverse and it's easy to see how that would be confusing.

ORLY?

"4:5:6:7 is basically a Justly-tuned dominant 7th chord, and
it seems that there is something psychoacoustically tense
about dom7's that causes them to want to resolve cadentially"

and

"no matter how you gussy it up, it sounds like a dom7 chord"

and

"I don't think the septimal otonal tetrad (4:5:6:7) is a
viable analogue to the 5-limit triad as a harmonic basis for
making tonal music."

By now you know my stance on these.

-Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > If 12 note near-proper scales are the problem, then avoid them. If you look on the
> > Chromatic pairs page, for myna you'll find 7, 11 and 15 note scales; for magic 7, 10, 13, > and 15; for sensi 5, 8, 11 and 19; for orwell 9 and 13.
>
> And how many of these scales of <11 notes would actually be useful for abundant septimal tetradic harmonies?

And how many meantone scales with less than 11 notes are much good at tetradic septimal harmony? You keep treating meantone as a special case, instead of one of the gang. I think it's one of the gang.

> I might question whether any of the scales up there that I like should actually be considered manifestations of those temperaments, since they're too poor in septimal otonal tetrads (the harmonic unit they were designed to produce optimally) to make music based on such harmonies. But that's another discussion.

How do you know what harmony they were "designed" to produce? Maybe I think myna was designed for the 2.5/3.7/3 subgroup. Maybe like everyone else on Planet Myna, I started out with 23 or 27 edo and only later, when the exciting new discovery of tetrads swept us all up, got to thinking of it in terms of tetrads. Myna would still be myna, but how I thought of it would be different.

> For the record, so have many systems that I'd call "pleasantly novel"--such as the ones you mentioned above--but they get their novelty for reasons unrelated to the motivations that led to their discovery.

What do they get their mojo from?

> All I'm saying that most high-accuracy temperaments that give abundant septimal otonal tetrads produce scales that are either a) too familiar or b) too outlandish (too improper, too large, etc.) to be intelligible to me (let alone a naive listener).

I would say that marvel tempering produces a lot of stuff which is neither overly familiar nor outlandish, just for starters. But what is outlandish, in your view? Is 19 notes to the octave outlandish?

> What I've said from the beginning is that I do believe 4:5:6:7 can escape the "pull" of meantone/12-TET functionality if you can put it in a scale that's far enough removed from 12-TET structures. The trouble is that any such scale is going to be of much higher complexity or much greater impropriety...or greater error.

Well, no. See my comment re marvel, for instance.

> In all seriousness, though--if people find what I write unlistenable or unpleasant on account of the harmony, I would prefer to hear about it than not.

I don't want to be dismissed as a grump, but I'll think about it.

> However, I really would be surprised to learn that the many people who have heaped praise on the various "out-of-tune" works produced by various list members were just "being nice" and actually found the works quite objectionable on account of the harmonies.

And what about the people who didn't saty anything?

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:

> Put another way: If a 996-cent 16/9 sounds more normal than a 7/4, then
> either the Tenney Height model isn't right in general, or the force of
> attraction of these traditional tones is stronger -- and therefore even
> more relevant -- than the Tenney Height.

You are conflating sonance with functional harmony; apples, oranges. The 16/9 chord sticks the root of IV into V, and hence has a very strong effect of establishing tonality when V7 resolves to I. But that doesn't mean it sounds more consonant than an otonal tetrad, which it certainly does not.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> ORLY?
>
> "4:5:6:7 is basically a Justly-tuned dominant 7th chord, and
> it seems that there is something psychoacoustically tense
> about dom7's that causes them to want to resolve cadentially"

Okay, you got me there. Though the "basically" modifier is supposed to weaken the equation. In any case I think I've made it clear in subsequent posts that I'm aware of the distinction, insofar as a dom7 names a tuning-nonspecific functionally-specific chord from diatonic theory and a 4:5:6:7 is a tuning-specific functionally-nonspecific chord from JI theory.

> "no matter how you gussy it up, it sounds like a dom7 chord"

Referring to the chord on its own, played to an audience assumed to have a shared background in western music theory.

> "I don't think the septimal otonal tetrad (4:5:6:7) is a
> viable analogue to the 5-limit triad as a harmonic basis for
> making tonal music."

The key phrases of course being "analogue to the 5-limit triad" and "harmonic basis". Probably I should have clarified this further. In meantone harmony, we use 5-limit otonal and utonal triads as the "base" harmonic units, and an integral feature of tonality is the alternation and contrast between the otonal and the utonal. That's the "basic" model and people deviate from it all the time in interesting ways (i.e. "I am the Walrus") but when I talk about "tonal" music I mean the basic "Theory 101" shit. You got your major chords and your minor chords and one's "happy" and the other's "sad". The dumbed-down entry-level basics from which we can build and get all clever and whatnot. So if someone wants to show me an "all septimal otonal or utonal tetrad" progression that makes me go "ah" the way a basic I-vi-ii-V-I progression does, I'll eat my words.

But I suppose it's not really even worth talking about because no one's actually trying to do it anyway, in fact it's kindergarten stuff compared to the 11-limit stuff that Gene and Graham produce. Which, I'll admit, I do not even begin to understand the motivation for and a lot of it tends to make my brain go gooey if I try to figure out what's happening. I guess I'm just blowing off steam since my finals are over.

-Igs

Hi Jake,

> I'm not convinced that 12 EDO (as it became used in the late
> 19th / early 20th century) or 12-tET (as it started in the
> decades before that) should really be thought of as a
> prime-limit system. It looks like its roots were historical
> and practical as much as (or more than?) mathematical.

The roots were historical, but that history is one of the
development of a style of 5-limit harmony. It's the story
of the journey from meantone temperament, which tempers out
81/80 only, to 12-ET, which additionally tempers out 128/125
and 648/625. This was understood by theorists here and
there, but mostly it happened organically. Only in the last
several decades have theorists put it all together and made
predictions about alternative ways the history might have
gone -- tuning forks in the road, as it were.

> Put another way: If a 996-cent 16/9 sounds more normal than
> a 7/4, then either the Tenney Height model isn't right in
> general, or the force of attraction of these traditional
> tones is stronger -- and therefore even more relevant --
> than the Tenney Height.

As Gene says, Tenney height is about concordance, whereas the
concept of a "dominant chord" is entirely due to the logic of
functional harmony. Concordance will influence which chords
are chosen for which roles in a functional style, but other
things are involved too. I already mentioned vanishing commas,
which have to do with how chords relate to one another in chord
progressions. And there are additional factors that aren't
fully understood.

> maybe there are times when step sizes are paramount and
> looking at ratios is mostly worthless.

It certainly is possible to write music where this is true.
A solo monophonic line is a basic example.

> When I pick a non-12 piece -- whether it's common-practice
> music from before the dominance of 12 EDO or one of my own
> attempts at composing outside of 12 EDO -- and render it
> with 12 EDO, it never sounds out of tune. Ugly, boring,
> inelegant, sure, but not "out of tune".

Hm. To me, this
http://www.youtube.com/watch?v=FHjitZIyaRc

sounds like an out of tune version of this
http://www.youtube.com/watch?v=EHExcd6PYxQ

And I can't hear it any other way. It is of course possible
to produce an even worse version. Sky's the limit there.
It's really a matter of degrees I guess.

-Carl

--- "cityoftheasleep" <igliashon@...> wrote:

> So if someone wants to show me an "all septimal otonal or
> utonal tetrad" progression that makes me go "ah" the way a
> basic I-vi-ii-V-I progression does, I'll eat my words.

Without passing go or collecting $200, you can swap the
triads in that cadence for o- and u-tonal tetrads and you
should have your meal.

Then there's Decatonic Swing, which I think works beautifully.
I was at its premiere in NY in 1999 and my parents thought
it was in standard tuning! Admittedly it does use pentads etc.
for color, just as tetrads like this dom7 thing you may have
heard about are used in Theory 101.

What'd you make of the barbershop link I posted?

> But I suppose it's not really even worth talking about
> because no one's actually trying to do it anyway,

It was certainly Paul's goal, as stated in his 22-ET paper.
Others too. To me, Decatonic Swing is de facto proof that
everything Paul did in that paper worked just as he said
it would.

-Carl

I wrote:

> Hm. To me, this
> http://www.youtube.com/watch?v=FHjitZIyaRc
>
> sounds like an out of tune version of this
> http://www.youtube.com/watch?v=EHExcd6PYxQ

And if your youtube settings are like mine, ET is getting
a huge unfair advantage here by being available in 480p,
which has much better audio fidelity. To hear how crappy
it really sounds in comparison, set the first video down
to 360p! -Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> And how many meantone scales with less than 11 notes are much good at tetradic
> septimal harmony? You keep treating meantone as a special case, instead of one of the
> gang. I think it's one of the gang.

I agree. I must just be choosing my words poorly if I've given you the contrary impression.

> How do you know what harmony they were "designed" to produce? Maybe I think myna
> was designed for the 2.5/3.7/3 subgroup. Maybe like everyone else on Planet Myna, I
> started out with 23 or 27 edo and only later, when the exciting new discovery of tetrads > swept us all up, got to thinking of it in terms of tetrads. Myna would still be myna, but
> how I thought of it would be different.

I'm confused. Are you saying that a 2.5/3.7.3 temperament is the same thing as a full 7-limit temperament? Because Myna in 23-EDO doesn't ever lead to remotely decent 7-limit tetrads, so it doesn't seem right to group it together with a tuning that does.

> What do they get their mojo from?

I'm honestly not too sure. I don't have any elegant formulations to explain why I seem to like the tunings I do, which is one of the reasons I'm hoping more people will get interested in them--but maybe I'm just a freak?

> I would say that marvel tempering produces a lot of stuff which is neither overly familiar > nor outlandish, just for starters. But what is outlandish, in your view? Is 19 notes to the > octave outlandish?

"Outlandish" is another thing I don't have a rigorous definition for. It's sort of a continuum of impropriety and size--a small but highly improper scale like Magic[7] would be outlandish, a large but still proper scale like Orwell[13] would be outlandish. But something like Superpyth[7] isn't, or Cynder[11]--though they're both cutting it close.

> Well, no. See my comment re marvel, for instance.

Negri is definitely the closest thing to an exception I can think of. Maybe there's a progression hiding in negri[10] that'll do the trick. I've got a 19-tone guitar so I'll give it a whirl.

> And what about the people who didn't saty anything?

Who knows? I don't comment on everything I listen to and like, so I just don't factor them in.

-Igs

On 17 April 2011 11:25, cityoftheasleep <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

>> How do you know what harmony they were "designed" to produce? Maybe I think myna
>> was designed for the 2.5/3.7/3 subgroup. Maybe like everyone else on Planet Myna, I
>> started out with 23 or 27 edo and only later, when the exciting new discovery of tetrads > swept us all up, got to thinking of it in terms of tetrads. Myna would still be myna, but
>> how I thought of it would be different.
>
> I'm confused.  Are you saying that a 2.5/3.7.3 temperament is the same thing as a full 7-limit temperament?  Because Myna in 23-EDO doesn't ever lead to remotely decent 7-limit tetrads, so it doesn't seem right to group it together with a tuning that does.

2.5/3.7/3 was the question. 2.5/3.7.3 would give a different answer,
because it's a different way of looking at the 7-limit, instead of a
subgroup. In that case, it's essentially the same as the 7-limit.
2.5/3.7/3, however, is a 7-limit subgroup, the same as the 5-limit is.
The question is analogous to whether you'd put 5-limit meantone in
the same group as 7-limit meantone. Maybe with a focus on 26-equal,
which is a meantone that doesn't extend well to the 7-limit with the
standard mapping.

I think Gene's remark holds. Meantone would still be meantone, but
how you thought of it would be different. This is an important point.

Magic is ideal in the 9-limit but also works in the 11-limit. You
don't need full pentads for the 9-limit harmony to shine through --
you can mix 5-limit chords with "sus4" and 6:7:9 approximations. If
you add more notes to get those 9-limit pentads, what you have will
still be magic, but how you think of it will be different. You can
also note that some dissonances have 11-limit rationalizations.

Orwell was first noted (that I'm aware of) in the 11-limit. You may
approach it as a 7-limit temperament, but note that the dissonances
have 11-limit rationalizations. You're bound to hit those dissonances
because they're some of the simplest intervals. You may treat it as a
small scale with incomplete 11-limit harmony from the start. Or you
may treat it as a system for allowing puns in full 11-limit harmony
without looking at scales. You can even start with 13-limit subgroups
(that may entail the variant I've called "Blair") as you suggested to
me once. Whatever you do, it's still orwell, but how you think of it
will be different.

The point is that these systems (regular temperaments or regular
mappings or temperament classes, whatever you call them) are
discovered, not designed. It doesn't matter what the first person to
discover them had in mind.

Graham

On 17 April 2011 10:28, cityoftheasleep <igliashon@...> wrote:

>> "no matter how you gussy it up, it sounds like a dom7 chord"
>
> Referring to the chord on its own, played to an audience assumed to have a shared background in western music theory.

Why are you assuming that background? It wasn't clear in the original
context. I'm not even sure if it's a background I share. I'd expect
any audience to have some exposure to global pop music, which is
influenced by western theory, but not to recognize dominant sevenths.
I'd hope they've also been exposed to jazz or blues where sevenths are
used without the dominant function.

Sometimes it's nice to play tricks with people who have a theoretical
background. Comma pumps are good for this. My 60x60 submission was
an example -- a magic comma pump spread over nearly a minute. The
idea is that composers would get to hear it, and would try and work
out what was going on. Unfortunately, it wasn't selected for
"performance" so that fell through. Anyway, I've had some success,
given:

> But I suppose it's not really even worth talking about because no one's actually trying to do it anyway, in fact it's kindergarten stuff compared to the 11-limit stuff that Gene and Graham produce.  Which, I'll admit, I do not even begin to understand the motivation for and a lot of it tends to make my brain go gooey if I try to figure out what's happening.  I guess I'm just blowing off steam since my finals are over.

Gene's music should be required listening for professors of music.
Either they should explain what's going on harmonically, or justify
why they keep drawing a salary as an expert in the field. We can
dream, eh?

Graham

Me:
>> Paul Erlich's "Decatonic Swing" is a good example of
>> 7-limit harmony.  I believe it's all seventh chords, and
>> they work.  Even given the poor approximations of
>> Pajara/22, the harmonic logic makes sense.

Igliashon:
> I'm not saying 7-limit harmony doesn't "work".  I'm saying it doesn't work analogously to 5-limit harmony.

You originally said ". . . I don't think the septimal otonal tetrad
(4:5:6:7) is a viable analogue to the 5-limit triad as a harmonic
basis for making tonal music." That sounds exactly like the logic
behind the decatonic scales.

>> You're still saying you "would be" surprised when people
>> have already told you they have a different view.
>
> No, they really haven't.  Slightly different views have been expressed, but no one seems to hear a 4:5:6:7 as being entirely unlike a dominant 7th.

Of course it isn't entirely unlike a dominant 7th, and nobody would
have disagreed with you if you had said that. It is, however,
something that can be separated from ". . . the 12-ET-based functions
of a dominant 7th . . ."

>
>> By now
>> you should have been surprised.  I'll add myself to the
>> list.  I don't hear "12-ET-based functions" when I hear a
>> 4:5:6:7.  I don't even know what a 12-ET-based function
>> would sound like.  4:5:6:7 sounds like a pure chord, and the
>> 12-ET dominant seventh doesn't. I never hear the half-octave
>> "wanting to resolve" a particular way.  I always thought
>> that was a convenient fiction harmony teachers use to
>> explain conventional chord sequences (which sound fine;
>> I'm not knocking them).
>
> Well, color me surprised by your views.
>
>> I can hear the 7 of 4:5:6:7 as being out of tune.  So can
>> the 5 for that matter.  I think it's because they're
>> outside the expected melodic framework.  The solution is to
>> emphasize different melodic patterns.  It may help to treat
>> the 7 as a dissonance when you use it first.
>
> Wouldn't that be defeating the purpose of using 4:5:6:7 as a base harmonic unit analogous to a 4:5:6?

Maybe, but that wasn't the point I was responding to.

>> Another problem with 4:5:6:7 is that it sounds too pure and
>> fused.  It doesn't bring an interesting new sonority to the
>> table.  The solution there is to tie it in with scrunchier
>> chords that hold the 7.
>
> That's also kind of beside the point I was trying to make.

It looks relevant to the point of the paragraph I was replying to,
which was about the relative perception of 4:5:6:7 and dominant
sevenths.

>> I don't think functional considerations are leading me
>> anywhere.  I don't think most listeners out there in the
>> big wide world are at all sensitive to the Common Practice
>> formula for treatment of dominant sevenths.
>
> Really?  You don't hear a G7 progressing to a C major (in 12-ET or any other meantone or pythagorean tuning) as being a strong, natural, resolved progression?  You don't think most people hear it that way?  The "rules" of common practice are totally arbitrary and not at all based in some fundamental aspect of hearing?

A G7 progressing to C major sounds great. So do lots of other chord
sequences, some ending on a seventh chord. If you tested me, maybe
I'd show some preferences for G7 to resolve in the common practice way
given a common practice or diatonic context. It doesn't stop me
following the music I wrote in other contexts . . . and doesn't seem
to stop you understanding it either.

The rules of common practice are partly arbitrary and partly based in
fundamental aspects of hearing. The G7 to C is a good cadence because
it involves stepwise resolutions, it's diatonic, and it ends on the
major tonic. There are other good cadences out there. The
expectation that a G7 should always resolve this way was an artifact
of the common practice era and that's over now. Some people, with
either classical training or a large amount of exposure to common
practice music, will hear it that way. Most people won't.

The last two chords in the fragment I linked to make what sounds to me
to be a strong, natural, resolved progression. It's essentially Fh7
to C (F harmonic seventh to C major). The F itself is omitted, so you
could call it other things, but it still means the tritone is
resolving in the wrong direction. In magic temperaments, that's
likely to be the common direction because it's simpler on the spiral
of thirds than Gh7 to C.

If anybody wants to re-use this cadence (I claim no copyright over it)
note that it can be written over a common root as 6:10:12:14:18
resolving to 6:9:12:15:18. There's no need to temper it but certain
steps become equalized in Magic.

>> A lot of us
>> are attuned to the liberal use of seventh chords in rock
>> and blues.  They have a spicy feel and can you can use one
>> as the tonic.  I don't find a 4:5:6:7 has the same feel at
>> all so I don't think it's altering my perceptions, other
>> than making be receptive to the use of the 7 as coloration.
>
> Jon Catler would disagree with you, and so (I would suspect) harmonic entropy.  The canonical line I've always heard from people in the tuning community is 12-TET's dominant 7th chords are just out-of-tune septimal otonalities.  I'll admit a reasonably-pure 4:5:6:7 lacks the spiciness of 12-TET, but Catler sure rocks them pretty hard in his own blues and it seems to work.

Saying that a dominant seventh is heard as an out of tune harmonic
seventh is not the same as saying a harmonic seventh is heard as a
dominant seventh. I don't follow the latter because I don't hear the
harmonic seventh requiring a dominant function. Whether the former is
true I don't know. It's always struck me as an unfalsifiable
hypothesis. A 12-TET dominant seventh sounds like what it is and a
4:5:6:7 sounds like what it is. They certainly don't sound the same
because the tempered chord is out of tune.

>> I don't know how strong the associations are for you.  I
>> have noticed that you don't focus on microtonal harmony.
>
> That's not entirely true.  Just because I don't focus on integrating extended JI (or temperaments thereof) doesn't mean I don't focus on harmony.  Quite the contrary, the coloration of different (and extreme) mistunings of standard 5-limit chords is pretty much an integral feature of my music.

What microtonal piece do you have with harmony in the foreground? You
may consider your chords to be integral, but they're usually in the
background when microtonal. I'm suspicious about the pad sounds you
use because they can have a high bandwidth that obscures the tuning.
You also tend to put a bass line against a high melody, so that
there's little interaction.

>> Your Map of an Internal Landscape (that's you, right?) is
>> good microtonal music, but it doesn't have much harmony.
>
> It's got as much harmony as most music in the same genre, i.e. rock or pop.  Almost every single track has at least triadic harmony happening, except for the tracks in 11, 23, and 28 (because at the time I was a bit more conservative with using wonky 3-limit approximations).  But indeed I paid more attention to melodies and root movements, since that seemed like a better starting-place for exploration.  Getting some basics down first seemed a more sensible move than trying to go whole-hog for extended otonalities (which I generally dislike, even when Just).

Specific tracks from Finity that seem to have prominent harmony: Seas
of Glass; Ribbons and Bows; Anger, Hate, and the World Beyond. I may
be tricked by the distortion, but it sounds like the sound of the
chords is your starting off point and they can be right up in the mix.
Where have you done the same thing microtonally? If you haven't, it
suggests you prefer the chords in 12. If you have, of course, I'll
listen to it. I don't follow everything and it isn't all correctly
filed.

> Gene's music gets its wow factor for me mainly because he's juggling so many notes, and George's I really haven't heard any of except for his 11-EDO piece (which was awesome).  Your work reminds me a lot of Gene's, in that both have some really funky alien progressions that definitely require me to work against my "programming" (though I rarely succeed).  To be frank, though, I think that bringing in totally unusual harmonies as well as very unusual and complex scales, and doing very intricate and complex things with these harmonies and scales, is an approach that it's a bit too ahead of its time for me.  It's hard for me to make it through an entire piece by either of you because I feel like there's nothing for me to latch on to.  Neither of you write particularly rhythmically-oriented music, either, so there isn't even that as a "safety-net".  But hey, to each his own.  The both of you come from very different musical backgrounds than I do and have a very different set of goals.  But anyway the point is that my "lack of focus" on extended harmony probably makes more sense if you take into account my background and the "compositional problems" I turned to microtonality to solve.

You don't think my music's rythmically-oriented??

You can have different goals if you like. But you shouldn't then be
saying the tools we're using to achieve our goals are inadequate.
We're getting what we want by focusing on low error temperaments. I
don't hear anybody getting the same results any other way. You say
you and others make good music with other tunings, and that's correct.
(It sounds fine to me.) But I say you aren't getting good harmony.

There's plenty of music to be made that ignores or sidelines the
harmony, but some of us want good harmony, and that's why we moved
into microtonality. When it comes to extending the harmony, you need
tend to imply new and complex scales. I'm fine with that if the two
are well integrated. The fact you can accept my resolutions means you
can't be hearing things much different to me.

>> And then you say you don't see the point of
>> close approximations to simple ratios, that they don't have
>> musical value for you. So, fine, if it doesn't work for
>> you, try something that does.
>
> I don't recall saying anything quite so drastic, but it's true that accuracy is pretty far down my list of priorities.  Mostly because it seems to take care of itself well enough, insofar as no scale is completely devoid of some form of consonance.

Right, you'll get some form of consonance, but if you want really good
chords you have to go out and look for them.

Graham

I wrote:

>> So if someone wants to show me an "all septimal otonal or
>> utonal tetrad" progression that makes me go "ah" the way a
>> basic I-vi-ii-V-I progression does, I'll eat my words.
>
> Without passing go or collecting $200, you can swap the
> triads in that cadence for o- and u-tonal tetrads and you
> should have your meal.

Here's one rendition. First up, 5-limit version.
Scala sequence:
http://lumma.org/temp/cadence/Cadence5.seq

In meantone temperament, tuned in 12-ET:
http://lumma.org/temp/cadence/Cadence5_12.mid

In JI, tuned in 99-ET:
http://lumma.org/temp/cadence/Cadence5_99.mid

If your MIDI cello has vibrato, er, try a different
patch or complain to me and I'll change it.

7-limit sequence:
http://lumma.org/temp/cadence/Cadence7.seq

In the suspiciously-named "dominant" temperament,
tuned in 12-ET:
http://lumma.org/temp/cadence/Cadence7_12.mid

In JI, tuned in 99-ET:
http://lumma.org/temp/cadence/Cadence7_99.mid

Here are the ratios (view fixed-width font):

7/4 27/14 7/4
3/2 10/7 27/16 3/2 3/2
5/4 5/4 27/20 21/16 5/4
1/1 1/1 9/8 9/8 1/1
15/16
5/6

Peace! -Carl

On 17 April 2011 05:20, cityoftheasleep <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>> If 12 note near-proper scales are the problem, then avoid them. If you look on the
>> Chromatic pairs page, for myna you'll find 7, 11 and 15 note scales; for magic 7, 10, 13, > and 15; for sensi 5, 8, 11 and 19; for orwell 9 and 13.
>
> And how many of these scales of <11 notes would actually be useful for abundant septimal tetradic harmonies?  I love almost all of them--Myna[7], Sensi[8], and Orwell[9], and to an extend Magic [10] (though not so much Magic [7] because its humongous impropriety makes it melodically absurd), but for reasons entirely unrelated to septimal tetradic harmony.

A tetrad has -- shock! -- 4 notes. Three tetrads (minimum for
"abundant" I'd have thought) give 12 notes. Of course, there's some
overlap, and if only the root/fifth overlap you'll end up with 10
notes. But you shouldn't be surprised if you can't get a tetradic
scale with less than 10 notes. That's pretty much what Paul found
with the decatonics. If you want septimal tetradic harmony, you
should look at Paul's work. Otherwise I don't know why you brought
all this up.

Graham

On Sat, Apr 16, 2011 at 6:03 PM, genewardsmith
<genewardsmith@...> wrote:
>
> That seemed to me what Igs was saying.

I had a discussion with Igs about this offlist before this post, and
so I don't think that's what he was saying. We seem to share some kind
of similar ideal of what kind of music we want to write, and for that
ideal the theory isn't perfectly applicable. You are one of the only
people who is actually using the math to find and generate scales that
suit your needs, and for your needs you don't mind composing in
46-equal or using really large MOS's.

I, on the other hand, am trying to find "tonal" sounding scales that
sound completely different. I'd like for them to fit into a compact
size, similar to that of meantone[7] or blackwood[10], and I'd like
for them to sound completely different than anything I've ever heard
before. Pajara might be such a scale, and if Paul had figured it out
in the 1800's before dominant 7 chords were being used as tonal
sonorities, it would have blown everyone's mine. But he didn't, he
figured it out today, and so it doesn't sound that "xenharmonic" to
me.

Maybe part of it is that if you're dealing with 13-limit heptads, then
it's just hard to find a 7-10 note scale that fits a lot in it. I've
been trying to work with subgroups involving only three primes, like
2.7.11, to find a temperament with a complexity rivaling that of
meantone. Machine is the obvious winner here. Since having no-3's
might be kind of rough, I'm also trying to check out 2.3.7.11, which
might lead to some xenharmonic 10-note scales if we can get 3 tetrads
that share a common 3/2. Finally, I note that with more complex 12-tet
music, like Great American Songbook stuff or stuff by Gershwin, or
even the blues - where they do tend to use something like 4:5:6:7 as a
base harmony - they often stick to a meantone "understructure," but
just add 7 (or 9, or the #11, or the b9 and #9 which are really close
to ratios of 17 and 19) as they will. Maybe this lends itself to
thinking away in rank 3 or higher - rank 2 (meantone) understructure,
addition of no-13's 19-limit harmonics on top to enrich that
structure.

For 40s American pop standards, they will change the scales that
they're using over every single chord, so maybe it really is rank 2,
but where the chords don't derive from the base scale - just (most of)
the melody. Then again, with the blues, people tend to sing in a 5-7
note scale (that isn't even proper) over the ENTIRE chord progression
of a 12-bar blues, so perhaps it's worth it for us to find "melodic
subsets" of these larger scales, and then still just use them
directly. Or maybe we just need to get more into the MODMOS's of each
scale, or maybe I just need to move on with the omnitetrachordal stuff
(like defining it to your satisfaction). But either way, nobody's
talking about deep sixing anything, we're just trying to find better
ways to use the math to predict useful scales.

I continually bring up the above examples because they represent very
real ways that we think and have thought about music for over 100
years now, but these truths are generally not well represented in
academia and so many don't know them. I have some insight into this
because I was fortunate enough to have excellent jazz teachers in
college - but "jazz" and all that entails isn't the point here. Many
of these concepts were pioneered by folks like Debussy, Stravinsky,
Gershwin, folks like Cole Porter, etc. The bigger picture has nothing
to do with the stylistic inklings of "jazz" (which I'm not always a
fan of), but that there's a story being told of higher-limit
harmonies, 3D/4D structures on top of rank 2 substructures, use of
"modal" (MODMOS) harmonies, ascalar tonality, etc.

The truth is that academia's take on "jazz" is even worse than its
take on microtonality, so I want to try and at least set the record
straight on a list like this where people are down to figure out what
is really going on. All of my contributions on the MODMOS topic so far
are my attempt to generalize modal harmony concepts that I learned at
school to xenharmonic scales, so so far it seems to be working. Maybe
by developing melodic subsets of larger scales (the blues), or coming
up with a rank-2 "skeleton" while enriching it with higher-limit
chords (Gershwin, the whole sound of the 40s, etc), or working out
some "tonal" sounding omnitetrachordal scales to find useful MODMOS's
(which I haven't defined satisfactorily yet), we'll make some huge
progress into coming up with cognitively coherent scales that are
packed with higher-limit harmony. Anyway, now I'm the guy who's
ranting. But none of these developments have anything to do with
deep-sixing anything.

> Before I ever heard a note of either 19 or 22, I expected them to sound familiar in certain ways--19 because it shared 81/80 with 12, and 22 because it shared 64/63. And I was not disappointed. In those days, that did not prevent them from sounding, to my ears which had never heard such things, new and exciting. I worked with 19, with 22, and with 7-limit JI and to me it was a new world. Perhaps we are a little jaded.

They are new and exciting, but it is my particular artistic goal to
find something that, to the average person, sounds completely
different and fresh, makes "sense" in some kind of strange way, but
they don't know why -- yet they can immediately comprehend it. I don't
want to overwhelm and blast them with novelty that they can't
comprehend, and I don't want to show them something that just sounds
like a more "in-tune" version of what they already know (Pajara in
22-tet). Personally, I don't want to have to deal with really
high-error temperaments either, because while I'm getting used to
them, it would be nice to be able to pile on the harmony. So that's my
goal. Some parts of 22 have fit into this (porcupine), some have not
(Pajara).

> As for the linear temperaments of fairly low complexity I've been discussing, 12 shares 99/98, 176/175 and 225/224 with orwell; 126/125 with myna and sensi; 100/99 and 225/224 with magic. It's bound to share something with a rank two 7 limit temperament because it can't increase the rank to four, although what it shares might be pretty remote from the realities of either.

It shares 50/49 with pajara, and 64/63 with dominant...? What do you mean?

> > In many cases, 5-limit systems with "new puns" will sound more xenharmonic than 7-limit systems forming proper MOS's at 12, at least to me. Perhaps you hear it differently. But I'd be surprised if you disagree.
>
> Except Igs is dismissing all these temperaments I mentioned above which don't form proper MOS at 12.

Because for many of these temperaments, the MOS's by themselves don't
do much. Like miracle[10], where I again predict that the MODMOS's
will be particularly magical.

-Mike

On Sun, Apr 17, 2011 at 9:05 AM, Mike Battaglia <battaglia01@...> wrote:
> The truth is that academia's take on "jazz" is even worse than its
> take on microtonality, so I want to try and at least set the record
> straight on a list like this where people are down to figure out what
> is really going on.

In fact, everything I just said can be summed up in this article:

http://en.wikipedia.org/wiki/Mystic_chord

It is completely ridiculous.

-Mike

Hi Igs,

though you don't have a definition for outlandish - why would you think "a
large but still proper scale like Orwell[13] would be outlandish." ?

This is an orchestral piece composed in 13 note subset of 31 notes per
octave called “Orwell”.

http://chrisvaisvil.com/?p=341

sounds... well "normal" but a bit twisted though obviously after some years
of listening to microtonal music, both concordant and discordant, I hear
things differently now.

Or is there a different meaning for Orwell [13] ?

Chris

On Sun, Apr 17, 2011 at 3:25 AM, cityoftheasleep <igliashon@...>wrote:

>
>
>
>
> "Outlandish" is another thing I don't have a rigorous definition for. It's
> sort of a continuum of impropriety and size--a small but highly improper
> scale like Magic[7] would be outlandish, a large but still proper scale like
> Orwell[13] would be outlandish. But something like Superpyth[7] isn't, or
> Cynder[11]--though they're both cutting it close.
>
>
> -Igs
>
>
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> In meantone harmony, we use 5-limit otonal and utonal triads as the "base" harmonic units, and an integral feature of tonality is the alternation and contrast between the otonal and the utonal.

You mean in meantone harmony of the common practice period, I think. It is hardly a feature of meantone (an excellent 7-limit system which can be extended to higher limits) as such that it must be used as Byrd or Couperin would have used it.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
You can even start with 13-limit subgroups
> (that may entail the variant I've called "Blair") as you suggested to
> me once. Whatever you do, it's still orwell, but how you think of it
> will be different.

Could you define "Blair"? Actually, I'd be interested in whatever names you've concocted.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> The last two chords in the fragment I linked to make what sounds to me
> to be a strong, natural, resolved progression.

Could you give the link again? I don't recall seeing a link.

On Apr 17, 2011, at 10:40 AM, Chris Vaisvil <chrisvaisvil@...> wrote:

Hi Igs,

though you don't have a definition for outlandish - why would you think "a
large but still proper scale like Orwell[13] would be outlandish." ?

This is an orchestral piece composed in 13 note subset of 31 notes per
octave called “Orwell”.

http://chrisvaisvil.com/?p=341

sounds... well "normal" but a bit twisted though obviously after some years
of listening to microtonal music, both concordant and discordant, I hear
things differently now.

Or is there a different meaning for Orwell [13] ?

Chris

Orwell[13] means - take 13 successive instances of the Orwell "generator"
and smush them together into an octave.

If you don't know what that means, then think about meantone: the generator
for meantone is a fifth, four of which make a major third + some octaves. If
you take 6 meantone fifths going up, and one going down, you get the
following notes:

F C G D A E B

smushed within an octave you get

C D E F G A B C

and there's your major scale, which as we can see is also meantone[7].

Likewise, orwell[13] is 13 notes of the orwell generator, which is a
subminor third of around 270 cents. The whole thing is tempered so three of
them make a minor sixth. Two of them make an approximate 11/8. Orwell[13] is
13 of those 270 cent generators stacked on top of one another, reduced
within an octave.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > As for the linear temperaments of fairly low complexity I've been discussing, 12 shares 99/98, 176/175 and 225/224 with orwell; 126/125 with myna and sensi; 100/99 and 225/224 with magic. It's bound to share something with a rank two 7 limit temperament because it can't increase the rank to four, although what it shares might be pretty remote from the realities of either.
>
> It shares 50/49 with pajara, and 64/63 with dominant...? What do you mean?

12 supports both pajara and dominant. It shares all of the pajara commas with pajara, therefore, and all of the dominant commas with dominant.

> Because for many of these temperaments, the MOS's by themselves don't
> do much. Like miracle[10], where I again predict that the MODMOS's
> will be particularly magical.

I draw your attention to the scales smithgw72a.scl to smithgw72j.scl in the Scala scale directory. Of these, two are ten-note miracle MODMOS: smithgw72b.scl and smithgw72j.scl. Here they are in terms of secors:

smithgw72b: -8, -7, -6, -2, -1, 0, 1, 5, 6, 7
smithgw72j: -13, -8, -7, -6, -2, -1, 0, 5, 6, 11

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Igs,
>
> though you don't have a definition for outlandish - why would you think "a
> large but still proper scale like Orwell[13] would be outlandish." ?
>
> This is an orchestral piece composed in 13 note subset of 31 notes per
> octave called "Orwell".

Still my favorite piece of yours, and I'm still wondering what it would sound like in 19\84 tuning.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> You mean in meantone harmony of the common practice period, I think. It is hardly a
> feature of meantone (an excellent 7-limit system which can be extended to higher limits) as > such that it must be used as Byrd or Couperin would have used it.

What I meant by "base" is that it's unlikely for harmonically-based meantone music to use a harmonic unit simpler than a 5-limit triad, unlike in pythagorean-based music preceding the common practice where the "base" unit was the trine of 2:3:4, and any augmentation thereof was treated as a dissonance that had to resolve.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> 7-limit sequence:
> http://lumma.org/temp/cadence/Cadence7.seq
>
> In the suspiciously-named "dominant" temperament,
> tuned in 12-ET:
> http://lumma.org/temp/cadence/Cadence7_12.mid
>
> In JI, tuned in 99-ET:
> http://lumma.org/temp/cadence/Cadence7_99.mid

The first two chords sounded really cool, but I would be lying if I said the resolution felt finished. Sorry, it's not working for me. Is it working for you? In this context I'm unquestionably hearing that I7 at the end as the dominant of the IV. Tell you what: tack on a 5-limit triad built on the IV after the I7 in your 7-limit progression and tell me how it feels.

-Igs

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> 2.5/3.7/3 was the question.

Sorry, it was late where I was.

> 2.5/3.7/3, however, is a 7-limit subgroup, the same as the 5-limit is.
> The question is analogous to whether you'd put 5-limit meantone in
> the same group as 7-limit meantone.

Is it? It seems to me that 23-EDO is a more than acceptable tuning of the former (2.5/3.7/3) but a horrendous tuning of the 7-limit. Is that insignificant?

> I think Gene's remark holds. Meantone would still be meantone, but
> how you thought of it would be different. This is an important point.

I don't think looking at 5-limit meantone vs 7-limit meantone is necessarily a good analogy. It's pretty hard to find a good tuning of 5-limit meantone that, when extended a bit beyond 7 notes, has excellent tunings of the 7-limit. In the case of 23-EDO as "Myna", it's a good tuning of the subgroup that never reaches a good tuning of the full 7-limit.

> Magic is ideal in the 9-limit but also works in the 11-limit. You
> don't need full pentads for the 9-limit harmony to shine through --
> you can mix 5-limit chords with "sus4" and 6:7:9 approximations. If
> you add more notes to get those 9-limit pentads, what you have will
> still be magic, but how you think of it will be different. You can
> also note that some dissonances have 11-limit rationalizations.

The question that Paul always put to me was whether rationalized intervals had psychoacoustic justifications. I'm agnostic about whether a naked 11-limit ratio has any psychoacoustic identity, but possibly Paul (and definitely Carl) seemed pretty convinced that they don't. So the question of whether or not Magic "works" in the 11-limit is a question of whether it produces 11-limit harmonies that are psychoacoustically valid.

> Orwell was first noted (that I'm aware of) in the 11-limit. You may
> approach it as a 7-limit temperament, but note that the dissonances
> have 11-limit rationalizations. You're bound to hit those dissonances
> because they're some of the simplest intervals. You may treat it as a
> small scale with incomplete 11-limit harmony from the start. Or you
> may treat it as a system for allowing puns in full 11-limit harmony
> without looking at scales. You can even start with 13-limit subgroups
> (that may entail the variant I've called "Blair") as you suggested to
> me once. Whatever you do, it's still orwell, but how you think of it
> will be different.

But what "makes it" Orwell? Commas? Again, in the case of Orwell, if you treat it as a 2.7/6.11/8 subgroup, then 13-EDO is an Orwell temperament, while if you treat it as a 7-limit temperament, 13-EDO is NOT an Orwell temperament. Paul has been insistent about the latter for years now, and if you think 13-EDO is an Orwell temperament, you might try taking it up with him.

> The point is that these systems (regular temperaments or regular
> mappings or temperament classes, whatever you call them) are
> discovered, not designed. It doesn't matter what the first person to
> discover them had in mind.

And yet, it comes down to psychoacoustic considerations to tell us where one temperament ends and another begins. What's the difference between Dimisept and Dimipent, or Negrisept and Negripent? They're treated as different temperaments while Meantone[5-limit] and Meantone[7-limit], you seem to be saying, are not. Or if they are different temperaments, then your earlier analogy is invalid.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> The first two chords sounded really cool, but I would be lying if I said the resolution felt finished. Sorry, it's not working for me. Is it working for you?

The 99et version sounds perfectly resolved to me.

Thanks, I'm glad you like it.

Changing tuning should be easy to do. Is there a synonym for 19/84 tuning?
I don't seem to find it in my tuning directory.
If not could you provide a scala file?

Chris

On Sun, Apr 17, 2011 at 11:48 AM, genewardsmith <genewardsmith@...
> wrote:

>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Hi Igs,
> >
> > though you don't have a definition for outlandish - why would you think
> "a
> > large but still proper scale like Orwell[13] would be outlandish." ?
> >
> > This is an orchestral piece composed in 13 note subset of 31 notes per
> > octave called "Orwell".
>
> Still my favorite piece of yours, and I'm still wondering what it would
> sound like in 19\84 tuning.
>
>
>
>

On Apr 17, 2011, at 11:56 AM, "genewardsmith" <genewardsmith@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > As for the linear temperaments of fairly low complexity I've been
discussing, 12 shares 99/98, 176/175 and 225/224 with orwell; 126/125 with
myna and sensi; 100/99 and 225/224 with magic. It's bound to share something
with a rank two 7 limit temperament because it can't increase the rank to
four, although what it shares might be pretty remote from the realities of
either.
>
> It shares 50/49 with pajara, and 64/63 with dominant...? What do you mean?

12 supports both pajara and dominant. It shares all of the pajara commas
with pajara, therefore, and all of the dominant commas with dominant.

Right, but above you said it was bound to share something with a rank 2
7-limit temperament, as if it were a mystery, so I gave some examples that I
wasn't sure why you left out. I see I misunderstood.

> Because for many of these temperaments, the MOS's by themselves don't
> do much. Like miracle[10], where I again predict that the MODMOS's
> will be particularly magical.

I draw your attention to the scales smithgw72a.scl to smithgw72j.scl in the
Scala scale directory. Of these, two are ten-note miracle MODMOS:
smithgw72b.scl and smithgw72j.scl. Here they are in terms of secors:

smithgw72b: -8, -7, -6, -2, -1, 0, 1, 5, 6, 7
smithgw72j: -13, -8, -7, -6, -2, -1, 0, 5, 6, 11

It's at this point I wish I had Scala for iPhone.

I was hoping you'd have some feedback on the planar temperaments in 12-equal
stuff, but perhaps my epic rant was... A bit too epic.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> It's pretty hard to find a good tuning of 5-limit meantone that, when extended a bit beyond 7 notes, has excellent tunings of the 7-limit.

On the contrary, it's so easy it was found by accident, in the form of 1/4 comma meantone.

> The question that Paul always put to me was whether rationalized intervals had psychoacoustic justifications. I'm agnostic about whether a naked 11-limit ratio has any psychoacoustic identity, but possibly Paul (and definitely Carl) seemed pretty convinced that they don't. So the question of whether or not Magic "works" in the 11-limit is a question of whether it produces 11-limit harmonies that are psychoacoustically valid.

I don't think the any-old-tuning-will-do approach produces anything much like actual 11 or 13 limit harmonies, so to my ears that question is settled.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Thanks, I'm glad you like it.
>
> Changing tuning should be easy to do. Is there a synonym for 19/84 tuning?
> I don't seem to find it in my tuning directory.
> If not could you provide a scala file?

Could you post the Scala file you used? I want to get the notes to correspond exactly. If any old range of generators will do, there's this:

http://xenharmonic.wikispaces.com/orwell13

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I was hoping you'd have some feedback on the planar temperaments in 12-equal
> stuff, but perhaps my epic rant was... A bit too epic.

Somehow the discussion of planar temperaments in 12edo eluded me. Perhaps it was the rant. What in the world is there to be said about it?

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> Why are you assuming that background? It wasn't clear in the original
> context. I'm not even sure if it's a background I share. I'd expect
> any audience to have some exposure to global pop music, which is
> influenced by western theory, but not to recognize dominant sevenths.
> I'd hope they've also been exposed to jazz or blues where sevenths are
> used without the dominant function.

Is there a better term for 7th chords with a minor 7th and a major 3rd? I thought "dominant 7th" was the most unambiguous way to refer to them, since that's the name I've ever seen them given (though in chord charts they're just written "7", as opposed to "m7" or "M7"). But I'm not using the term to exclusively refer to dominant functionality.

> Sometimes it's nice to play tricks with people who have a theoretical
> background. Comma pumps are good for this. My 60x60 submission was
> an example -- a magic comma pump spread over nearly a minute. The
> idea is that composers would get to hear it, and would try and work
> out what was going on. Unfortunately, it wasn't selected for
> "performance" so that fell through. Anyway, I've had some success,
> given:

I agree. Chord progressions in Blackwood and Porcupine do pleasantly weird things to my brain. Melodic comma pumps are fun, too, and there are some great ones in 11 and 13-EDO.

> Gene's music should be required listening for professors of music.
> Either they should explain what's going on harmonically, or justify
> why they keep drawing a salary as an expert in the field. We can
> dream, eh?

Indeed. Gene's music is probably the most "progressive" stuff ever written by a human being.

-Igs

> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > It's pretty hard to find a good tuning of 5-limit meantone that, when extended a bit beyond 7 notes, has excellent tunings of the 7-limit.
>
> On the contrary, it's so easy it was found by accident, in the form of 1/4 comma meantone.

*Groan* this is why posting first thing in the morning is a bad idea. I meant it's pretty hard to find a good 5-limit tuning that *doesn't* have good tunings of the 7-limit.

> I don't think the any-old-tuning-will-do approach produces anything much like actual 11 > or 13 limit harmonies, so to my ears that question is settled.

Huh? What does the "any-old-tuning-will-do" approach have to do with anything I said?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:

> Indeed. Gene's music is probably the most "progressive" stuff ever written by a human being.

Wow, Igs! I didn't think you even liked it much.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> *Groan* this is why posting first thing in the morning is a bad idea. I meant it's pretty hard to find a good 5-limit tuning that *doesn't* have good tunings of the 7-limit.

I wondered why you said that. 1/4-comma meantone is the 5-limit minimax tuning, but it just happens to be the 7 and 9 limit minimax tuning also, and as if that weren't enough, the minimax meanpop tuning. And all discovered by people who had never heard of minimax, much less meanpop. :)

> > I don't think the any-old-tuning-will-do approach produces anything much like actual 11 > or 13 limit harmonies, so to my ears that question is settled.
>
> Huh? What does the "any-old-tuning-will-do" approach have to do with anything I said?

If 11-limit intervals have no psychoacoustic validity, then any-old-tuning-will-do should work just as well for extensions to the 11-limit as accurate tuning.

On Apr 17, 2011, at 12:32 PM, "genewardsmith" <genewardsmith@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I was hoping you'd have some feedback on the planar temperaments in
12-equal
> stuff, but perhaps my epic rant was... A bit too epic.

Somehow the discussion of planar temperaments in 12edo eluded me. Perhaps it
was the rant. What in the world is there to be said about it?

If you're sticking to a meantone understructure, but you're enriching random
chords with 7's and such a la Gershwin, it might be better thought of as
that you're working within the 81/80 7-limit planar temperament. And if
you're dealing with b9's and #9's, which in 12-equal are pretty close to
ratios of 17 and 19, then you can think in even higher ranks, all with the
extensions being freely thrown in over a general meantone[7] skeleton (with
the extensions generally coming in over dominant 7 chords.

The blues takes an interesting approach in that the scale that it uses for
melody is not the same as the one it uses for chords. The 81/80 planar
approach also makes sense here, particularly with some jazz variants of the
blues. However, the scale that's used for melody is often a 5-6 note scale
which fits over each chord differently, often related to one or two modes of
meantone[5]. This could be a great way to use scales like myna[9], or
orwell[9], which don't produce rooted tetrads or triads - just use the scale
anyway and draw from outside the scale.

The two approaches are conflated in jazz, where proper scales are
retrofitted as melodic structures for extended harmonies - like the use of
diminished[8] for dom7b9#11nat13 chords or lydian dominant for C9#11. This
reconciles all of the following problems:

- use of easily cognizable scales for melody
- retention of a tonal understructure
- higher-limit implications
- avoidance of thinking directly in huge complex scales containing the full
gamut of pitches all at once

This has historically been our approach to higher-limit harmony in 12-equal
- not the "find MOS -> stick with that approach." The diatonic scale also
does all of these, but isn't as hip. Regular mapping can improve on all of
this.

Hopefully the MODMOS search will provide us with a scale as compact in
hipness as the diatonic scale. But if not, since we want hipness, we should
also consider the planar approach as outlined above, as well as systems
where melody and harmony don't come from the same scale. These are "natural"
behaviors and have to be worth something.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> If you're sticking to a meantone understructure, but you're enriching random
> chords with 7's and such a la Gershwin, it might be better thought of as
> that you're working within the 81/80 7-limit planar temperament. And if
> you're dealing with b9's and #9's, which in 12-equal are pretty close to
> ratios of 17 and 19, then you can think in even higher ranks, all with the
> extensions being freely thrown in over a general meantone[7] skeleton (with
> the extensions generally coming in over dominant 7 chords.

This sounds more like a recipe for detempering jazz than a method of composing new music.

> This could be a great way to use scales like myna[9], or
> orwell[9], which don't produce rooted tetrads or triads - just use the scale
> anyway and draw from outside the scale.

I'd call that the obvious approach.

> Hopefully the MODMOS search will provide us with a scale as compact in
> hipness as the diatonic scale.

A scale for what temperament? What did you think of my two 10-note miracle MODMOS?

On Apr 17, 2011, at 2:01 PM, "genewardsmith" <genewardsmith@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> If you're sticking to a meantone understructure, but you're enriching
random
> chords with 7's and such a la Gershwin, it might be better thought of as
> that you're working within the 81/80 7-limit planar temperament. And if
> you're dealing with b9's and #9's, which in 12-equal are pretty close to
> ratios of 17 and 19, then you can think in even higher ranks, all with the
> extensions being freely thrown in over a general meantone[7] skeleton
(with
> the extensions generally coming in over dominant 7 chords.

This sounds more like a recipe for detempering jazz than a method of
composing new music.

...why? What makes you think I want to detemper jazz? What does any of this
have to do with jazz? The point is that they stick loosely to meantone and
throw higher-limit extensions over the chords. They didn't just find another
MOS and stick with that. Even when they did find an interesting new MOS,
like the 19-limit interpretation of diminished[8], they would often use it
as a temporary stopping point in this larger planar+ structure I'm
suggesting, etc. They'd feel free to leave it, and suggests that if we're
working with something like 6 primes, a similar approach could be useful.

> This could be a great way to use scales like myna[9], or
> orwell[9], which don't produce rooted tetrads or triads - just use the
scale
> anyway and draw from outside the scale.

I'd call that the obvious approach.

Oh.

> Hopefully the MODMOS search will provide us with a scale as compact in
> hipness as the diatonic scale.

A scale for what temperament?

Any temperament. A 2.3.7.11 subgroup search would be hip. Some decatonic
2.3.7.11 scales could be incredibly hip.

What did you think of my two 10-note miracle MODMOS?

I can't listen now because I only have access to an iPhone.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Even when they did find an interesting new MOS,
> like the 19-limit interpretation of diminished[8], they would often use it
> as a temporary stopping point in this larger planar+ structure I'm
> suggesting, etc.

Who is "they"? Apparently all I know about "them" is that they have nothing to do with jazz.

> Any temperament. A 2.3.7.11 subgroup search would be hip. Some decatonic
> 2.3.7.11 scales could be incredibly hip.

So far as I know no one has even looked at the MOS for Radon, Skwares or Hemif yet, much less MODMOS. Radon and Skwares have an 11-note MOS, and Hemif in its incredible hipness a 10-note MOS. Of course, the 7 of Hemif may be too complex to suit you, but the 11 and 13 make up for it. Radon is pretty complex on the 11. Maybe Skwares is the best starting point for you, though Radon and Hemif would be obvious MODMOS candidates.

I wrote:
> Here are the ratios (view fixed-width font):
>
> 7/4 27/14 7/4
> 3/2 10/7 27/16 3/2 3/2
> 5/4 5/4 27/20 21/16 5/4
> 1/1 1/1 9/8 9/8 1/1
> 15/16
> 5/6

I've updated this a bit. Decide that ii rooted
on 10/9 is better for the JI version

(a)
7/4 40/21 7/4
3/2 10/7 3/2 3/2
5/4 5/4 4/3 21/16 5/4
1/1 1/1 10/9 9/8 1/1
15/16
5/6 5/6

That's with the minor 6th rooting for the utonal chords.
ii rooted on 9/8 works better with the half-dim7 rooting.

(b)
7/4 63/32 7/4
3/2 10/7 63/40 3/2 3/2
5/4 5/4 21/16 21/16 5/4
1/1 1/1 9/8 9/8 1/1
15/16
5/6

And so, updated links.

http://lumma.org/temp/cadence/Cadence7.seq
(a) version
In "dominant" temperament, tuned in 12-ET:
http://lumma.org/temp/cadence/Cadence7_12.mid
In JI, tuned in 99-ET:
http://lumma.org/temp/cadence/Cadence7_99.mid
(b) version
In "dominant" temperament, tuned in 12-ET:
http://lumma.org/temp/cadence/Cadence7b_12.mid
In JI, tuned in 99-ET:
http://lumma.org/temp/cadence/Cadence7b_99.mid

And for something slightly different, a hexany-based
progression rendered to mp3:
http://lumma.org/temp/cadence/HexanyProgression.mp3

Chow! -Carl

On Apr 17, 2011, at 2:40 PM, genewardsmith <genewardsmith@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Even when they did find an interesting new MOS,
> like the 19-limit interpretation of diminished[8], they would often use it
> as a temporary stopping point in this larger planar+ structure I'm
> suggesting, etc.

Who is "they"? Apparently all I know about "them" is that they have nothing
to do with jazz.

They do have something to do with jazz, but the bigger picture is that this
is what everyone at the time was doing. Jazz took a lot of its harmonic cues
from the music and standards of the time, and this is what people were
doing. Frank Sinatra's arrangements
would utilize techniques like this. It isn't really a niche "jazz"
stylistic offshoot or something like that. And it has less to do with
detempering than to identify rank 3 structures appearing in 12-tet, as are
there rank 1 structures appearing there.

> Any temperament. A 2.3.7.11 subgroup search would be hip. Some decatonic
> 2.3.7.11 scales could be incredibly hip.

So far as I know no one has even looked at the MOS for Radon, Skwares or
Hemif yet, much less MODMOS. Radon and Skwares have an 11-note MOS, and
Hemif in its incredible hipness a 10-note MOS. Of course, the 7 of Hemif may
be too complex to suit you, but the 11 and 13 make up for it. Radon is
pretty complex on the 11. Maybe Skwares is the best starting point for you,
though Radon and Hemif would be obvious MODMOS candidates.

Hemif might make for an interesting planar structure with 5 in it. One could
probably take some interesting cues from maqam music about how to work with
hemif. But how do you see people using hemif without 7? 8:9:11:12:13?

If you've thought of a lot of this before, it would be interesting to hear
your insights on how to use these scales.

-Mike

--- "cityoftheasleep" <igliashon@...> wrote:

> The first two chords sounded really cool, but I would be
> lying if I said the resolution felt finished. Sorry, it's not
> working for me. Is it working for you?

Yes!

> In this context I'm
> unquestionably hearing that I7 at the end as the dominant of
> the IV. Tell you what: tack on a 5-limit triad built on the
> IV after the I7 in your 7-limit progression and tell me how
> it feels.

Again, an entirely spurious objection. Tack a trine on the
end of the 5-limit version.

-Carl

--- "cityoftheasleep" <igliashon@...> wrote:
>
> Is there a better term for 7th chords with a minor 7th and
> a major 3rd?

LOL, no. Not when you ask that way!

> Unfortunately, it wasn't selected for
> "performance" so that fell through.

Not so unfortunate from my perspective. I think tape
performances are really lame. Unless you're all on
pillows on the floor in a dark room. And even then
it's borderline.

-Carl

> > Is there a better term for 7th chords with a minor 7th and
> > a major 3rd?
>
> LOL, no. Not when you ask that way!

By the way, I will *curse* you if you use this diatonic
lingo in your primer.

Have a good day :)

-Carl

Igs:
> > The first two chords sounded really cool, but I would be
> > lying if I said the resolution felt finished. Sorry, it's not
> > working for me. Is it working for you?
>
> Yes!

May I ask you to try the new versions I posted, and maybe
weigh in on the hexany progression (which is in some ways
a more natural one)? -Carl

Me:
> > Put another way: If a 996-cent 16/9 sounds more normal than a 7/4,
> > then either the Tenney Height model isn't right in general, or the
> > force of attraction of these traditional tones is stronger -- and
> > therefore even more relevant -- than the Tenney Height.

Gene:
> You are conflating sonance with functional harmony; apples, oranges.
> The 16/9 chord sticks the root of IV into V, and hence has a very
> strong effect of establishing tonality when V7 resolves to I. But
> that doesn't mean it sounds more consonant than an otonal tetrad,
> which it certainly does not.

Well, I was trying to relate back to what Michael said, which sounded like he was talking about how the dyad sounded, or possibly how it sounded when tacked onto a major chord. It didn't sound like he was specifically talking about how it worked in a chord progression.

What I think you're saying is that adding the 7 into a 4:5:6 chord to make 4:5:6:7 is an independent harmonic change, whereas sticking an F into a G chord in the key of C adds to the sense of tonal resolution in a V-I progression, regardless of whether you're in 12 equal or JI or something in between. If I have you right, then I accept that these are two different things. If Michael was talking about functional harmony, then my Tenney Height argument is irrelevant.

That leaves unresolved in my mind the question of whether people will hear the 7 in 4:5:6:7 as "close enough" to 1000 cents for it to function as a dominant 7th anyway -- even though it's obviously not simply an F. As Carl says, "Concordance will influence which chords are chosen for which roles in a functional style, but other things are involved too." So unless other arguments are brought to bear, the possibility still seems open that conditioning might lead people to hear the harmonic 7th (harmonically) as a dominant 7th (functionally), which seemed to be Igs's point. But that's just a possibility, not something I'm hanging my hat on.

Carl:
> The roots [of 12-tET] were historical, but that history is one of
> the development of a style of 5-limit harmony. It's the story of
> the journey from meantone temperament, which tempers out 81/80
> only, to 12-ET, which additionally tempers out 128/125 and
> 648/625. This was understood by theorists here and there, but
> mostly it happened organically. Only in the last several decades
> have theorists put it all together and made predictions about
> alternative ways the history might have gone -- tuning forks in
> the road, as it were.

But that's part of my point: It happened organically, such that piano tuners were trained to tune a fifth perfectly and then make it flat "just a little bit, about two beats per second, to avoid getting a wolf fifth" or some such stuff. That's a human and practical method, not a prime-limit-related one. It can be described with prime limits and commas, and some people even knew the math involved, and it led to great 3-limit and acceptable 5-limit harmony -- but it sure doesn't look like they were focused on getting 19-limit harmony. So, even though we *can* retrofit 19-limit harmony onto it, why *should* we? For historical purposes, I just don't see why that would be relevant. When talking about current conditioning, I'm also not sure why it would make sense to talk about prime limits, when that's not the way most people use the scale.

On the other hand, it's reasonable to talk about it for 19-limit harmony *now*, for new compositions. Now we can approach the scale as 12-EDO rather than as 12-tET, and use it just as we would any other EDO.

Me:
> > When I pick a non-12 piece -- whether it's common-practice
> > music from before the dominance of 12 EDO or one of my own
> > attempts at composing outside of 12 EDO -- and render it
> > with 12 EDO, it never sounds out of tune. Ugly, boring,
> > inelegant, sure, but not "out of tune".

Carl:
> Hm. To me, this
> http://www.youtube.com/watch?v=FHjitZIyaRc
>
> sounds like an out of tune version of this
> http://www.youtube.com/watch?v=EHExcd6PYxQ
>
> And I can't hear it any other way.

That's interesting. The meantone version sounds a little richer, maybe, but the 12-tET version doesn't sound out of tune. How can the 12-tET version be "in tune" and the meantone one be "more in tune"? But that's the way I hear it.

That said, my ear is no doubt a lot less well-trained than yours.

It's a very nice piece, by the way, and one that I've never heard before. Thanks for the links.

Regards,
Jake

On 17 April 2011 18:49, genewardsmith <genewardsmith@...> wrote:

> Could you define "Blair"? Actually, I'd be interested in whatever names you've concocted.

Blair is the 13-limit Orwell extension that isn't mainstream Orwell or
Winston. 13 is mapped to 3 generators.

http://x31eq.com/cgi-bin/rt.cgi?ets=9+22&limit=13

I also have it in the 2.3.5.11.13 subgroup.

I like the idea of the database of names to be like an Easter egg
hunt, where you find new names cropping up. But, a spirit of full
disclosure, here's a run-down on what I've added since about 2008, and
that could plausibly be called temperaments.

Not all links are tested. If the wrong thing comes up, tell me.

Marvel is extended to the 13-limit (I think you picked up on that
because there's no longer a collision with the wiki) and reduced to
the 7-limit (I must have originally picked it up in the 11-limit
only). There's also a simpler 13-limit extension called "Tripod" that
tempers out 144:143, and so makes the neutral seconds of the tripod
scale approximate both 12:11 and 13:12. Other Marvel extensions may
be notable but aren't named.

http://x31eq.com/cgi-bin/rt.cgi?ets=72_31_53&limit=13

http://x31eq.com/cgi-bin/rt.cgi?ets=19p_31_41&limit=13

Prodigy, Thrush, Minerva, and Athena are extended to the 13-limit.

History is a mixture of Harry and Mystery. In 7, 11, 13-limits

http://x31eq.com/cgi-bin/rt.cgi?ets=15_58_72&limit=13

There's something called "breed" which is the only name not
capitalized for some reason.

Big Brother is a planar Orwell variant.

http://x31eq.com/cgi-bin/rt.cgi?ets=9_31_8d&limit=11

Guanyin I think you've seen. It extends into the 13-limit as both
Guanyin and Avalokitesvara, these being different names for
essentially the same deity. Which is which is arbitrary in that I had
a devious, logical scheme for differentiating them, and applied it
wrongly.

http://x31eq.com/cgi-bin/rt.cgi?ets=53_31_58&limit=13

http://x31eq.com/cgi-bin/rt.cgi?ets=27e_31_9&limit=13

Siegfried wins out over Odin for very low errors.

Starling, Hemifamity, Gamelan, Orwellian, Rasmic, and Landscape are
all in there. Either they came from you or they're related to yours.
They look like 7-limit planar.

Spectacle looks like 11-limit planar.

Hades is in the 11-limit, originating from this list. It's also in
the 7-limit and 13-limit.

http://x31eq.com/cgi-bin/rt.cgi?ets=152f_72_58&limit=13

Vicentino is the 5-limit contorted meantone with the same pattern as Mohajira.

Semaphore and Injera look like 5-limit reductions. Slendric,
Dominant, Semaphore, Beatles, Hemififths, Miracle, Pajara, Vulture,
Liese, Squares, Stones are added to the 2.3.7-limit. Oh, Stones is
mine, isn't it? It's related to Beatles. Semaphore, Hemififths,
Miracle 2.3.7.11-limit. Magic, Meanpop, Sensisept, Catakleismic,
Winston 2.3.5.7.13-limit. Blair, Orwell, Winston 2.3.5.11.13-limit.

Rodan added to higher limits. Mohajira added to a load of different
limits. Darjeeling is something I had a long time ago as Keemun, but
it contradicts what the wiki calls Keemun in this limit.

Incidentally, the wiki is (or was) inconsistent over "Unidec" and "Hendec".

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> By the way, I will *curse* you if you use this diatonic
> lingo in your primer.

I'm sure as hell not using ratios. Currently I'm using a system of 48 diatonic-related subclasses (like subminor, supermajor, neutral, etc. as well as terms like "third-fourth" and "tritone-fourth" to apply to quarter-tone/maximal-entropy intervals that straddle classes). This is how I learned microtonal intervals, this is how a lot of people even in this community talk about them, and since I'm writing for people who are straight out of 12-TET, I think this way conveys a lot of easily-intelligible qualitative information about what the intervals sound like (if not how they function). There's no universal way to classify intervals, and ratios are often ambiguous or irrelevant in EDOs. If you've got a better idea, I'm all ears, but currently this is the best I've got, and I'm going with it.

-Igs

On 17 April 2011 19:02, genewardsmith <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
>> The last two chords in the fragment I linked to make what sounds to me
>> to be a strong, natural, resolved progression.
>
> Could you give the link again? I don't recall seeing a link.

I think it was

http://x31eq.com/music/dingfei.ogg

http://x31eq.com/music/dingfei.pdf

I am working on it again, so it may be improved at the weekend.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "cityoftheasleep" <igliashon@> wrote:
>
> > The first two chords sounded really cool, but I would be
> > lying if I said the resolution felt finished. Sorry, it's not
> > working for me. Is it working for you?
>
> Yes!

Then I must be an outlier.

> > In this context I'm
> > unquestionably hearing that I7 at the end as the dominant of
> > the IV. Tell you what: tack on a 5-limit triad built on the
> > IV after the I7 in your 7-limit progression and tell me how
> > it feels.
>
> Again, an entirely spurious objection. Tack a trine on the
> end of the 5-limit version.

Tried it, and nope. I'm well-conditioned to accept the 5-limit triad as a final resting place.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > Indeed. Gene's music is probably the most "progressive" stuff ever written by a human
> being.
>
> Wow, Igs! I didn't think you even liked it much.
>

"Like" and "appreciate" are different things for me. It's on the level of Ferneyhough for me--something that's beyond my ken, sort of outside of any aesthetic judgment I might have due to its herculean complexity. Clearly you know what you're doing with these scales, on a level that is far beyond what I am capable of understanding. I kind of *have to* appreciate that.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> If 11-limit intervals have no psychoacoustic validity, then any-old-tuning-will-do should > work just as well for extensions to the 11-limit as accurate tuning.

You should take this up with Carl. He's the one who convinced me that most ratios of 11 don't exist perceptually as dyads (except maybe low Tenney Height ones like 11/6, 11/5, 11/4, and 11/3), and only really come into being when incorporated into larger otonal chords. Honestly, I'm agnostic about it, because I don't really like the sound of most 11-limit intervals in harmony except as dissonances, in which case they can tolerate plenty of mistuning (since they're supposed to sound painful, being dissonances and all).

-Igs

On 17 April 2011 20:12, cityoftheasleep <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>> 2.5/3.7/3, however, is a 7-limit subgroup, the same as the 5-limit is.
>>  The question is analogous to whether you'd put 5-limit meantone in
>> the same group as 7-limit meantone.
>
> Is it?  It seems to me that 23-EDO is a more than acceptable tuning of the former (2.5/3.7/3) but a horrendous tuning of the 7-limit.  Is that insignificant?

It's significant, but I gave 26-EDO as a meantone example. It's a
5-limit meantone but not a 7-limit meantone. If it works backwards,
and the optimal 7-limit tuning work for the subgroup, I'm happy.

>> I think Gene's remark holds.  Meantone would still be meantone, but
>> how you thought of it would be different.  This is an important point.
>
> I don't think looking at 5-limit meantone vs 7-limit meantone is necessarily a good analogy.  It's pretty hard to find a good tuning of 5-limit meantone that, when extended a bit beyond 7 notes, [doesn't have] excellent tunings of the 7-limit.  In the case of 23-EDO as "Myna", it's a good tuning of the subgroup that never reaches a good tuning of the full 7-limit.

There's 26-EDO.

I'm not that familiar with Myna so I don't know how characteristic
23-EDO would be. I assume it's at one end of a range of acceptable
tunings that also cover the usual Myna range. I'll guess that if you
wrote something in 23-EDO, and only observed the Myna approximations,
it would still work in a more mainstream 7-limit Myna tuning. In that
case, you were getting experience with Myna. If you depended on other
approximations, you were using 23-EDO, not Myna.

> The question that Paul always put to me was whether rationalized intervals had psychoacoustic justifications.  I'm agnostic about whether a naked 11-limit ratio has any psychoacoustic identity, but possibly Paul (and definitely Carl) seemed pretty convinced that they don't.  So the question of whether or not Magic "works" in the 11-limit is a question of whether it produces 11-limit harmonies that are psychoacoustically valid.

Yes, this is another question I have little interest in. For me,
Magic works in the 11-limit because in the example you have I used
11-limit otonalities, according to the theoretical mapping, and they
sound smoother than random dissonances. If you don't think it works,
that barely affects your tuning or scale choice, but may lead you to
different chords. Maybe the 11-limit otonalities sound smooth for
reasons unrelated to them being 11-limit otonalities. I don't care.
Naked 11-limit approximations will sound like what they sound like.

>> Orwell was first noted (that I'm aware of) in the 11-limit.  You may
>> approach it as a 7-limit temperament, but note that the dissonances
>> have 11-limit rationalizations.  You're bound to hit those dissonances
>> because they're some of the simplest intervals.  You may treat it as a
>> small scale with incomplete 11-limit harmony from the start.  Or you
>> may treat it as a system for allowing puns in full 11-limit harmony
>> without looking at scales.  You can even start with 13-limit subgroups
>> (that may entail the variant I've called "Blair") as you suggested to
>> me once.  Whatever you do, it's still orwell, but how you think of it
>> will be different.
>
> But what "makes it" Orwell?  Commas?  Again, in the case of Orwell, if you treat it as a 2.7/6.11/8 subgroup, then 13-EDO is an Orwell temperament, while if you treat it as a 7-limit temperament, 13-EDO is NOT an Orwell temperament.  Paul has been insistent about the latter for years now, and if you think 13-EDO is an Orwell temperament, you might try taking it up with him.

Paul hasn't been talking to me for years now, so I don't know what his
views are. Going by the Middle Path paper, his concept of
"temperament" is closer to my concept of "temperament" than
"temperament class" but there have been violent disagreements about
this. I'd say "an Orwell temperament" means "a member of the Orwell
temperament class". Any subgroup would count as Orwell to me. 13-EDO
would not be a 7-limit Orwell but may be a subgroup Orwell. If the
tunings are clearly different they're different temperaments.

You'd probably want to define 13-EDO in a 13-limit subgroup, in which
case it would probably be Winston or Blair, in which case the same
name would likely cascade to the 11-limit subgroup, but that wouldn't
stop it being Orwell as well. Certain properties, like the mapping of
some chords and the pattern of large/small steps, will be consistent,
and you should have a way of saying so.

> And yet, it comes down to psychoacoustic considerations to tell us where one temperament ends and another begins.  What's the difference between Dimisept and Dimipent, or Negrisept and Negripent?  They're treated as different temperaments while Meantone[5-limit] and Meantone[7-limit], you seem to be saying, are not.  Or if they are different temperaments, then your earlier analogy is invalid.

The "sept"/"pent" distinction was according to a rule I never agreed
with. I think it was that the TOP tunings had to be the same for the
name to be the same. Gene ignores it. I don't care much either way
for established names, but I may have to keep "Sensisept" because it
exists in a higher limit. I can see the rule makes some sense if
we're talking about temperaments, as I understand them. The existence
of the rule may indicate Paul was understanding temperaments a similar
way. But as I understand temperament classes (which is similar to how
others understand regular temperaments) the tuning is allowed to vary
over a wide range. There are subjective rules I follow when I share
names over different limits and we can talk about individual cases if
you like. I don't have a fixed definition, or deterministic
algorithm, for deciding if two things in different limits are the
same, and I don't want one.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> It's significant, but I gave 26-EDO as a meantone example. It's a
> 5-limit meantone but not a 7-limit meantone. If it works backwards,
> and the optimal 7-limit tuning work for the subgroup, I'm happy.

So...does that mean we shouldn't be naming subgroups then, since all subgroup temperaments will of course work in a full n-limit temperament, where n is the highest prime in the subgroup?

> There's 26-EDO.

Which is not a "good" tuning for Meantone by any stretch of the imagination.

> I'm not that familiar with Myna so I don't know how characteristic
> 23-EDO would be. I assume it's at one end of a range of acceptable
> tunings that also cover the usual Myna range. I'll guess that if you
> wrote something in 23-EDO, and only observed the Myna approximations,
> it would still work in a more mainstream 7-limit Myna tuning. In that
> case, you were getting experience with Myna. If you depended on other
> approximations, you were using 23-EDO, not Myna.

To me, to say two tunings are both the same temperament (or temperament class if you prefer) implies that we should be able to translate freely between them in either direction without damaging the harmonies beyond reason. Yes, we could translate 2.5/3.7/3 harmonies from 23-EDO into a better Myna tuning like 27-EDO and back again, but we can't do the same for the full 7-limit without damaging the harmonies beyond reasonable psychoacoustic bounds. Why call two things that are clearly different by the same name?

> Yes, this is another question I have little interest in. For me,
> Magic works in the 11-limit because in the example you have I used
> 11-limit otonalities, according to the theoretical mapping, and they
> sound smoother than random dissonances. If you don't think it works,
> that barely affects your tuning or scale choice, but may lead you to
> different chords. Maybe the 11-limit otonalities sound smooth for
> reasons unrelated to them being 11-limit otonalities. I don't care.
> Naked 11-limit approximations will sound like what they sound like.

Well I'm really just regurgitating objections I've heard from Paul and Carl. I'm agnostic about the psychoacoustic validity of the 11-limit. But in any case, I might ask what the point of limiting a temperament to a particular prime is, since we can undoubtedly find a generator for every temperament that eventually leads to an approximation of any arbitrary prime.

> Paul hasn't been talking to me for years now, so I don't know what his
> views are. Going by the Middle Path paper, his concept of
> "temperament" is closer to my concept of "temperament" than
> "temperament class" but there have been violent disagreements about
> this. I'd say "an Orwell temperament" means "a member of the Orwell
> temperament class". Any subgroup would count as Orwell to me. 13-EDO
> would not be a 7-limit Orwell but may be a subgroup Orwell. If the
> tunings are clearly different they're different temperaments.

Interesting. So it seems like consensus on this stuff wasn't reached?

> You'd probably want to define 13-EDO in a 13-limit subgroup, in which
> case it would probably be Winston or Blair, in which case the same
> name would likely cascade to the 11-limit subgroup, but that wouldn't
> stop it being Orwell as well. Certain properties, like the mapping of
> some chords and the pattern of large/small steps, will be consistent,
> and you should have a way of saying so.

That was more or less my argument to Paul as to why I though 13-EDO should be considered an Orwell temperament. His disagreement amounted to insisting that anything you can do in one Orwell temperament you should be able to do in another, at least insofar as the 11-limit is concerned. Since you can do things in 31-EDO and 22-EDO that you can't do in 13, like play 4:5:6:7:9:11 hexads that actually sound like 4:5:6:7:9:11 hexads, 13 is not an Orwell temperament. I'm not saying I agree, but that was his argument.

> But as I understand temperament classes (which is similar to how
> others understand regular temperaments) the tuning is allowed to vary
> over a wide range.

Paul insists that the range of a temperament, if it is to be defined, should be defined psychoacoustically, i.e. the boundaries will be wherever the tuning stops producing intervals that sound reasonably like what the mapping says they should sound like. In that case, 13-EDO and 23-EDO both lack intervals that sound reasonably like 7/1 or 3/1, so the Orwell and Myna mappings (respectively) when applied to those tunings are out of bounds. But you are saying that as long as some of the intervals retain their character--13-EDO still retains a good 7/3 and 11/1, 23-EDO still retains a good 5/3 and 7/3--then the temperament still applies. This contradicts Paul's view.

> There are subjective rules I follow when I share
> names over different limits and we can talk about individual cases if
> you like. I don't have a fixed definition, or deterministic
> algorithm, for deciding if two things in different limits are the
> same, and I don't want one.

I would've hoped for a more rigorous approach in establishing conventions, but given that my interest in this sort of thing is academic at best, I can't really complain. If it's working for you, more power to you.

-Igs

Jake>"Well, I was trying to relate back to what Michael said, which sounded

like he was talking about how the dyad sounded, or possibly how it

sounded when tacked onto a major chord. It didn't sound like he was

specifically talking about how it worked in a chord progression."

   Correct, I'm not talking about functional harmony or any outside context other than the dyad itself (and nothing else).

>"That's interesting. The meantone version sounds a little richer, maybe, but the 12-tET version doesn't sound out of tune. How can the 12-tET version be "in tune" and the meantone one be "more in tune"? But that's the way I hear it."

  Pardon my "over-simplification"...but I think most of this can be translated back to simple dyadic analysis.  Meantone (assuming 1/4 comma) has its point of near-perfection in maximizing the accuracy of just dyads...but where 12EDO goes off seems to be the areas with the most tolerance for error...making it "still fairly in tune".

  However, meanwhile, the notes 12EDO gets off (error wise) most are ones like a sharp major third where major third has large tonal gravity to start with and clearly to my ears tolerates error sharp more than flat.  Same goes for its very sharp 5/3 sixth...which just happens to double as making it more in-tune Pythagorean-wise as 27/16 is a perfect fifth from 9/8...which goes back to the "flatten 5ths to avoid wolfs" mantra Jake mentioned.  And as for the 16/9...is seems to be in a convenient range where it can act as a 7/4 or 16/9 without much struggle...the mood between those two seems quite similar.  Same goes for 12EDO's sharp major 7th...which sounds much closer in mood to 15/8 than you would think.  I don't quite just believe this is "cultural conditioning" but, on a greater level, evidence that certain dyadic ranges are more flexible error-wise than others and 12EDO just happens to take advantage of many of these flexible area.
 
   
Big looming question: do you know any tuning that does better so far as strong dyads per note as 12EDO does across all roots?  It seems obvious to me, no matter how much people hate less-than-triadic theories...that the one clear metric of efficiency for 12EDO is dyads.

On 18 April 2011 11:03, cityoftheasleep <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
>> It's significant, but I gave 26-EDO as a meantone example.  It's a
>> 5-limit meantone but not a 7-limit meantone.  If it works backwards,
>> and the optimal 7-limit tuning work for the subgroup, I'm happy.
>
> So...does that mean we shouldn't be naming subgroups then, since all subgroup temperaments will of course work in a full n-limit temperament, where n is the highest prime in the subgroup?

I'm not giving original names in subgroups. Other people are, and I
allow them to filter through from the wiki.

>> There's 26-EDO.
>
> Which is not a "good" tuning for Meantone by any stretch of the imagination.

But it is a meantone.

> To me, to say two tunings are both the same temperament (or temperament class if you prefer) implies that we should be able to translate freely between them in either direction without damaging the harmonies beyond reason.  Yes, we could translate 2.5/3.7/3 harmonies from 23-EDO into a better Myna tuning like 27-EDO and back again, but we can't do the same for the full 7-limit without damaging the harmonies beyond reasonable psychoacoustic bounds.  Why call two things that are clearly different by the same name?

We're already sharing names for different limits. Meantone is well
established in the 5- and 7-limits. There's also an 11-limit
Meantone, and I don't know where it came from, but it's been there for
a long time. If Myna's qualitatively different in this subgroup,
maybe it can have a different name. I though you originally said it
was the same.

Complexity is a consideration you can bring up. If the simplest
harmonies don't get damaged they're looking like the same thing. But
the more complex harmonies will also likely be the most sensitive to
mistuning. Focusing on the simplest harmonies contradicts the tuning
ranges.

>> Paul hasn't been talking to me for years now, so I don't know what his
>> views are.  Going by the Middle Path paper, his concept of
>> "temperament" is closer to my concept of "temperament" than
>> "temperament class" but there have been violent disagreements about
>> this.  I'd say "an Orwell temperament" means "a member of the Orwell
>> temperament class".  Any subgroup would count as Orwell to me.  13-EDO
>> would not be a 7-limit Orwell but may be a subgroup Orwell.  If the
>> tunings are clearly different they're different temperaments.
>
> Interesting.  So it seems like consensus on this stuff wasn't reached?

I consensus is reached not when everybody agrees, but when everybody
can stomach their objections. I thought we had a consensus on the
names in the Middle Path paper. That's different to a consensus on
the rules for choosing them.

>> You'd probably want to define 13-EDO in a 13-limit subgroup, in which
>> case it would probably be Winston or Blair, in which case the same
>> name would likely cascade to the 11-limit subgroup, but that wouldn't
>> stop it being Orwell as well.  Certain properties, like the mapping of
>> some chords and the pattern of large/small steps, will be consistent,
>> and you should have a way of saying so.
>
> That was more or less my argument to Paul as to why I though 13-EDO should be considered an Orwell temperament.  His disagreement amounted to insisting that anything you can do in one Orwell temperament you should be able to do in another, at least insofar as the 11-limit is concerned.  Since you can do things in 31-EDO and 22-EDO that you can't do in 13, like play 4:5:6:7:9:11 hexads that actually sound like 4:5:6:7:9:11 hexads, 13 is not an Orwell temperament.  I'm not saying I agree, but that was his argument.

In so far as the 11-limit is concerned, what you have is 11-limit
Orwell. An 11-limit subgroup temperament wouldn't be 11-limit Orwell.
Paul was happy with a 7-limit temperament being Orwell, but not the
5-limit.

> Paul insists that the range of a temperament, if it is to be defined, should be defined psychoacoustically, i.e. the boundaries will be wherever the tuning stops producing intervals that sound reasonably like what the mapping says they should sound like.  In that case, 13-EDO and 23-EDO both lack intervals that sound reasonably like 7/1 or 3/1, so the Orwell and Myna mappings (respectively) when applied to those tunings are out of bounds.  But you are saying that as long as some of the intervals retain their character--13-EDO still retains a good 7/3 and 11/1, 23-EDO still retains a good 5/3 and 7/3--then the temperament still applies.  This contradicts Paul's view.

That's immediately a problem in that we don't know or agree on where
the boundaries should be drawn. But, even being liberal, will the
boundaries ever be identical in different limits? Does anybody think
they are for 5- and 7-limit meantones? I'd expect the boundaries to
be narrower in higher limits.

I'm suggesting that only the intervals (or suitably simple intervals
for open-ended limits) in the subgroup you're explicitly looking at
should retain their character. If you were thinking of other
intervals you should have defined the subgroup accordingly.

> I would've hoped for a more rigorous approach in establishing conventions, but given that my interest in this sort of thing is academic at best, I can't really complain.  If it's working for you, more power to you.

A rigorous approach gave us Pontiac over Garibaldi as the Schismatic
extension. I don't know who's using Pontiac. I thought it was too
complex to worry about. Of course, we disagreed on that. But any
strict rule is bound to give cases you disagree with. I'd rather
choose the names that seem to make sense. If history proves me wrong,
that's not such a big deal.

Also, there are cases where a higher-limit name is already taken.
Like I decided a certain 13-limit planar temperament should be called
"Tripod" because it fit with tripod notation. That left a certain
other extension as the default Marvel (unless somebody else had
already made that decision). If the rigorous approach had told us
that Tripod should have been a synonym for Marvel, what would have
been the point? We'd have one more name to think of for Marvel
extensions.

My interest now is mostly in having some friendly names coming out of
the searches instead of lists of numbers (now with warts). As the
same list of numbers is given on the right anyway, new names can't be
worse than useless. Using a familiar name in an unfamiliar limit can
be useful. If you see a list of temperaments in an unfamiliar
subgroup, but some of them have names you're familiar with in the full
prime-limit, that should give you a good idea of what those
temperaments are going to behave like. You can still check the
tunings.

I'd also like to check the explosion of names. My database (stored as
a Python dictionary) can handle a large number of mappings. As a
human being I find it confusing to deal with a lot of different names.
We already have well over 300 and going through all the subgroups
could potentially give us thousands. I try to be as unoriginal as
possible, like with legal precedent.

Graham

Igs>"Tried it, and nope. I'm well-conditioned to accept the 5-limit triad as a final resting place."

    Ever come to think that we've come to accept 9-odd-limit as more resolved than 7 odd limit?

Try the chord 9:12:16....and compare to 5:6:7......

Gene>"You should take this up with Carl. He's the one who convinced me that
most ratios of 11 don't exist perceptually as dyads (except maybe low
Tenney Height ones like 11/6, 11/5, 11/4, and 11/3)"

At the very least, I'd suggest adding 11/7 and 11/9 to that mix of intervals: 11/7 in particular sounds more resolved to me in many ways than 8/5.

  But agreed...anything about that (think 15/11 or its inverse if 22/15, or 18/11) is going to sound quite off center unless it is heard in the context of a larger chord IE 11:16:18 or 15:18:22.  Then the trick becomes to use 11-limit as a way to build large chords...which often causes the "neutral" 11-limit intervals to swap identities (major/minor/suspended/diminished/etc.)...making for many more compositional options without any sort of largely noticeable addition of "out of control dissonance".

On Mon, Apr 18, 2011 at 9:37 AM, Michael <djtrancendance@...> wrote:
>
> Igs>"Tried it, and nope. I'm well-conditioned to accept the 5-limit triad as a final resting place."
>
>     Ever come to think that we've come to accept 9-odd-limit as more resolved than 7 odd limit?
>
> Try the chord 9:12:16....and compare to 5:6:7......

I hear 5:6:7 as sounding more resolved, but 9:12:16 has a more restful
quality to it.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> (b) version
> In "dominant" temperament, tuned in 12-ET:
> http://lumma.org/temp/cadence/Cadence7b_12.mid
> In JI, tuned in 99-ET:
> http://lumma.org/temp/cadence/Cadence7b_99.mid
>
> And for something slightly different, a hexany-based
> progression rendered to mp3:
> http://lumma.org/temp/cadence/HexanyProgression.mp3

Okay, you win. I don't know why the (b) version works for me and the (a) version doesn't, but it does. Well, the JI version anyway. The 12-ET doesn't. Also the hexany version works great, probably the best so far, but that doesn't at all surprise me as it's quite a radoical recontextualization of that chord (and most of the sonorities sound pretty nasty to me...I'd never have known it was JI if you hadn't mentioned the hexany).

-Igs

>"I hear 5:6:7 as sounding more resolved, but 9:12:16 has a more restful

quality to it."

So "resolved" is not "restful"?  As if the confusion/debate between concordance vs. consonance vs. tonality vs. resolvedness...is not confusing enough already.  Can't we just figure out one mutually-agreed upon terms that has the ultimately meaning "can easily be used as a resting point in music"?

--- On Mon, 4/18/11, Mike Battaglia <battaglia01@gmail.com> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Is 9-odd-limit, bizarrely enough, heard as more resolved than 7-limit?
To: tuning@yahoogroups.com
Date: Monday, April 18, 2011, 9:05 AM

On Mon, Apr 18, 2011 at 9:37 AM, Michael <djtrancendance@...> wrote:

>

> Igs>"Tried it, and nope. I'm well-conditioned to accept the 5-limit triad as a final resting place."

>

>     Ever come to think that we've come to accept 9-odd-limit as more resolved than 7 odd limit?

>

> Try the chord 9:12:16....and compare to 5:6:7......

I hear 5:6:7 as sounding more resolved, but 9:12:16 has a more restful

quality to it.

-Mike

On Mon, Apr 18, 2011 at 12:39 PM, Michael <djtrancendance@...> wrote:
>
> >"I hear 5:6:7 as sounding more resolved, but 9:12:16 has a more restful
> quality to it."
>
> So "resolved" is not "restful"?  As if the confusion/debate between concordance vs. consonance vs. tonality vs. resolvedness...is not confusing enough already.  Can't we just figure out one mutually-agreed upon terms that has the ultimately meaning "can easily be used as a resting point in music"?

You can use either of them as a resting point in music.

-Mike

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> Try the chord 9:12:16....and compare to 5:6:7......
>

Try just going up the series, too: try 5:6:7, 6:7:8, 7:8:9, 8:9:10, 9:10:11. Then try the chords that are the mediants between them: 11:13:15, 13:15:17, 15:17:19, and 17:19:21.

I tend to find 15:17:19 and 17:19:21 feel very similar to 7:8:9 and 8:9:10 despite being radically less blended.

It's a jungle in there, really. Who knows what will work and what won't? I was dead-convinced that I'd never be able to hear 4:5:6:7 as the final resting place in a progression, but Carl's example made me eat my words. I've reached the point where I really have to just give up on the theory and follow my ears, because if I wait for theory to pave the way, I'll never get any music made.

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> So "resolved" is not "restful"?  As if the confusion/debate between concordance vs.
> consonance vs. tonality vs. resolvedness...is not confusing enough already.  Can't we
> just figure out one mutually-agreed upon terms that has the ultimately meaning "can
> easily be used as a resting point in music"?

Of course it's confusing. No one has it figured out, we have lots of little pieces but no map of the big picture yet. There's not going to be any way to "settle" these "debates" except with music. I was blathering on and on about the inescapability of 12-TET associations when hearing 4:5:6:7 chords and then Carl played me a simple 4-chord progression that shut me right up. That's usually how it goes...a "theorist" says "this won't work" and then a musician says "oh yeah?" and demonstrates that it does work, and then it's back to the drawing board. Of course, I'm not usually the "theorist" in this equation. But anyway I don't see why we need to settle the debate at all. It's not like we don't have plenty ideas that are worth exploring already. The music should come first, and then we can find theories to explain it.

-Igs

Igs,

With all due respect, ears write the theory not the other way around. I
believe it has always been like that. Music theory is for the most part
after the fact retrospective analysis.

What I plan to do is to start analyzing what works for my ears - and try to
get rid of the 12 edo hang over stuff, that is the chaff, and find some
wheat in progression not possible in 12 edo.

Chris

On Mon, Apr 18, 2011 at 1:05 PM, cityoftheasleep <igliashon@...>wrote:

> I've reached the point where I really have to just give up on the theory
> and follow my ears, because if I wait for theory to pave the way, I'll never
> get any music made.
>
> -Igs
>
>
>
>

On Mon, Apr 18, 2011 at 1:05 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> > Try the chord 9:12:16....and compare to 5:6:7......
> >
>
> Try just going up the series, too: try 5:6:7, 6:7:8, 7:8:9, 8:9:10, 9:10:11. Then try the chords that are the mediants between them: 11:13:15, 13:15:17, 15:17:19, and 17:19:21.
>
> I tend to find 15:17:19 and 17:19:21 feel very similar to 7:8:9 and 8:9:10 despite being radically less blended.

This is yet another instance in which "periodicity" buzz doesn't have
anything to do with harmonic entropy. 15:17:19 and 17:19:21 "feel"
similar to 7:8:9 and 8:9:10 because they get sucked into the fields of
attraction for those chords. But, they don't "blend" as well because
the partials align differently. You might also find that
15:17:19:21:23 feels similar to either 8:9:10:11:12 or 7:8:9:10:11,
depending on your mood. And you might also find that 17:19:21:23:25
feels the same way, except now it's either 8:9:10:11:12 or
9:10:11:12:13.

The "feeling" or "quality" generally has to do with periodicity (HE,
if it sounds "rooted" or not, all that), but how well it "blends" as
you said has more to do with partials beating in sync/notes beating in
sync in general/periodicity buzz. As we discussed offlist, neither of
these things should stop you from learning to distinguish any of these
chords from one another.

-Mike

As a last note, as you'd expect from the size of the "fifth," 13-equal
approximates some of these chords pretty decently. Try 3 3 2 2 2 for
17:20:23:26:29:32, and try 3 3 2 for 17:20:23. Or also try

13:17:20:23 -> 13:18:20:23 -> 13:17:20:23 -> 13:16:20:23 ->
13:17:20:23 -> 13:18:20:23 -> 13:17:20:23

If you've played around in 13-equal a lot, that should sound really
familiar, except the whole thing will beat in sync beautifully with
itself. Congratulations, you now have a beautiful, adaptive-RI version
of father temperament. Exploring stuff like this could be a good way
to attenuate some of the "puke" feeling, as people are fond of calling
it, for high-error temperaments like father.

TL;DR, finding some sweet microtemperaments in subgroups built around
chords like the above would be awesome. Then they'd still have the
father "feel" to them, but everything would connect in a completely
different way, and you could also have crazy sync-beating like with
the above as well.

-Mike

On Mon, Apr 18, 2011 at 1:49 PM, Mike Battaglia <battaglia01@...> wrote:
> And 17:20:23:26 should also sound like 6:7:8:9 with a father-sized
> fifth, and also blend differently. Try 17:20:23:26:29 or
> 17:20:23:26:29:35 for extra mojo. 17:20:23:26:29:32:35 may be the
> winner.
>
> -Mike

And 17:20:23:26 should also sound like 6:7:8:9 with a father-sized
fifth, and also blend differently. Try 17:20:23:26:29 or
17:20:23:26:29:35 for extra mojo. 17:20:23:26:29:32:35 may be the
winner.

-Mike

On Mon, Apr 18, 2011 at 1:44 PM, Mike Battaglia <battaglia01@...> wrote:
> On Mon, Apr 18, 2011 at 1:05 PM, cityoftheasleep
> <igliashon@...> wrote:
>>
>> --- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>> > Try the chord 9:12:16....and compare to 5:6:7......
>> >
>>
>> Try just going up the series, too: try 5:6:7, 6:7:8, 7:8:9, 8:9:10, 9:10:11. Then try the chords that are the mediants between them: 11:13:15, 13:15:17, 15:17:19, and 17:19:21.
>>
>> I tend to find 15:17:19 and 17:19:21 feel very similar to 7:8:9 and 8:9:10 despite being radically less blended.
>
> This is yet another instance in which "periodicity" buzz doesn't have
> anything to do with harmonic entropy. 15:17:19 and 17:19:21 "feel"
> similar to 7:8:9 and 8:9:10 because they get sucked into the fields of
> attraction for those chords. But, they don't "blend" as well because
> the partials align differently. You might also find that
> 15:17:19:21:23 feels similar to either 8:9:10:11:12 or 7:8:9:10:11,
> depending on your mood. And you might also find that 17:19:21:23:25
> feels the same way, except now it's either 8:9:10:11:12 or
> 9:10:11:12:13.
>
> The "feeling" or "quality" generally has to do with periodicity (HE,
> if it sounds "rooted" or not, all that), but how well it "blends" as
> you said has more to do with partials beating in sync/notes beating in
> sync in general/periodicity buzz. As we discussed offlist, neither of
> these things should stop you from learning to distinguish any of these
> chords from one another.
>
>
> -Mike
>

On Mon, Apr 18, 2011 at 2:17 PM, Mike Battaglia <battaglia01@...> wrote:
>
> TL;DR, finding some sweet microtemperaments in subgroups built around
> chords like the above would be awesome. Then they'd still have the
> father "feel" to them, but everything would connect in a completely
> different way, and you could also have crazy sync-beating like with
> the above as well.

To that effect there's a list here:

http://x31eq.com/cgi-bin/pregular.cgi?limit=2.13.17.20&error=5.0

The winner is a generator with about half the size of the father one,
it's a mohajira-ized version of father. Next up is what is called
"Hanson+," which is actually father temperament. There are other
subgroups that could also rationalize the father triad, 11:14:17 being
one a little further out there. This approach might really be magical
with things like Blackwood, where once you find the magic sync-beating
JI triad once, it's automatically replicated over every other step of
the scale.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> If you've played around in 13-equal a lot, that should sound really
> familiar, except the whole thing will beat in sync beautifully with
> itself.

What makes it beat in sync?

-Igs

On Mon, Apr 18, 2011 at 4:21 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > If you've played around in 13-equal a lot, that should sound really
> > familiar, except the whole thing will beat in sync beautifully with
> > itself.
>
> What makes it beat in sync?

Did you listen to it? Does it not sound like it's beating in sync to you?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Did you listen to it? Does it not sound like it's beating in sync to you?

Yes, but how did you know it would?

-Igs

On Apr 18, 2011, at 5:07 PM, cityoftheasleep <igliashon@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Did you listen to it? Does it not sound like it's beating in sync to you?

Yes, but how did you know it would?

-Igs

I wasn't the first to figure it out, but for me it came out of the stuff
involving periodicity buzz, which is actually synchronized roughness. That
is, 16:17:18:19 exhibiting "periodicity buzz" is actually it exhibiting
equal or proportional beating, and if you stretch the chord uniformly (using
sine waves) it will still buzz.

Since nobody cares about sine waves, an important class of these chords are
omni-sync beating chords, where all of the partials of each note also beat
against one another in sync with everything else. Mathematically this leaves
us with RI chords as our only option (more promising stuff may be developed
later). Of these, recurrent sequences will exhibit the strongest effect
(like 11:14:17:20:23:etc).

So I found a recurrent sequence that was reasonably low numbered and matches
13-equal well. The good news is, harmonic entropy is still in effect, so the
outer dyad will still sound like a 3/2, albeit a father sized one. The
better news is that periodicity buzz is not harmonic entropy, so you get
this sync-beating sweet spot at this higher-limit recurrent sequence - even
though the root tones themselves approximate things like mistuned 3/2 and
5/4's. It's a win win.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "cityoftheasleep" <igliashon@> wrote:
> >
> > > > The thing is, though, in barbershop they don't add the 7th to
> > > > every chord, or even the majority of chords.
> > >
> > > They don't add it to the minor chords, but yes it is present
> > > in a majority of the chords. -Carl
> >
> > Really? Have you done a statistical analysis?
> >
> > -Igs
>
> No, but I have done some barbershop arranging. Check out
> Aaron Wolf's arrangements, which he performed in Melodyne
> in JI, for some concrete examples. -Carl
>

Another way to do it is google barbershop harmony and look for a song called Down Our Way. It is one of the main polecat songs all barbershoppers know and it will give you a sample of just how thickly basted in dominant 7th chords the music is.

Billy

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Apr 18, 2011, at 5:07 PM, cityoftheasleep <igliashon@...>
> wrote:
>
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > Did you listen to it? Does it not sound like it's beating in sync to you?
>
> Yes, but how did you know it would?
>
> -Igs
>
> I wasn't the first to figure it out, but for me it came out of the stuff
> involving periodicity buzz, which is actually synchronized roughness. That
> is, 16:17:18:19 exhibiting "periodicity buzz" is actually it exhibiting
> equal or proportional beating, and if you stretch the chord uniformly (using
> sine waves) it will still buzz.
>
> Since nobody cares about sine waves, an important class of these chords are
> omni-sync beating chords, where all of the partials of each note also beat
> against one another in sync with everything else. Mathematically this leaves
> us with RI chords as our only option (more promising stuff may be developed
> later). Of these, recurrent sequences will exhibit the strongest effect
> (like 11:14:17:20:23:etc).
>
> So I found a recurrent sequence that was reasonably low numbered and matches
> 13-equal well. The good news is, harmonic entropy is still in effect, so the
> outer dyad will still sound like a 3/2, albeit a father sized one. The
> better news is that periodicity buzz is not harmonic entropy, so you get
> this sync-beating sweet spot at this higher-limit recurrent sequence - even
> though the root tones themselves approximate things like mistuned 3/2 and
> 5/4's. It's a win win.
>
> -Mike
>

Erv Wilson and Jacques Dudon have worked on recurrent sequences for decades. Most of us into such things are gone from this list, but I'm still dumbfounded that you and Igs haven't been aware of this stuff for ages.

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >

> >
> > So I found a recurrent sequence that was reasonably low numbered and matches
> > 13-equal well. The good news is, harmonic entropy is still in effect, so the
> > outer dyad will still sound like a 3/2, albeit a father sized one. The
> > better news is that periodicity buzz is not harmonic entropy, so you get
> > this sync-beating sweet spot at this higher-limit recurrent sequence - even
> > though the root tones themselves approximate things like mistuned 3/2 and
> > 5/4's. It's a win win.

Mike, have you really thought about the implications of harmonic entropy meaning "the outer dyad will still sound like a 3/2"?

MikeB>"The good news is, harmonic entropy is still in effect, so the outer dyad will still sound like a 3/2, albeit a father sized one.

Lobawad>"Mike, have you really thought about the implications of harmonic entropy meaning "the outer dyad will still sound like a 3/2"? "

  Seriously...I'd say no.  17/11 alone, to my ear, will never sound like 3/2...don't get me wrong, there's an HE-generated field of attraction around 3/2, but in not so God-like in size/width.

  Now if the recurrent sequence chord pushes 17/11 to sound like a 3/2...my take is that MULTIPLE fields of attraction within the chord must be involved.  17/11 is fairly ambiguous in by nature...just like 22/15....it takes at least 2 and likely at least 3 other notes to put it in a strong enough context to "warp" into feeling like a 3/2.
 
   It's one thing I constantly see as a conclusion on this list: that is takes very little to make fields of attraction work.  On the contrary...I think it takes a lot: many notes and general larger context in composition...all working together to make anything act as a 5-odd-limit (or less) identity 20+ cents away from it. 

On 17 April 2011 04:41, Carl Lumma <carl@...> wrote:

> To me the version with 9/5 is the worst (has a sour quality),
> followed by 12-ET, then 4:5:6:7, and I agree with Mark that the
> version with 16/9 is best for this cadence.

I don't have the facilities to listen now. Instead, I'll randomly
state that all intervals in the 16/9 version become 9-limit
consonances in marvel temperaments (with 225:224 tempered out). The
tritone (augmented fourth) approximates 7:5, the added minor third
approximates 7:6, and everything else was 9-limit to begin with.

Its tritone substitution is a 4:5:6:7 chord, because the augmented
fourth moves to the right place for a 7:5. (Or the other pitches move
around it.) That gives a formula for the resolution of a 4:5:6:7.

Graham

The test of "theory" is as easy as pie: run it backwards and see if music comes out.

Igliashon is using moment of symmetry scales- that's "theory"-based, the original theory of Erv Wilson's being derived from observation. In my opinion starting with MOS scales is not the best approach for what Igliashon is doing.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Igs,
>
> With all due respect, ears write the theory not the other way around. I
> believe it has always been like that. Music theory is for the most part
> after the fact retrospective analysis.
>
> What I plan to do is to start analyzing what works for my ears - and try to
> get rid of the 12 edo hang over stuff, that is the chaff, and find some
> wheat in progression not possible in 12 edo.
>
> Chris
>
> On Mon, Apr 18, 2011 at 1:05 PM, cityoftheasleep <igliashon@...>wrote:
>
> > I've reached the point where I really have to just give up on the theory
> > and follow my ears, because if I wait for theory to pave the way, I'll never
> > get any music made.
> >
> > -Igs
> >
> >
> >
> >
>

Th whom and to what in particular of the below quotes are you responding
to?

Sorry - I'm confused by your statement. It appear to contradict, and then
affirm, my position.

On Tue, Apr 19, 2011 at 7:52 AM, lobawad <lobawad@yahoo.com> wrote:

>
>
> The test of "theory" is as easy as pie: run it backwards and see if music
> comes out.
>
> Igliashon is using moment of symmetry scales- that's "theory"-based, the
> original theory of Erv Wilson's being derived from observation. In my
> opinion starting with MOS scales is not the best approach for what Igliashon
> is doing.
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Igs,
> >
> > With all due respect, ears write the theory not the other way around. I
> > believe it has always been like that. Music theory is for the most part
> > after the fact retrospective analysis.
> >
> > What I plan to do is to start analyzing what works for my ears - and try
> to
> > get rid of the 12 edo hang over stuff, that is the chaff, and find some
> > wheat in progression not possible in 12 edo.
> >
> > Chris
> >
> > On Mon, Apr 18, 2011 at 1:05 PM, cityoftheasleep <igliashon@...>wrote:
>
> >
> > > I've reached the point where I really have to just give up on the
> theory
> > > and follow my ears, because if I wait for theory to pave the way, I'll
> never
> > > get any music made.
> > >
> > > -Igs
> > >
> > >
> > >
> > >
> >
>
>
>

On Tue, Apr 19, 2011 at 12:35 AM, lobawad <lobawad@...> wrote:
>
> Erv Wilson and Jacques Dudon have worked on recurrent sequences for decades. Most of us into such things are gone from this list, but I'm still dumbfounded that you and Igs haven't been aware of this stuff for ages.

Sorry, thought I mentioned them in my post but I see I didn't. It's
quite a pain to be typing stuff on iPhone. Gene did a lot of work with
sync beating chords as well. Like I said, I'm not the first to figure
it out... :)

-Mike

On Tue, Apr 19, 2011 at 1:55 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"The good news is, harmonic entropy is still in effect, so the outer dyad will still sound like a 3/2, albeit a father sized one.
>
> Lobawad>"Mike, have you really thought about the implications of harmonic entropy meaning "the outer dyad will still sound like a 3/2"? "
>
>   Seriously...I'd say no.  17/11 alone, to my ear, will never sound like 3/2...don't get me wrong, there's an HE-generated field of attraction around 3/2, but in not so God-like in size/width.

I wasn't referring to 11:14:17 specifically, just for sync-beating
chords in general. As for approximating a father-tempered 4:5:6,
11:14:17 might be a bit too large for your taste, but then there's
always things like 17:22:26. If you don't like that, then just find
one that sounds like a father-tempered 3/2 to you, and construct
chords around it, and the chord will beat in sync with itself.
Generally, the higher up in the harmonic series you go, the less
strongly the chord will sync-beat, but the closer you'll be able to
get it to approximate what you want, so there's a tradeoff involved.

>   Now if the recurrent sequence chord pushes 17/11 to sound like a 3/2...my take is that MULTIPLE fields of attraction within the chord must be involved.  17/11 is fairly ambiguous in by nature...just like 22/15....it takes at least 2 and likely at least 3 other notes to put it in a strong enough context to "warp" into feeling like a 3/2.

I agree with this, but then again that's how father temperament works too.

>    It's one thing I constantly see as a conclusion on this list: that is takes very little to make fields of attraction work.  On the contrary...I think it takes a lot: many notes and general larger context in composition...all working together to make anything act as a 5-odd-limit (or less) identity 20+ cents away from it.

No, that's how lots of people think on here. 11/9 to me doesn't really
sound like a resolved 11/9 dyad pointing to a VF when played by
itself. This is actually part of what makes it so magical. But if you
put it in 4:5:6:7:9:11, then it sounds resolved. The same with 19:24 -
you might just hear that as a slightly sharp 5/4, but in the context
of 4:5:6:7:9:11:13:15:17:19:21:23:24, it'll sound fine.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Gene did a lot of work with
> sync beating chords as well. Like I said, I'm not the first to figure
> it out... :)

My focus was more on tuning regular temperaments rather than recurrent sequences except when talking to Jacques Dudon.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> Igliashon is using moment of symmetry scales- that's "theory"-based, the original theory
> of Erv Wilson's being derived from observation. In my opinion starting with MOS scales is
> not the best approach for what Igliashon is doing.

What do you perceive me to be doing, and why are MOS scales not the best approach for it?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > Igliashon is using moment of symmetry scales- that's "theory"-based, the original theory
> > of Erv Wilson's being derived from observation. In my opinion starting with MOS scales is
> > not the best approach for what Igliashon is doing.
>
> What do you perceive me to be doing,

Making music within unusual equal divisions of the octave, intending melody and harmony, where harmony also has purpose/shape of its own (ie, chord movement).

>and why are MOS scales not the best approach for it?

Although I'd love for it to be true that MOS scales somehow automagically enable meaningful harmonic possibilites, I've never found any evidence to support this, especially when it comes to equal divisions of the octave whose few concidences with ratios found in the harmonic series are complex to begin with. To the contrary, I've found in my own experience that harmonic movement in such tunings, if it wishes to avoid a "wonky" sound, requires lumps and gaps that don't fit the regularity of step sizes which is created by moments of symmetry.

As you've surely discovered by now, "harmonic entropy" is actually indistinguishable from a Procrustean diatonic grid and is barking up the wrong tree. So is starting with MOSs.

Igs>"What do you perceive me to be doing, and why are MOS scales not the best approach for it?"

     Your composition style seems based more upon hearing/"figuring things out by ear" than adherence to any one theory.   You keep on saying your style is MOS scales under EDO tunings.

  But, on any theoretical level, I think the only consistent thing you gravitate to is strictly proper scales...and tending to like EDO tunings and MOS scale are a side-effect of this (since both of those often tend toward creating strictly proper scales). 
---------
   Let me go out on a limb and say you might really enjoy irrational tunings based on chords you think "sound good" that also meet the criterion of being strictly proper.   You may also find, through experimentation, you find things equal beating as desired for some chords and not others...I say let it be at you liberty to decide when you do/don't apply such things and don't worry about being a "scientist".  Your greatest strength IMVHO by far is your excellent sense of what sounds good...it shines in your composition and, often more often than not, renders "scientific musical theories" somewhat irrelevant to what you do (heck, even Paul Elrich hinted at that...and he's supposedly the "scientist of all scientists" in this field).
 

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> >and why are MOS scales not the best approach for it?
>
> Although I'd love for it to be true that MOS scales somehow automagically enable
> meaningful harmonic possibilites, I've never found any evidence to support this,
> especially when it comes to equal divisions of the octave whose few concidences with
> ratios found in the harmonic series are complex to begin with. To the contrary, I've
> found in my own experience that harmonic movement in such tunings, if it wishes to
> avoid a "wonky" sound, requires lumps and gaps that don't fit the regularity of step sizes > which is created by moments of symmetry.

I do agree that there is nothing magical about MOS's, and in fact I do think the vast majority of MOS scales out there are not worth a damn. I certainly don't think MOS always leads to "good" scales, and that non-MOS always don't. In any given EDO within the "practical on guitar" range, I only expect maybe to find maybe 2 to 6 decent MOS scales, and that's usually how it goes. The only reason I favor MOS scales is because I find them easier to understand structurally--which is also why I favor EDOs. And I have found some very good MOS scales that don't feel wonky at all; if I hadn't, I would have given up the approach long ago.

Also, the way I function as a composer sort of requires that my musical elements are laid out for me beforehand; I don't know how to just pick a set of pitches to work with ex nihilo. I'm a horribly indecisive person, and the more choices I have open to me, the more impossible I find it to choose from them. Limiting myself to MOS scales within EDOs narrows the field to a manageable size for me. The "gems" are more apparent that way.

Often times, if I find a particular chord I like in an EDO, there's going to be an MOS that gives me plenty of that chord within a natural-sounding tonal framework. Let me give some examples:

11-EDO: I like the 0-4-9 triad, or 0-2-4 in inversion, and the 6L+1s MOS scale gives a ton of 'em, all neatly chained together.

13-EDO: I love the 0-2-5 and 0-3-5 triads, which can be expanded into consonant pentads in various ways (0-2-5-7-10, 0-3-5-8-10, 0-2-5-8-10, 0-3-5-7-10), and lo and behold the 5L+3s scale is great for these chords.

15-EDO: the 5L+5s scale is probably my favorite scale ever, because every degree forms either a 0-5-9 or 0-4-9 triad, and all the 0-5-9 triads expand to both 0-5-9-12 and 0-5-9-14 tetrads, which I love also. More importantly, you can move up or down from any triad by a 720-cent interval, and you can use leading-tone resolutions to any of the 0-5-9 triads. In essence, all of the "major triads" can function as tonics *or* "dominants", and that's just really fucking cool to me. I haven't exploited this in composition yet, but I definitely plan to in the future.

16-EDO: My three favorite tetrads are 0-5-13-19, 0-5-13-18, and 0-6-14-19, and whaddaya know, the 4L+2s scale has two of each of them!

18-EDO: 0-5-9 and 0-4-9 both pretty solidly approximate 5:6:7 and 1/(5:6:7), and the 2L+6s scale has four of each, one on each root. It also has a slightly improper version of the 5L+3s scale from 13-EDO with harmonies that sound even smoother and work pretty much the same way as they do in 13.

23-EDO: there's just too much to list here, really. 23 is so full of good MOS scales it makes me want to pee myself.

I haven't found any of these scales sound "wonky" in the slightest, since they're all proper, and the chords are all pretty evenly spaced out over the scale.

I'm sure there are other approaches I'm overlooking in these EDOs that would lead to some great music, but I'm pretty well satisfied with what I've found in the MOS approach. And of course there's also the MODMOS's, which I haven't even begun to look at but Mike and Gene seem pretty confident there's lots of untapped potential in that direction. Maybe if they come up with some good-looking ones I'll check it out.

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>   But, on any theoretical level, I think the only consistent thing you gravitate to is strictly
> proper scales...

Now that is patently false. In 18-EDO, my favorite scale is 3 1 3 3 1 3 3 1, which is improper. In 19-EDO, I'm a big fan of 3 1 3 1 3 1 3 1 3, which is also improper. And in 17-EDO, the diatonic scale (which I get a good bit of mileage out of) is 3 3 1 3 3 3 1, also improper. And in 23-EDO, I'm a huge fan of 5 2 2 5 2 5 2, 5 1 5 1 5 1 5, and 4 1 4 4 1 4 4 1, all of which are improper-to-wildly-improper. Looking at 11, 13, 14, and 15, most of my favorite scales are proper but not strictly proper. It's really only in 16 and 20 that strictly-proper scales make up the majority of my favorite scales (note that in 20-EDO, the 3 1 3 1 3 1 3 1 3 1 scale is strictly proper, despite the fact that L:s is 3:1).

-Igs

Ok, bad guess.
    So what draws you, in general, to MOS scales then?  Or is it somewhat a side effect of not having tried non-MOS scales in EDO tunings? 

--- On Tue, 4/19/11, cityoftheasleep <igliashon@...> wrote:

From: cityoftheasleep <igliashon@...>
Subject: [tuning] Re: Is 9-odd-limit, bizarrely enough, heard as more resolved than 7-limit?
To: tuning@yahoogroups.com
Date: Tuesday, April 19, 2011, 1:15 PM

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>   But, on any theoretical level, I think the only consistent thing you gravitate to is strictly

> proper scales...

Now that is patently false. In 18-EDO, my favorite scale is 3 1 3 3 1 3 3 1, which is improper. In 19-EDO, I'm a big fan of 3 1 3 1 3 1 3 1 3, which is also improper. And in 17-EDO, the diatonic scale (which I get a good bit of mileage out of) is 3 3 1 3 3 3 1, also improper. And in 23-EDO, I'm a huge fan of 5 2 2 5 2 5 2, 5 1 5 1 5 1 5, and 4 1 4 4 1 4 4 1, all of which are improper-to-wildly-improper. Looking at 11, 13, 14, and 15, most of my favorite scales are proper but not strictly proper. It's really only in 16 and 20 that strictly-proper scales make up the majority of my favorite scales (note that in 20-EDO, the 3 1 3 1 3 1 3 1 3 1 scale is strictly proper, despite the fact that L:s is 3:1).

-Igs

Raises hand - me too! " And in 17-EDO, the diatonic scale (which I get a
good bit of mileage out of) is 3 3 1 3 3 3 1, also improper."

Chris

On Tue, Apr 19, 2011 at 4:15 PM, cityoftheasleep <igliashon@...>wrote:

>
>
> --- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> > But, on any theoretical level, I think the only consistent thing you
> gravitate to is strictly
> > proper scales...
>
> Now that is patently false. In 18-EDO, my favorite scale is 3 1 3 3 1 3 3
> 1, which is improper. In 19-EDO, I'm a big fan of 3 1 3 1 3 1 3 1 3, which
> is also improper. And in 17-EDO, the diatonic scale (which I get a good bit
> of mileage out of) is 3 3 1 3 3 3 1, also improper. And in 23-EDO, I'm a
> huge fan of 5 2 2 5 2 5 2, 5 1 5 1 5 1 5, and 4 1 4 4 1 4 4 1, all of which
> are improper-to-wildly-improper. Looking at 11, 13, 14, and 15, most of my
> favorite scales are proper but not strictly proper. It's really only in 16
> and 20 that strictly-proper scales make up the majority of my favorite
> scales (note that in 20-EDO, the 3 1 3 1 3 1 3 1 3 1 scale is strictly
> proper, despite the fact that L:s is 3:1).
>
> -Igs
>
>
>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > To me the version with 9/5 is the worst (has a sour quality),
> > followed by 12-ET, then 4:5:6:7, and I agree with Mark that the
> > version with 16/9 is best for this cadence.
> >
> > What does anybody else think?
>
> I thought the JI tetrad sounded the most different from the rest, that the 16/9 chord sounded the most like a dominant 7th (kind of surprising, given that 12edo was in the mix) and that the 9/5 chord was interesting and not awful sounding, but not as good as a dominant 7th.
>

It is true that the tuning according to the standard just major scale is the 16/9 tuning. But if you to use some secondary dominant 7ths like one built on the 3rd degree, you would get the wide 9/5 tuning. It would seem to me if it were at all permissible to inject a comma to correct this, you may as well use the same trick to adjust them all to 4:5:6:7's. So the 16/9 sounds most dominant of the tunings. I suppose the 9/5 sound would suggest there to be such a thing as a "secondary dominant sound". The 4:5:6:7 tuning would sound like something of a blues tonality where this quadad has a function as basic as the triad in traditional music. I suppose if some time in the renaissance music was taught to count to 5, resulting in the introduction of meantone tuning, then music of the blues variety has similarly taught music to count to 7.

Billy

--- "lobawad" <lobawad@...> wrote:

> Igliashon is using moment of symmetry scales- that's
> "theory"-based, the original theory of Erv Wilson's being
> derive from observation.

Not sure what you meant here, but for the record Erv arrived
at MOS by playing with numbers, not sounds. Of course he
enthusiastically built instruments to audition them. But I'm
not aware that he ever tested MOS vs. other scale construction
techniques. For him, MOS is justified by theory alone, and
happens to produce nice-sounding scales.

-Carl

Billy wrote:

> Another way to do it is google barbershop harmony and look for
> a song called Down Our Way. It is one of the main polecat songs
> all barbershoppers know and it will give you a sample of just
> how thickly basted in dominant 7th chords the music is.

One of the first microtonal experiments I did was to multitrack
myself singing this tune, trying to make it accurate JI.
My old Tascam portastudio! Unfortunately the only copy was
stolen out of my car in Oakland. :(

> if you to use some secondary dominant 7ths like one built on
> the 3rd degree, you would get the wide 9/5 tuning. It would
> seem to me if it were at all permissible to inject a comma to
> correct this, you may as well use the same trick to adjust
> them all to 4:5:6:7's.

If you can't inject a comma you'll run into trouble with
plain triads - forget 7th chords.

> So the 16/9 sounds most dominant of the tunings. I suppose
> the 9/5 sound would suggest there to be such a thing as a
> "secondary dominant sound".

This assumes a fixed JI scale (with 2nd = 9/8) which in
practice is never used. So I'd be surprised if listeners
showed any tendency to prefer the 9/5 tuning as a secondary
dominant.

-Carl

Jake wrote:

>> The roots [of 12-tET] were historical, but that history is one
>> of the development of a style of 5-limit harmony. It's the
>> story of the journey from meantone temperament, which tempers
>> out 81/80 only, to 12-ET, which additionally tempers out
>> 128/125 and 648/625. This was understood by theorists here
>> and there, but mostly it happened organically. Only in the
>> last several decades have theorists put it all together and
>> made predictions about alternative ways the history might
>> have gone -- tuning forks in the road, as it were.
>
> But that's part of my point: It happened organically, such that
> piano tuners were trained to tune a fifth perfectly and then
> make it flat "just a little bit, about two beats per second, to
> avoid getting a wolf fifth" or some such stuff. That's a human
> and practical method, not a prime-limit-related one. It can be
> described with prime limits and commas, and some people even
> knew the math involved, and it led to great 3-limit and
> acceptable 5-limit harmony -- but it sure doesn't look like
> they were focused on getting 19-limit harmony. So, even though
> we *can* retrofit 19-limit harmony onto it, why *should* we?

I don't know who mentioned 19-limit harmony. It's possible
to build completely new and different but still "functional"
styles in the 5-limit. Take porcupine (named after a piece
by Herman). It tempers out 250/243 instead of 81/80 and is
associated with a whole sequence of scales different from those
of meantone/12-ET. There are a variety of these 5-limit
systems, and even more of them by the time we get to the
19-limit. In no case are we bolting anything on to existing
music theory. Well, it's possible to extend the chords of the
diatonic scale -- as I did in the chord progression I posted
for Igs. That in itself is a fertile direction some
microtonalists have tried. But no, the men of tuning-math
are after tougher stuff.

> For historical purposes, I just don't see why that would be
> relevant. When talking about current conditioning, I'm also not
> sure why it would make sense to talk about prime limits, when
> that's not the way most people use the scale.

12-ET is usually used in a 5-limit manner. Sometimes in
a 7-limit one. Beyond that its approximations start to
break down, but interesting suspensions can be made
(e.g. "quartal harmony").

>> Hm. To me, this
>> http://www.youtube.com/watch?v=FHjitZIyaRc
>> sounds like an out of tune version of this
>> http://www.youtube.com/watch?v=EHExcd6PYxQ
>
> That's interesting. The meantone version sounds a little
> richer, maybe, but the 12-tET version doesn't sound out of
> tune. How can the 12-tET version be "in tune" and the
> meantone one be "more in tune"? But that's the way I hear it.

Like I said, I think it's a matter of degrees.

> It's a very nice piece, by the way, and one that I've never
> heard before. Thanks for the links.

Sweelinck is one of my favorite composers and this piece
made quite an impact on me when I first heard it.

-Carl

Chris wrote:

> With all due respect, ears write the theory not the other way
> around. I believe it has always been like that. Music theory
> is for the most part after the fact retrospective analysis.

How do you explain Gene's music, Herman's music, Igs' music...
pretty much any of the music on these lists? Did Carlo find
Carlos gamma one day when retrospectively analyzing one of his
keyboard jams? Igs spontaneously tuned his guitar to the
3335333 scale in 23-ET?

-Carl

Igs wrote:

> Tried it, and nope. I'm well-conditioned to accept the 5-limit
> triad as a final resting place.

Blimey. Even after all the power-chord shredding of the
'80s and '90s?

> Okay, you win. I don't know why the (b) version works for me
> and the (a) version doesn't, but it does. Well, the JI version
> anyway. The 12-ET doesn't.

Wooho!

> Also the hexany version works great, probably the best so far,
> but that doesn't at all surprise me as it's quite a radoical
> recontextualization of that chord (and most of the sonorities
> sound pretty nasty to me...I'd never have known it was JI if
> you hadn't mentioned the hexany).

It also works better for me than the extended diatonic
progression. But I find the chords silky smooth!!

> > By the way, I will *curse* you if you use this diatonic
> > lingo in your primer.
> I'm sure as hell not using ratios. Currently I'm using a
> system of 48 diatonic-related subclasses (like subminor,
> supermajor, neutral, etc. as well as terms like "third-fourth"
> and "tritone-fourth" to apply to quarter-tone/maximal-entropy
> intervals that straddle classes)

Bubble bubble, toil and trouble...

-Carl

Carl>"Igs spontaneously tuned his guitar to the 3335333 scale in 23-ET?"

    No, rather, it seems obvious to me Igs and people like him simply picked a bunch of theories and decided by ear which ones worked for them.  

>"How do you explain Gene's music, Herman's music, Igs' music...pretty much any of the music on these lists?  "

  While people like Igs are good at discussing theory, in the end of the day, it doesn't seem to have much bearing in how they actually compose.  Chris and Igs, IMVHO, are easily the most prolific musicians on here, at least online...and neither of them seem to have any hard ties to any given theory: in fact I think their open-mindedness is largely responsible for their success.  Meanwhile, Gene and MikeB seem to be among the best, if not the best people for discussing theory.   Yet their music, to me at least, just isn't on the same level of someone like Chris's.  Same (even!) goes for someone like Paul Erlich and (yes) even Wendy Carlos: there's a certain deliberation and theoretical seriousness about their works that often makes them less fun and playful to listen to.

  But, again: I think both "scientific" theory-based musicians and more freestyle ones both have a place...the scientific ones come up with theories, but the freestyle ones ultimately decide what works emotionally and make the great music.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>   But, again: I think both "scientific" theory-based musicians and more freestyle ones both have a place...the scientific ones come up with theories, but the freestyle ones ultimately decide what works emotionally and make the great music.

Right. We can't have careful thought infecting music, or it will end up like classical music, where people can take years to work out a piece but which everyone knows isn't great music.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> Meanwhile, Gene and MikeB seem to be among the best, if not the best people for discussing theory.   Yet their music, to me at least, just isn't on the same level of someone like Chris's.

I'm glad to have any notoriety at all, being as I've only written one composition, which was more of a technical exercise in 13-limit counterpoint than an art piece.

-Mike

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Ok, bad guess.
>     So what draws you, in general, to MOS scales then?  Or is it somewhat a side effect > of not having tried non-MOS scales in EDO tunings? 

Oh, I tried out *plenty* of non-MOS scales in the beginning, when I was still under the sway of the "JI or the highway" thinking that go me into microtonality in the first place. The reason I stick mostly to MOS these days is because I hate juggling many sizes of interval per interval class. I have a hard enough time on guitar memorizing which root has which harmonies when I only have two sizes of each class to memorize. Non-MOS scales make it that much harder. Of course, this isn't much of a problem in the low EDOs from 11 to about 17, where I can generally keep my bearings even playing fully chromatically. 19 seems to stay okay too, probably just because I can super-impose a 12-TET grid on it in my head and see the new notes as colorations of the old, but 18 and from 20 up, the simplest patterns on the fretboard tend to be MOS (though not all MOS are simple).

When I'm playing keyboard, it doesn't matter at all whether a scale is MOS or not. You can throw any old 12-note scale at me and I'll be able to deal with it just fine, whether it's proper or MOS or not. Thing is, I'm not a very good keyboardist and I'm most interested in what I can put on a guitar. So all of my thinking about "what's good" and "what works" is inherently tied to my limitations as a player on my particular instrument. If I was predominantly a vocalist, I'd probably be more into JI, because it's easier to sing.

-Igs

Me>   But, again: I think both "scientific" theory-based musicians and
more freestyle ones both have a place...the scientific ones come up with
theories, but the freestyle ones ultimately decide what works
emotionally and make the great music.

Gene>"Right. We can't have careful thought infecting music, or it will end up
like classical music, where people can take years to work out a piece
but which everyone knows isn't great music."

  Gene, I never thought you'd try to incite a flame-thread like that...  My point was the music that connects emotionally, in general, quite often tends to be inspired by theorists, but not made by them.  I'm not saying that theorists never make across-the-board well received music...but rather that having a great theorist and public-received-musician is often rare. 

  Far as classical music...I recall Daniel said something about some 5% of the population (only) feeling connection to it.  And that's regardless of how well-worked it is technically.  If other people like it, great and I'm glad it's around to please them...on the other hand, the idea that people should have to like it just because it's technically advanced/sound/...is absurd.  Same thing works in reverse as well...I'm (even) glad cheesy pop music is around, some people obvious enjoy it...even though I absolutely hate most of it (IE just because technically-speaking it stinks doesn't mean it can't emotionally click with people).

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Gene>"Right. We can't have careful thought infecting music, or it will end up
> like classical music, where people can take years to work out a piece
> but which everyone knows isn't great music."
>
>   Gene, I never thought you'd try to incite a flame-thread like that...  My point was the music that connects emotionally, in general, quite often tends to be inspired by theorists, but not made by them.  I'm not saying that theorists never make across-the-board well received music...but rather that having a great theorist and public-received-musician is often rare. 

This is a rare group of people.

Michael, what are your thoughts on Stravinsky? Say the Rite of Spring?

>   Far as classical music...I recall Daniel said something about some 5% of the population (only) feeling connection to it.  And that's regardless of how well-worked it is technically.  If other people like it, great and I'm glad it's around to please them...on the other hand, the idea that people should have to like it just because it's technically advanced/sound/...is absurd.  Same thing works in reverse as well...I'm (even) glad cheesy pop music is around, some people obvious enjoy it...even though I absolutely hate most of it (IE just because technically-speaking it stinks doesn't mean it can't emotionally click with people).

If you write music and you're consciously worrying about what some audience will think, I say you're doing it wrong.

-Mike

>"Michael, what are your thoughts on Stravinsky? Say the Rite of Spring?"

   Utterly amazing composition-wise...yet quite forced sounding and somewhat unrelateable emotion-wise.  So I respect it strongly, yet would not listen to it nor feel inspiration from it (or want to try and recreate something like it).  It's like watching a painter make an incredibly detailed reflection of a pin on a knife in a tiny corner of a painting...vs. something like Japanese Manga where the detail, frankly, is often fairly crude but the emotion indicated is startling.   It's funny because the opposite is people like Mozart and even Tchaikovsky...whose music is often quite simple, but gets quite impressive "bang per note".

>"If you write music and you're consciously worrying about what some audience will think, I say you're doing it wrong."

  Good point...but that's not what I do.  The only audience I worry about at all (at least for the first draft of a song) is myself IE will I still be listening to this in 5 months.
    One way I could worry about what the audience thinks (at least on this list) is by composing largely classical music on purpose...the other is adhering strongly to popular genres like hip-hop/pop-style-dance/alt-rock.  I do neither: I start with a mood, energy level, and abstractness-level I want and build the song around that.

  Back to tuning (finally?)...it seems certain dyads have certain mood/"characters"...which chords mix into larger "characters".  9-limit seems to have a more agreeable character to me...it's funny because before...you said a more 7-limit chord was more resolved while a not-far-off 9-limit version was "more relaxing" and that either could be used as a relaxing point in a piece of music.  I find it bizarre (my efforts included) that it seems few to no one has tried to categorize chords into groups by "character" beyond suspended/major/minor/diminished. 

   It's funny because I like theory as well...but see it as a palette: while picking the wrong one can make things much trickier...it's how much emotion you can get out of how few notes that really seems to matter...and that seems to ultimately come from your imagination putting different "skews" on the palette, and not some clever formula.

--- In tuning@yahoogroups.com, "battaglia01" <battaglia01@...> wrote:
> If you write music and you're consciously worrying about what some audience will think, I
> say you're doing it wrong.

Unless you're being paid to write, say for an ad or a movie or to back-up a pop starlet.

I tend to agree that agonizing over an hypothetical audience is no way to be an artist, but how many of us really write music without indulging a bit in imagining how other people might react to it? If I expected that everyone was going to hate and/or ignore my music entirely, I'd stop sharing it (if not stop writing it). One of the things that keeps me so involved in making and sharing music is the fact that people seem to like it.

In fact, one of the main inspirations that got me back into making microtonal music was the fact that at the time (early 2009) my one micro album (at the time, "Map of an Internal Landscape") was getting drastically more plays than any of my other albums (according to last.fm) and was also getting me a lot more attention. It occurred to me that if I wanted to make music that wasn't just going to get lost in the airwaves, making more micro stuff was a good bet. Sure, the audience may be small, but it's bigger than the audience for all of my 12-TET stuff combined, despite the fact that I think the artistic quality of my 12-TET stuff far exceeds that of my micro stuff (so far). I'm not necessarily trying to please the microtonal community, but if people here weren't so generally receptive to my stuff, I'd probably have just stuck with 12-TET for simplicity's sake. As it is, writing microtonal music that people like makes me feel at least a little bit important in the grand scheme of things, and that makes a big difference to me. Hopefully I'll eventually get to a point where I'm writing stuff that the non-micro community enjoys. Does the fact that I hope for this make me a sell-out?

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>   Gene, I never thought you'd try to incite a flame-thread like that... 

I think you incited it, and are still pouring kerosene on the flames; I just responded.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"Michael, what are your thoughts on Stravinsky? Say the Rite of Spring?"
>
>    Utterly amazing composition-wise...yet quite forced sounding and somewhat unrelateable emotion-wise.  So I respect it strongly, yet would not listen to it nor feel inspiration from it (or want to try and recreate something like it).  It's like watching a painter make an incredibly detailed reflection of a pin on a knife in a tiny corner of a painting...vs. something like Japanese Manga where the detail, frankly, is often fairly crude but the emotion indicated is startling.   It's funny because the opposite is people like Mozart and even Tchaikovsky...whose music is often quite simple, but gets quite impressive "bang per note".

Alright. Well it's not to your taste. If even Stravinsky doesn't meet your standards for emotional appeal, I don't feel as bad about you dismissing Gene's music as lifeless.

> >"If you write music and you're consciously worrying about what some audience will think, I say you're doing it wrong."
>
>   Good point...but that's not what I do.  The only audience I worry about at all (at least for the first draft of a song) is myself IE will I still be listening to this in 5 months.
>     One way I could worry about what the audience thinks (at least on this list) is by composing largely classical music on purpose...the other is adhering strongly to popular genres like hip-hop/pop-style-dance/alt-rock.  I do neither: I start with a mood, energy level, and abstractness-level I want and build the song around that.

OK.

>   Back to tuning (finally?)...it seems certain dyads have certain mood/"characters"...which chords mix into larger "characters".  9-limit seems to have a more agreeable character to me...

OK, so don't hate on theory then...?

> it's funny because before...you said a more 7-limit chord was more resolved while a not-far-off 9-limit version was "more relaxing" and that either could be used as a relaxing point in a piece of music.  I find it bizarre (my efforts included) that it seems few to no one has tried to categorize chords into groups by "character" beyond suspended/major/minor/diminished. 

So do it!

>    It's funny because I like theory as well...but see it as a palette: while picking the wrong one can make things much trickier...it's how much emotion you can get out of how few notes that really seems to matter...and that seems to ultimately come from your imagination putting different "skews" on the palette, and not some clever formula.

Oh please. You've been saying for years that critical band interactions destroy the consonance of chords. Meanwhile, I've been playing chords like G E F B C G A B for years because I like the emotional feeling of the roughness in that chord. Who's the one making art, and who's the one trying to stifle it with theory?

-Mike

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> It's funny because the opposite is people like Mozart and even Tchaikovsky...whose music is often quite simple, but gets quite impressive "bang per note".

This is silly. Mozart's String Trio "Divertimento" K563 gets a lot of bang from its three parts, but it's not because Mozart is an unsophisticated composer of "quite simple" music. If you got a copy and played it once a day for 50 days, it might be a pretty good way to learn some things you never suspected about classical music.

MikeB>"Alright. Well it's not to your taste. If even Stravinsky doesn't meet
your standards for emotional appeal, I don't feel as bad about you
dismissing Gene's music as lifeless."

   Never said Gene's was lifeless far as emotional appeal to me...more like fair to pretty good whereas Chris and Igs are more like good to great.  Far as technique though, I'd say Gene's music wins fair and square.

>"OK, so don't hate on theory then...?"
  
  I don't hate it...just
1) I don't think it's anywhere near the only way to skin the cat and can't stand it when people say "the theory is good...so anyone who dislikes it must be a lesser listener/musician"
2) I think the attitude of "theory over all else" is going too far...and often ends up draining some emotion from music.  Some theory is good, even necessary...it's just the attitude that theory is everything that bugs me.

Me> it's funny because before...you said a more 7-limit chord was more
resolved while a not-far-off 9-limit version was "more relaxing" and
that either could be used as a relaxing point in a piece of music.  I
find it bizarre (my efforts included) that it seems few to no one has
tried to categorize chords into groups by "character" beyond
suspended/major/minor/diminished. 

MikeB>So do it!

   I'll try.  Though most of my (ahem) theories get little traction here.  Igs...if you want to work together on this, I'd be happy to collaborate.

>"Oh please. You've been saying for years that critical band interactions destroy the consonance of chords."

    In extreme cases...yes.  Extreme cases mean things like notes closer than 12/11...or several 12/11's stacked with no further spaced notes around them to "balance them out".   From the other thread I made...that's "the tragedy of the semitone". :-D

   However I don't think critical band matters between, say, sine waves at 6/5 and 5/4 apart...and never said they have.  ...that's where it switches over more toward the kind of "periodicity buzz" style consonance you usually talk about plus several other things, some of which aren't even defined in any theories yet.  From the other thread I made...that's "the tragedy of the tri-tone". :-D

   But when I compose I don't use either of these things.  Rather...I just stick to using scales that partly solve them problem for me by giving me many easy options to avoid problems like the above.  So the "theory" process only extends to how I pick the palette...so I don't get caught up in it when composing and can, instead, concentrate on the emotions.

 >"Meanwhile, I've been playing chords like G E F B C G A B for years
because I like the emotional feeling of the roughness in that chord."

    Well that qualifies to me somewhat as the other extreme: art with very little theory (at least in terms of critical band compliance).  To me that chord sounds so extremely crowded you can take many notes out of the chord and still get the same mood without the added "grating".  G E F C B seems to "say" the same thing to me as G E F B C G A B...it's like taking a dirty pair of glasses and cleaning it and then viewing the same painting.

  Two 17/16-ish semitones in a chord, to me, is going too far...though something not much "better" theory-wise (IE a 17/16 semitone somewhere and a 12/11 somewhere else a fifth or more away or so would be close enough to not sound garbled to me).

>"Who's the one making art, and who's the one trying to stifle it with
theory?"
 
   There's no one-or-the-other.  I am a huge fan of free-style composition, but taking into account avoidance of inevitable extremes of "conflicts to theory" in designing scales/palettes I compose with.

--- Gene wrote:

> Mozart's String Trio "Divertimento" K563

I sometimes wonder if composers didn't intentionally
misclassify works to show off, false modesty like.
Beethoven seems to have taken this to a whole new level
("Cavatina" etc).

-Carl

On Wed, Apr 20, 2011 at 3:50 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "battaglia01" <battaglia01@...> wrote:
> > If you write music and you're consciously worrying about what some audience will think, I
> > say you're doing it wrong.
>
> Unless you're being paid to write, say for an ad or a movie or to back-up a pop starlet.

Sure, or if, say, you're improvising for an audience, but you're
hooked up to an electric shock machine that jolts you every time they
push the buzzer that they don't like something you did.

> I tend to agree that agonizing over an hypothetical audience is no way to be an artist, but how many of us really write music without indulging a bit in imagining how other people might react to it? If I expected that everyone was going to hate and/or ignore my music entirely, I'd stop sharing it (if not stop writing it). One of the things that keeps me so involved in making and sharing music is the fact that people seem to like it.

If people my age don't like what I'm writing because their musical
preconceptions limit them from getting into it, there's an entire
generation coming up right after them. I obviously can't claim that as
a 100% rule I never ever think about stuff like that, ever, but I used
to be paralyzed by it, and now I'm not. There are times when I want to
write music to communicate and reach people, but there are also times
I'm of the mindset that my music is between myself and, since you're a
philosophy major, we'll say "The Big Electron in the Sky."

> In fact, one of the main inspirations that got me back into making microtonal music was the fact that at the time (early 2009) my one micro album (at the time, "Map of an Internal Landscape") was getting drastically more plays than any of my other albums (according to last.fm) and was also getting me a lot more attention. It occurred to me that if I wanted to make music that wasn't just going to get lost in the airwaves, making more micro stuff was a good bet. Sure, the audience may be small, but it's bigger than the audience for all of my 12-TET stuff combined, despite the fact that I think the artistic quality of my 12-TET stuff far exceeds that of my micro stuff (so far). I'm not necessarily trying to please the microtonal community, but if people here weren't so generally receptive to my stuff, I'd probably have just stuck with 12-TET for simplicity's sake. As it is, writing microtonal music that people like makes me feel at least a little bit important in the grand scheme of things, and that makes a big difference to me. Hopefully I'll eventually get to a point where I'm writing stuff that the non-micro community enjoys. Does the fact that I hope for this make me a sell-out?

You mean writing microtonal music that the non-micro community enjoys,
or writing 12-TET stuff that the non-micro community enjoys?

-Mike

On Wed, Apr 20, 2011 at 5:23 PM, Michael <djtrancendance@...> wrote:
>
> 2) I think the attitude of "theory over all else" is going too far...and often ends up draining some emotion from music.  Some theory is good, even necessary...it's just the attitude that theory is everything that bugs me.

Says the guy who, further down in this very post, tells me that the
problem with my sus chord voicings is that there's not enough
"critical band compliance."

>    I'll try.  Though most of my (ahem) theories get little traction here.  Igs...if you want to work together on this, I'd be happy to collaborate.

I'd be happy to collaborate myself, but I don't know how exactly you
propose to narrow it down.

> >"Oh please. You've been saying for years that critical band interactions destroy the consonance of chords."
>
>     In extreme cases...yes.  Extreme cases mean things like notes closer than 12/11...or several 12/11's stacked with no further spaced notes around them to "balance them out".   From the other thread I made...that's "the tragedy of the semitone". :-D

Yeah, and I keep pointing chords and examples out where people use
chords with semitones all the time, and your response is usually "that
sounds like R&B." Here's a song with semitones in the first two chords
of the song: http://www.youtube.com/watch?v=IVvkjuEAwgU&feature=related

>  >"Meanwhile, I've been playing chords like G E F B C G A B for years because I like the emotional feeling of the roughness in that chord."
>
>     Well that qualifies to me somewhat as the other extreme: art with very little theory (at least in terms of critical band compliance).  To me that chord sounds so extremely crowded you can take many notes out of the chord and still get the same mood without the added "grating".  G E F C B seems to "say" the same thing to me as G E F B C G A B...it's like taking a dirty pair of glasses and cleaning it and then viewing the same painting.

I'm posting these notes in ascending order, they aren't crowded within
an octave. The lowest note is G3, an octave and a half below middle C,
and then it goes G3 E4 F4 B4 C5 G5 A5 B5. That is, G3 -> E4 is an
approximate 5/3.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- Gene wrote:
>
> > Mozart's String Trio "Divertimento" K563
>
> I sometimes wonder if composers didn't intentionally
> misclassify works to show off, false modesty like.
> Beethoven seems to have taken this to a whole new level
> ("Cavatina" etc).

I've never figured out why Mozart wrote a serious string trio and called it a divertimento, but my best guess is that he thought that would generate better sales. Beethoven I think just figured "Cavatina" was a nifty name from the singing character of that movement; I note he didn't call the Grosse Fugue anything silly so there were limits.

I vote the meantone is quite a bit richer to me. Lovely piece.

Thanks for the link.

>
> >> Hm. To me, this
> >> http://www.youtube.com/watch?v=FHjitZIyaRc
> >> sounds like an out of tune version of this
> >> http://www.youtube.com/watch?v=EHExcd6PYxQ
> >
> > That's interesting. The meantone version sounds a little
> > richer, maybe, but the 12-tET version doesn't sound out of
> > tune. How can the 12-tET version be "in tune" and the
> > meantone one be "more in tune"? But that's the way I hear it.
>
> Like I said, I think it's a matter of degrees.
>
> > It's a very nice piece, by the way, and one that I've never
> > heard before. Thanks for the links.
>
> Sweelinck is one of my favorite composers and this piece
> made quite an impact on me when I first heard it.
>
> -Carl
>
>
>
>

Yes, "richer" is the perfect word, it's like a Les Paul through a Mesa Boogie rather than a Telecaster through a Roland keyboard amp. :-)

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I vote the meantone is quite a bit richer to me. Lovely piece.
>
> Thanks for the link.
>
> >
> > >> Hm. To me, this
> > >> http://www.youtube.com/watch?v=FHjitZIyaRc
> > >> sounds like an out of tune version of this
> > >> http://www.youtube.com/watch?v=EHExcd6PYxQ
> > >
> > > That's interesting. The meantone version sounds a little
> > > richer, maybe, but the 12-tET version doesn't sound out of
> > > tune. How can the 12-tET version be "in tune" and the
> > > meantone one be "more in tune"? But that's the way I hear it.
> >
> > Like I said, I think it's a matter of degrees.
> >
> > > It's a very nice piece, by the way, and one that I've never
> > > heard before. Thanks for the links.
> >
> > Sweelinck is one of my favorite composers and this piece
> > made quite an impact on me when I first heard it.
> >
> > -Carl
> >
> >
> >
> >
>

Nice response there, Igliashon. I'm curious as to how you'll approach things if you get into thicker harmonies and chord progressions as musical entities of their own.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > >and why are MOS scales not the best approach for it?
> >
> > Although I'd love for it to be true that MOS scales somehow automagically enable
> > meaningful harmonic possibilites, I've never found any evidence to support this,
> > especially when it comes to equal divisions of the octave whose few concidences with
> > ratios found in the harmonic series are complex to begin with. To the contrary, I've
> > found in my own experience that harmonic movement in such tunings, if it wishes to
> > avoid a "wonky" sound, requires lumps and gaps that don't fit the regularity of step sizes > which is created by moments of symmetry.
>
> I do agree that there is nothing magical about MOS's, and in fact I do think the vast majority of MOS scales out there are not worth a damn. I certainly don't think MOS always leads to "good" scales, and that non-MOS always don't. In any given EDO within the "practical on guitar" range, I only expect maybe to find maybe 2 to 6 decent MOS scales, and that's usually how it goes. The only reason I favor MOS scales is because I find them easier to understand structurally--which is also why I favor EDOs. And I have found some very good MOS scales that don't feel wonky at all; if I hadn't, I would have given up the approach long ago.
>
> Also, the way I function as a composer sort of requires that my musical elements are laid out for me beforehand; I don't know how to just pick a set of pitches to work with ex nihilo. I'm a horribly indecisive person, and the more choices I have open to me, the more impossible I find it to choose from them. Limiting myself to MOS scales within EDOs narrows the field to a manageable size for me. The "gems" are more apparent that way.
>
> Often times, if I find a particular chord I like in an EDO, there's going to be an MOS that gives me plenty of that chord within a natural-sounding tonal framework. Let me give some examples:
>
> 11-EDO: I like the 0-4-9 triad, or 0-2-4 in inversion, and the 6L+1s MOS scale gives a ton of 'em, all neatly chained together.
>
> 13-EDO: I love the 0-2-5 and 0-3-5 triads, which can be expanded into consonant pentads in various ways (0-2-5-7-10, 0-3-5-8-10, 0-2-5-8-10, 0-3-5-7-10), and lo and behold the 5L+3s scale is great for these chords.
>
> 15-EDO: the 5L+5s scale is probably my favorite scale ever, because every degree forms either a 0-5-9 or 0-4-9 triad, and all the 0-5-9 triads expand to both 0-5-9-12 and 0-5-9-14 tetrads, which I love also. More importantly, you can move up or down from any triad by a 720-cent interval, and you can use leading-tone resolutions to any of the 0-5-9 triads. In essence, all of the "major triads" can function as tonics *or* "dominants", and that's just really fucking cool to me. I haven't exploited this in composition yet, but I definitely plan to in the future.
>
> 16-EDO: My three favorite tetrads are 0-5-13-19, 0-5-13-18, and 0-6-14-19, and whaddaya know, the 4L+2s scale has two of each of them!
>
> 18-EDO: 0-5-9 and 0-4-9 both pretty solidly approximate 5:6:7 and 1/(5:6:7), and the 2L+6s scale has four of each, one on each root. It also has a slightly improper version of the 5L+3s scale from 13-EDO with harmonies that sound even smoother and work pretty much the same way as they do in 13.
>
> 23-EDO: there's just too much to list here, really. 23 is so full of good MOS scales it makes me want to pee myself.
>
> I haven't found any of these scales sound "wonky" in the slightest, since they're all proper, and the chords are all pretty evenly spaced out over the scale.
>
> I'm sure there are other approaches I'm overlooking in these EDOs that would lead to some great music, but I'm pretty well satisfied with what I've found in the MOS approach. And of course there's also the MODMOS's, which I haven't even begun to look at but Mike and Gene seem pretty confident there's lots of untapped potential in that direction. Maybe if they come up with some good-looking ones I'll check it out.
>
> -Igs
>

Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
sound "resolved"? The harmonies "harmonic"?

I'm really curious how the community perceptions will compare with those of "civilians".

http://soundcloud.com/cameron-bobro/thistleflower-cbobro

On Wed, Apr 20, 2011 at 11:18 PM, lobawad <lobawad@...> wrote:
>
> Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
>
> sound "resolved"? The harmonies "harmonic"?
>
> I'm really curious how the community perceptions will compare with those of "civilians".
>
> http://soundcloud.com/cameron-bobro/thistleflower-cbobro

They generally sound like detuned 5-limit chords to me, and to my ears
resolve in the same way that regular ol meantone music does.

-Mike

I better be careful. Technology is getting awfully transparent. Wasn't it just recently that I was mentioning blues as a genre that has promoted the septimal quadad to the status of the triad. And what do I receive but an email ad from Amazon with these words:

"William C Gard,
Are you looking for something in our Blues department? If so, you might be interested in these items."

Billy

On Wed, Apr 20, 2011 at 11:33 PM, Billy <billygard@...> wrote:
>
> I better be careful. Technology is getting awfully transparent. Wasn't it just recently that I was mentioning blues as a genre that has promoted the septimal quadad to the status of the triad. And what do I receive but an email ad from Amazon with these words:
>
> "William C Gard,
> Are you looking for something in our Blues department? If so, you might be interested in these items."
>
> Billy

There you go. Although as a note, we tend to call four-note chords
"tetrads" around here, not "quadads," as the latter sounds somewhat
like a species of clam. I think the technical Latin term for it would
be "quadrad" or something similar anyway.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Apr 20, 2011 at 11:18 PM, lobawad <lobawad@...> wrote:
> >
> > Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
> >
> > sound "resolved"? The harmonies "harmonic"?
> >
> > I'm really curious how the community perceptions will compare with those of "civilians".
> >
> > http://soundcloud.com/cameron-bobro/thistleflower-cbobro
>
> They generally sound like detuned 5-limit chords to me, and to my ears
> resolve in the same way that regular ol meantone music does.
>
> -Mike
>

Since you're hearing this as being in a temperament, what would be your guess as to the temperament or general temperament type?

On Wed, Apr 20, 2011 at 11:45 PM, lobawad <lobawad@...> wrote:
>
> Since you're hearing this as being in a temperament, what would be your guess as to the temperament or general temperament type?

Sounds like it could be dicot.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > So the 16/9 sounds most dominant of the tunings. I suppose
> > the 9/5 sound would suggest there to be such a thing as a
> > "secondary dominant sound".
>
> This assumes a fixed JI scale (with 2nd = 9/8) which in
> practice is never used. So I'd be surprised if listeners
> showed any tendency to prefer the 9/5 tuning as a secondary
> dominant.
>
> -Carl

In the process of battling between the 10/9 and 9/8 notes, I find that it seems to be a dead heat. True the 10/9 corrects the minor triad on the supertonic. But when you half-cadence to the dominant, the root movement is a wolf-4th.

For a supertonic major triad, if you use the 10/9 you half to lower the raised 4th degree from 45/32 to 25/18 to avoid the pythagorean major 3rd. But if you use the 9/8, then you have to raise the 6th degree to a pythagorean to avoid a wolf 5th.

For this reason I've been continually revising the rules I wanted to follow to keep the tuning just. One of them is to use the Pythagorean tuning for root placement, which automatically puts the major 3rd of the chord on a 5-limit note. This assures that roots will move in just fifths in circle-of-fifth songs like Five Foot Two or Down Our Way.

Another more specific idea is to use Pythagorean only for the roots of major triads and 5-limit for roots of minor ones - which is really treating the minor triad as a major seventh chord whose root has stepped out for a minute.

Billy

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Apr 20, 2011 at 11:45 PM, lobawad <lobawad@...> wrote:
> >
> > Since you're hearing this as being in a temperament, what would be your guess as to the temperament or general temperament type?
>
> Sounds like it could be dicot.
>
> -Mike
>

Interesting- I'd better post this at nonoctave.com and see if the guys there even consider this "xenharmonic" at all.

On Thu, Apr 21, 2011 at 12:33 AM, lobawad <lobawad@...> wrote:
>
> Interesting- I'd better post this at nonoctave.com and see if the guys there even consider this "xenharmonic" at all.

Did I win? What was it?

-Mike

I'm going to wait for more responses- hopefully from Igliashon and Michael, as there are specific points to be addressed vis a vis (whatever that actually means :-) ) earlier posts.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Apr 21, 2011 at 12:33 AM, lobawad <lobawad@...> wrote:
> >
> > Interesting- I'd better post this at nonoctave.com and see if the guys there even consider this "xenharmonic" at all.
>
> Did I win? What was it?
>
> -Mike
>

If I had to guess EDOs, I'd say 23, owing to the combination of mild beating and solid beatlessness. Very xenharmonic and watery. Resolved? Not really, but who cares? It's got a neat sound to it.

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
> sound "resolved"? The harmonies "harmonic"?
>
> I'm really curious how the community perceptions will compare with those of "civilians".
>
> http://soundcloud.com/cameron-bobro/thistleflower-cbobro
>

That's an excellent guess- the same sneaky psychoacoustic trick that's the main ingredient here can be done just as well in 23-edo as well, nice! I'll wait for a few responses- whoops gotta run and take my kid to school.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> If I had to guess EDOs, I'd say 23, owing to the combination of mild beating and solid beatlessness. Very xenharmonic and watery. Resolved? Not really, but who cares? It's got a neat sound to it.
>
> -Igs
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
> > sound "resolved"? The harmonies "harmonic"?
> >
> > I'm really curious how the community perceptions will compare with those of "civilians".
> >
> > http://soundcloud.com/cameron-bobro/thistleflower-cbobro
> >
>

Hi Billy,

> For this reason I've been continually revising the rules I
> wanted to follow to keep the tuning just. One of them is to use
> the Pythagorean tuning for root placement, which automatically
> puts the major 3rd of the chord on a 5-limit note. This assures
> that roots will move in just fifths in circle-of-fifth songs
> like Five Foot Two or Down Our Way.

Using 1/4-comma meantone for the roots should be an improvement
for triads. When 7ths are in the mix, 12-ET is about the best
that can be done for a root tuning.

-Carl

Me> 2) I think the attitude of "theory over all else" is going too
far...and often ends up draining some emotion from music.  Some theory
is good, even necessary...it's just the attitude that theory is
everything that bugs me.

MikeB>"Says the guy who, further down in this very post, tells me that the

problem with my sus chord voicings is that there's not enough

"critical band compliance."

   Yes indeed...  I'm not contradicting myself I'm reinforcing my previous statement that "some theory
is good, even necessary".  In this case "some theory" would include not piling up multiple semitones in a single chord.  If you had, say, one semitone in the chord and one neutral tone a bit wider than the semitone...I'd consider the chord having "a bare minimum necessary amount of theory".
  Now if you want way-over-the-top too much abherence to theory...try something more like "no valid chord can have an interval smaller than 6/5 in it far as critical band and that all dyads must be within 3 cents of just.  And yet people through history have said just that sort of thing.

>"I'd be happy to collaborate myself, but I don't know how exactly you

propose to narrow it down."

  For starters, I'm thinking take all the kinds of triads within the octave (suspended, neutral, add2, minor, diminished, etc.)   Then find tetrachords that have the same feel.

>"Yeah, and I keep pointing chords and examples out where people use

chords with semitones all the time"

  My problem is not with semitones...but narrow 12EDO semitones and use of more than one of them per chord...or one of them very near IE about 9/8 away from several other tones.  It's not "unusable" but very limited in uses IE good luck using it as a point of resolve or holding it for any extended period of time without it sounding grating.

>"I'm posting these notes in ascending order, they aren't crowded within

an octave."

  Right, but G4 E5 F5 B5 C6 G6 A6 B6 still has an E-F semitone and a B C semitone regardless.  And when I said G E F C B...I mean with the same octave spacing as the above chord IE G4 E5 F5 C6 B6.  Granted...I love the chord G4 E5 F5 C6 B6...retains maybe 95% of the emotion for me with virtually none of the grating sound (thus allowing it to be more easily used in more musical contexts). :-D

Michael, I'm really curious as to your take on the little study I posted:

http://soundcloud.com/cameron-bobro/thistleflower-cbobro

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Me> 2) I think the attitude of "theory over all else" is going too
> far...and often ends up draining some emotion from music.  Some theory
> is good, even necessary...it's just the attitude that theory is
> everything that bugs me.
>
>
>
> MikeB>"Says the guy who, further down in this very post, tells me that the
>
> problem with my sus chord voicings is that there's not enough
>
> "critical band compliance."
>
>    Yes indeed...  I'm not contradicting myself I'm reinforcing my previous statement that "some theory
> is good, even necessary".  In this case "some theory" would include not piling up multiple semitones in a single chord.  If you had, say, one semitone in the chord and one neutral tone a bit wider than the semitone...I'd consider the chord having "a bare minimum necessary amount of theory".
>   Now if you want way-over-the-top too much abherence to theory...try something more like "no valid chord can have an interval smaller than 6/5 in it far as critical band and that all dyads must be within 3 cents of just.  And yet people through history have said just that sort of thing.
>
> >"I'd be happy to collaborate myself, but I don't know how exactly you
>
> propose to narrow it down."
>
>   For starters, I'm thinking take all the kinds of triads within the octave (suspended, neutral, add2, minor, diminished, etc.)   Then find tetrachords that have the same feel.
>
> >"Yeah, and I keep pointing chords and examples out where people use
>
> chords with semitones all the time"
>
>   My problem is not with semitones...but narrow 12EDO semitones and use of more than one of them per chord...or one of them very near IE about 9/8 away from several other tones.  It's not "unusable" but very limited in uses IE good luck using it as a point of resolve or holding it for any extended period of time without it sounding grating.
>
> >"I'm posting these notes in ascending order, they aren't crowded within
>
> an octave."
>
>   Right, but G4 E5 F5 B5 C6 G6 A6 B6 still has an E-F semitone and a B C semitone regardless.  And when I said G E F C B...I mean with the same octave spacing as the above chord IE G4 E5 F5 C6 B6.  Granted...I love the chord G4 E5 F5 C6 B6...retains maybe 95% of the emotion for me with virtually none of the grating sound (thus allowing it to be more easily used in more musical contexts). :-D
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
> sound "resolved"? The harmonies "harmonic"?

Yes to both questions. But I notice the piece is by some guy named Bobro. Tell him to keep up the good work for me.

  Now this piece (the Cameron Bobro piece) is weird.  The piece itself does not sound resolved to me without any thought...but everything seems to allude very strongly to 12EDO-like chords...and it's almost like I hear an after-chord echo in my mind of the standard chords playing.  So the echoed song I hear "in my head" sounds resolved...hey, some people say the best notes a musician makes are the ones the listener imagines used to fill in for a note that "is pointed to and should be there".  The overall effect is pretty solid...but not quite convincing enough for me to spread around to my friends and trust them to understand it.
   Listening to this is like viewing a painting through a tinted glass... 

--- On Thu, 4/21/11, genewardsmith <genewardsmith@...> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: Is 9-odd-limit, bizarrely enough, heard as more resolved than 7-limit?
To: tuning@yahoogroups.com
Date: Thursday, April 21, 2011, 8:32 AM

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

>

> Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions

> sound "resolved"? The harmonies "harmonic"?

Yes to both questions. But I notice the piece is by some guy named Bobro. Tell him to keep up the good work for me.

On Thu, Apr 21, 2011 at 2:28 AM, Michael <djtrancendance@...> wrote:
>
> Me> 2) I think the attitude of "theory over all else" is going too far...and often ends up draining some emotion from music.  Some theory is good, even necessary...it's just the attitude that theory is everything that bugs me.
>
> MikeB>"Says the guy who, further down in this very post, tells me that the
> problem with my sus chord voicings is that there's not enough
> "critical band compliance."
>
>    Yes indeed...  I'm not contradicting myself I'm reinforcing my previous statement that "some theory is good, even necessary".  In this case "some theory" would include not piling up multiple semitones in a single chord.  If you had, say, one semitone in the chord and one neutral tone a bit wider than the semitone...I'd consider the chord having "a bare minimum necessary amount of theory".

Right, but the point is that I have never heard, in my life, ever,
this rule that a chord can't contain more than one semitone in it.
Maybe if the semitones were right next to each other, but I could
probably make that work too. You have just arbitrarily decided it, and
now you're telling me that chords that I and others have been playing
for years are bad because they don't meet your "theory." So yes, you
are contradicting yourself, and quite blatantly as well.

The other part of it is that you can say whatever you want, but when
you start saying stuff like this then you're the guy throwing
ridiculous theoretical constraints into the picture. Just because you
want to pretend that this notion that two semitones invalidates a
chord is musical theory law doesn't actually mean it's true, or that I
care. I was turned onto these types of chords by this guy

http://en.wikipedia.org/wiki/Shelly_Berg

I doubt he'd care either.

>   Now if you want way-over-the-top too much abherence to theory...try something more like "no valid chord can have an interval smaller than 6/5 in it far as critical band and that all dyads must be within 3 cents of just.  And yet people through history have said just that sort of thing.

Overestimating someone's ability to adapt to critical band roughness
is also pretty over the top.

> >"I'd be happy to collaborate myself, but I don't know how exactly you
> propose to narrow it down."
>
>   For starters, I'm thinking take all the kinds of triads within the octave (suspended, neutral, add2, minor, diminished, etc.)   Then find tetrachords that have the same feel.

I've been working on a concept called the "simplest proper closure" of
a chord, which is the simplest proper scale that surrounds that chord.
You could also work this out with something like the simplest proper
tetrachord. The idea is that for a chord like C D E G A B, in 12-tet
the simplest proper closure would probably be C D E F G A B. The
challenge is in defining exactly what "simplest" means - is it that
you're minimizing the harmonic entropy of the scale as a whole, taken
as its own chord? Or that you're maximizing the harmonic entropy of
each subset? Or perhaps just of the triads? I don't know. All I do
know is that if you're playing C E F G A Bb C, and you don't specify a
D, it'll probably be more intuitive to stick a D natural in there
rather than Db.

> >"Yeah, and I keep pointing chords and examples out where people use
> chords with semitones all the time"
>
>   My problem is not with semitones...but narrow 12EDO semitones and use of more than one of them per chord...or one of them very near IE about 9/8 away from several other tones.  It's not "unusable" but very limited in uses IE good luck using it as a point of resolve or holding it for any extended period of time without it sounding grating.

Whatever, lol

> >"I'm posting these notes in ascending order, they aren't crowded within
> an octave."
>
>   Right, but G4 E5 F5 B5 C6 G6 A6 B6 still has an E-F semitone and a B C semitone regardless.  And when I said G E F C B...I mean with the same octave spacing as the above chord IE G4 E5 F5 C6 B6.  Granted...I love the chord G4 E5 F5 C6 B6...retains maybe 95% of the emotion for me with virtually none of the grating sound (thus allowing it to be more easily used in more musical contexts). :-D

So what if it's "grating" to you? It isn't grating to me. Sounds like
a job for acculturation.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> Right, but the point is that I have never heard, in my
> life, ever, this rule that a chord can't contain more
> than one semitone in it. Maybe if the semitones were
> right next to each other, but I could probably make that
> work too. You have just arbitrarily decided it, and now
> you're telling me that chords that I and others have been
> playing for years are bad because they don't meet your
> "theory." So yes, you are contradicting yourself, and
> quite blatantly as well.

Consecutive semitones would be a problem because you'd have
to introduce a chromatic interval. That's the same class
of problem as a false relation, which is a fairly well
established technique. Still, I found this (unsourced) in
Wikipedia: ". . . many (predominantly English) musicians
consider the device humorous owing to the false relation
which sounds unusual to the modern ear, being against the
generally accepted rules of harmony."

http://en.wikipedia.org/wiki/English_cadence

An extreme number of semitones would give us a tone
cluster, of course:

http://en.wikipedia.org/wiki/Tone_cluster

I've experimented with microtonal tone clusters based on
tripod notation. If you want to hear my experiments, why
not?

http://x31eq.com/music/chords.ogg

There's a score as well, because it originated in LilyPond:

http://x31eq.com/music/chords.pdf

Whether or not you understand the notation, there are
comments to tell you what's happening when. The electronic
sound of the "six-toed clusters" at the end is
unintentional, and probably to do with having the same
sample repeated at slightly different pitches. I don't
know what an acoustic instrument would make of them.

Graham

Graham>"Consecutive semitones would be a problem because you'd have

to introduce a chromatic interval"

   Right...but that is discussing things as far as compliance to the diatonic scale...which is not my point: my point has to do with critical band compliance.

>"You have just arbitrarily decided it, and now you're telling me that chords that I and others have been playing for years are bad because they don't meet your "theory."

   I'm not saying they are "bad"...but rather "could be a lot better" as in still maintain the same emotion without the added, ahem, critical band roughness.  Or the indirect affect of being much harder to use as point of resolve and not just points of tension.  Versatility is the key here...and a "somewhat dissonant" chord could be used as either resolve or tension...obviously something only usable for tension would be less versatile.  It's not that such a chord can't be used, but that its usability is very limited.

   Far as it being arbitrary...each semitone is near the maximum point of critical band roughness (ALA Sethares), which falls exponentially from that point (IE the difference in roughness even between 17/16 and 9/8 is huge on Sethares' graph).
  Put two of those 17/16 semitones in a chord and, well, you have to add those roughness ratings together.  My "arbitrary" theory is just a simple inference from Sethares...nothing new at all.

  If you want to prove me wrong...try composing something containing a chord with two semitones (octave equivalent tones not allowed) used within, say, a 2 octave range (typical for most composers and limits of instruments).  Even moreover, try making such a chord whose mood can not be virtually duplicated by a chord with only one semitone.  Not easy, is it?

On Thu, Apr 21, 2011 at 2:31 PM, Graham Breed <gbreed@...> wrote:
>
> Consecutive semitones would be a problem because you'd have
> to introduce a chromatic interval. That's the same class
> of problem as a false relation, which is a fairly well
> established technique.

I was thinking more along the lines of 16:17:18:19:20 being pretty
decently supported by 12-equal.

> Still, I found this (unsourced) in
> Wikipedia: ". . . many (predominantly English) musicians
> consider the device humorous owing to the false relation
> which sounds unusual to the modern ear, being against the
> generally accepted rules of harmony."
>
> http://en.wikipedia.org/wiki/English_cadence

Oh my god, that sounds terrible. Haha, man. Did this sound hip back in the day?

> I've experimented with microtonal tone clusters based on
> tripod notation. If you want to hear my experiments, why
> not?
>
> http://x31eq.com/music/chords.ogg

I like this! The dense linked 5-limit triads resolving to 7-limit
chords thing is a cool sound.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > http://en.wikipedia.org/wiki/English_cadence
>
> Oh my god, that sounds terrible. Haha, man. Did this sound
> hip back in the day?

Oh yeah, well, all the R&B you posted to facebook
sounds terrible. How do you like them apples! -C.

In ET I'm afraid but this one has always moved me. Gould
understood the depth of this music
http://www.youtube.com/watch?v=L4a-bn8AK3U&NR

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I vote the meantone is quite a bit richer to me. Lovely piece.
>
> Thanks for the link.

The examples on Wikipedia are in 12-tET. This choral-specific voice leading would be a prime example of something that certainly would not be performed in 12-tET in actual practice. It doesn't sound so cheesey in real life. With a choir doing it seriously, I mean. With instruments in 12-tET it reminds me of Monty Python.

The Corelli "clash" cadence, which we've all heard many a time, linked from that page also sounds good intoned in "real life".

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > > http://en.wikipedia.org/wiki/English_cadence
> >
> > Oh my god, that sounds terrible. Haha, man. Did this sound
> > hip back in the day?
>
> Oh yeah, well, all the R&B you posted to facebook
> sounds terrible. How do you like them apples! -C.
>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Returning to the original topic of "resolution", and apropos what Igliashon is doing with "xenharmonic" tunings, and some aspects of "tuning theory" in general, here's a little ditty. Do the resolutions
> > sound "resolved"? The harmonies "harmonic"?
>
> Yes to both questions. But I notice the piece is by some guy named Bobro. Tell him to keep up the good work for me.
>

That bastard owes me 20 Euros, but I'll tell him. :-)

I also hear the resolutions as pretty darn resolved, and the harmonious as oddly harmonic. This is the "civilian" response so far, by the way, to this and other more radical examples.

The tuning is 13 equal divisions of the octave. In order to be scanned in terms of "5-limit" tertian harmony, you'd have to accept a 741 cent "fifth", as I deliberately avoided the 16/11-ish interval of 13-edo as a "fifth". Most definitely not meantone, but there is a related feeling which will take some explaining.

There is a kind of temperament you recently posted to the xenwiki, can't remember the name, that is related to what's going on here, because you're taking things like a 9/7 within a 9/5 as the "root position principle triad".

Unfortunately I don't have time for anything in detail, and won't have for a good week or more.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> The examples on Wikipedia are in 12-tET. This choral-specific voice leading would be a prime example of something that certainly would not be performed in 12-tET in actual practice. It doesn't sound so cheesey in real life. With a choir doing it seriously, I mean. With instruments in 12-tET it reminds me of Monty Python.
>
> The Corelli "clash" cadence, which we've all heard many a time, linked from that page also sounds good intoned in "real life".

Sheppard has dissonance all over the place and still manages to sound very cool indeed.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> There is a kind of temperament you recently posted to the xenwiki, can't remember the name, that is related to what's going on here, because you're taking things like a 9/7 within a 9/5 as the "root position principle triad".

Terrain. But that's an ultra-ultra-super accurate temperament tempering out the landscape comma.

lobawad>"The tuning is 13 equal divisions of the octave. In order to be scanned
in terms of "5-limit" tertian harmony, you'd have to accept a 741 cent
"fifth", as I deliberately avoided the 16/11-ish interval of 13-edo as a
"fifth". Most definitely not meantone, but there is a related feeling
which will take some explaining."

   Still, it feels very "skewed 12TET".  I had the same experience listening to my attempts to compose in 13TET. 

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> lobawad>"The tuning is 13 equal divisions of the octave. In order to be scanned
> in terms of "5-limit" tertian harmony, you'd have to accept a 741 cent
> "fifth", as I deliberately avoided the 16/11-ish interval of 13-edo as a
> "fifth". Most definitely not meantone, but there is a related feeling
> which will take some explaining."
>
>    Still, it feels very "skewed 12TET".  I had the same experience listening to my attempts to compose in 13TET. 
>

Many times I find very big differences in perceptions between those in the online microtonal community and those out here in physical life. Others like myself don't seem to making the connection between 12-tET and things like 0-462-831 vertical sonorities in harmonic movement impossible in 12-tET.

But I'm intrigued as to how it's possible that you're hearing "skewed 12TET". Mike also heard "detuned 5-limit", which would imply some pretty odd temperament- tempering out the difference between an augmented fifth and a fifth, but not between a "major" and "minor" third, the fifth cycling to a fourth rather than a ditone... when I get time I'll have to cruise through it and figure out possible reasons as to why it could sound that way to some people.

lobawad>"temperament- tempering out the difference between an augmented fifth and
a fifth, but not between a "major" and "minor" third, the fifth cycling
to a fourth rather than a ditone."

   Hmm...well the 13TET fifth actually sounds more to me like 3/2 than 14/9 and the area around it while the major third seems closer to 5/4 than, say 11/9.  The minor seventh is weird because it seems nearer 9/5 than 12TET's 16/9...but 9/5 is the JI-diatonic-like ratio.  Simply put, I think 13TET has a lot of ratios which are far away from any "stable" ratios, but much safely far from the more sour areas (IE 20/11) causing them to easily get "sucked in" to the nearest 5-limit fields of attraction...such as 5/4.  Granted though, 13TET has a lot of "not sound in 12TET or any of tuning" sour spots, like the ratio near 13/8 and the fact the fifth around 23/15 is grossly off (IE yes, it falls into 3/2's field of attraction, but needs to be balanced out by strong dyads in a chord to really feel like anything solid).

--- On Fri, 4/22/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@yahoo.com>
Subject: [tuning] Re: Is 9-odd-limit, bizarrely enough, heard as more resolved than 7-limit?
To: tuning@yahoogroups.com
Date: Friday, April 22, 2011, 9:33 AM

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>

> lobawad>"The tuning is 13 equal divisions of the octave. In order to be scanned

> in terms of "5-limit" tertian harmony, you'd have to accept a 741 cent

> "fifth", as I deliberately avoided the 16/11-ish interval of 13-edo as a

> "fifth". Most definitely not meantone, but there is a related feeling

> which will take some explaining."

>

>    Still, it feels very "skewed 12TET".  I had the same experience listening to my attempts to compose in 13TET. 

>

Many times I find very big differences in perceptions between those in the online microtonal community and those out here in physical life. Others like myself don't seem to making the connection between 12-tET and things like 0-462-831 vertical sonorities in harmonic movement impossible in 12-tET.

But I'm intrigued as to how it's possible that you're hearing "skewed 12TET". Mike also heard "detuned 5-limit", which would imply some pretty odd temperament- tempering out the difference between an augmented fifth and a fifth, but not between a "major" and "minor" third, the fifth cycling to a fourth rather than a ditone... when I get time I'll have to cruise through it and figure out possible reasons as to why it could sound that way to some people.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> lobawad>"temperament- tempering out the difference between an augmented fifth and
> a fifth, but not between a "major" and "minor" third, the fifth cycling
> to a fourth rather than a ditone."
>
>    Hmm...well the 13TET fifth actually sounds more to me like 3/2 than 14/9 and the area around it while the major third seems closer to 5/4 than, say 11/9.  The minor seventh is weird because it seems nearer 9/5 than 12TET's 16/9...but 9/5 is the JI-diatonic-like ratio.  Simply put, I think 13TET has a lot of ratios which are far away from any "stable" ratios, but much safely far from the more sour areas (IE 20/11) causing them to easily get "sucked in" to the nearest 5-limit fields of attraction...such as 5/4.  Granted though, 13TET has a lot of "not sound in 12TET or any of tuning" sour spots, like the ratio near 13/8 and the fact the fifth around 23/15 is grossly off (IE yes, it falls into 3/2's field of attraction, but needs to be balanced out by strong dyads in a chord to really feel like anything solid).
>

This piece is absolutely lathered in the 831-cent interval, like a good deal of my music is and I find a big discrepancy between "pretty!" and and "sour".

On Thu, Apr 21, 2011 at 4:37 PM, Michael <djtrancendance@...> wrote:
>
>    I'm not saying they are "bad"...but rather "could be a lot better" as in still maintain the same emotion without the added, ahem, critical band roughness.  Or the indirect affect of being much harder to use as point of resolve and not just points of tension.  Versatility is the key here...and a "somewhat dissonant" chord could be used as either resolve or tension...obviously something only usable for tension would be less versatile.  It's not that such a chord can't be used, but that its usability is very limited.

I disagree.

>    Far as it being arbitrary...each semitone is near the maximum point of critical band roughness (ALA Sethares), which falls exponentially from that point (IE the difference in roughness even between 17/16 and 9/8 is huge on Sethares' graph).
>   Put two of those 17/16 semitones in a chord and, well, you have to add those roughness ratings together.  My "arbitrary" theory is just a simple inference from Sethares...nothing new at all.

To hell with that.

>   If you want to prove me wrong...try composing something containing a chord with two semitones (octave equivalent tones not allowed) used within, say, a 2 octave range (typical for most composers and limits of instruments).

http://www.youtube.com/watch?v=RW6WqgvYHgc

> Even moreover, try making such a chord whose mood can not be virtually duplicated by a chord with only one semitone.  Not easy, is it?

Who cares if it can't be duplicated?

-Mike

On Fri, Apr 22, 2011 at 1:36 PM, lobawad <lobawad@...> wrote:
>
> This piece is absolutely lathered in the 831-cent interval, like a good deal of my music is and I find a big discrepancy between "pretty!" and and "sour".

In the 13-tet example you just posted, were you using a 738 cent fifth
and a 369 cent major third? Or were you using the 462 cent interval as
a major third?

-Mike