Yahoo Tuning Groups Ultimate Backup tuning Practical collections of tempered intervals

Mike, I think you rocket off onto Life, The Universe, and Everything tangents too quickly.

The question is, "why not use Blackjack or Wizard(22)?" and I am answering that.

We are talking about practical music-making.

41-tET is close enough to Just for me, when using tall rational sonorities (up to the eleventh partial).

I am talking specifically about extending Western tradition here- for "xenharmonic" music I use other systems (and that is where I do most of my work).

I distinguish between dominant seventh chords and natural seventh chords. They are distinguished by function and tonal tendency, and these are tied to each other and to the absolute tuning of the chords.

I use both dominant and natural seventh chords. So even in a downright conventional piece I need the pitch set I use to give me intervals distinguishing between 7/6 and 6/5 in several places at least.

Surely you see the potential problems with these "practical subsets" of larger systems now? Just try it yourself and you will see that the simplest things will result in requiring clusters-and-gaps of intervals, the very thing that the elegantly spaced MOS scales avoid.

🔗gbreed@...

The question is about 22 notes of Magic (the haizhou scale) scale. Blackjack won't give complete chords so disregard it. Wizard was a mistake. The candidate is Magic.

Randomly suggesting desirable features as if every fool knows they lead to problems isn't good enough. I've done everything you describe in Magic and it works.

Another candidate would be Orwell. Perhaps we could consider that were you to come up with intelligent arguments against Magic.

Graham

------Original message------
From: lobawad <lobawad@yahoo.com>
To: <tuning@yahoogroups.com>
Date: Monday, February 6, 2012 12:04:28 PM GMT-0000
Subject: [tuning] Practical collections of tempered intervals

Mike, I think you rocket off onto Life, The Universe, and Everything tangents too quickly.

The question is, "why not use Blackjack or Wizard(22)?" and I am answering that.

We are talking about practical music-making.

41-tET is close enough to Just for me, when using tall rational sonorities (up to the eleventh partial).

I am talking specifically about extending Western tradition here- for "xenharmonic" music I use other systems (and that is where I do most of my work).

------------------------------------

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🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> The question is about 22 notes of Magic (the haizhou scale) scale. Blackjack won't give complete chords so disregard it. Wizard was a mistake. The candidate is Magic.
>
> Randomly suggesting desirable features as if every fool knows they lead to problems isn't good enough. I've done everything you describe in Magic and it works.
>
> Another candidate would be Orwell. Perhaps we could consider that were you to come up with intelligent arguments against Magic.
>
>
> Graham
>

Are you actually following this conversation? I find this hard to believe, for if you were, you would know that I am not "randomly suggesting desirable features". Gene asked if I would extend the little piece I made, and I am explaining the features that I would need to do so! They are not "random features", they are features that are already present in the little bit I made.

And I am not arguing against temperaments, where did get that idea? I am talking about the MOSs derived from them. I am talking about the practicalities of making music.

Magic 22 might work... nope, there is no cluster of 1° of 41. "Fa" is pitched 3 ways (comma altered) in the example I gave, see? But I might be able to take Magic22 and add a couple of pitches. This is how I work with Wuerschmidt- get an MOS and add in a few missing pitches.

🔗gbreed@...

The message I replied to started a new thread. There was no conversation to follow.

I've noticed in other threads that you tend to insult people and move the goalposts.

Graham

------Original message------
From: lobawad <lobawad@...>
To: <tuning@yahoogroups.com>
Date: Monday, February 6, 2012 2:53:27 PM GMT-0000
Subject: [tuning] Re: Practical collections of tempered intervals

And I am not arguing against temperaments, where did get that idea? I am talking about the MOSs derived from them. I am talking about the practicalities of making music.

------------------------------------

🔗genewardsmith <genewardsmith@...>

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

> I use both dominant and natural seventh chords. So even in a downright conventional piece I need the pitch set I use to give me intervals distinguishing between 7/6 and 6/5 in several places at least.

6/5 is fairly complex in miracle--twice as complex, at 16, as 7/6. But even so there are plenty of minor thirds. Wizard is similar. If you can't get enough of 6/5, you could always try catakleismic, I suppose, but since 41edo is well enough in tune for you and you also want 7/6, what about orwell?

Some spectrums (lowest to highest complexity)

Miracle: 8/7, 11/9, 7/5, 4/3, 5/4, 7/6, 12/11, 9/8, 6/5, 9/7, 11/8, 14/11, 10/9, 11/10
Wizard: 5/4, 11/10, 9/7, 11/8, 7/6, 4/3, 6/5, 12/11, 8/7, 7/5, 9/8, 10/9, 14/11, 11/9
Catakleismic: 6/5, 5/4, 4/3, 10/9, 9/7, 9/8, 7/6, 7/5, 11/8, 8/7, 11/10, 12/11, 11/9, 14/11
Orwell: 7/6, 11/8, 5/4, 12/11, 11/10, 14/11, 9/7, 4/3, 8/7, 6/5, 7/5, 11/9, 9/8, 10/9

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 6, 2012 at 7:04 AM, lobawad <lobawad@...> wrote:
>
> Mike, I think you rocket off onto Life, The Universe, and Everything tangents too quickly.

No offense, but I think this statement is rude. And I'm not sure what
specifically you think is a "tangent," because you didn't quote the
thing you're claiming is tangential to your point.

> The question is, "why not use Blackjack or Wizard(22)?" and I am answering that.
>
> We are talking about practical music-making.

I was hopefully talking about getting you to release a version of your
example which "completed" the relevant JI chords, so we could all hear
how they're not out of tune 5-limit things but are upper structures of
other, more complete chords.

> 41-tET is close enough to Just for me, when using tall rational sonorities (up to the eleventh partial).

OK, well I think the 5-limit in 41-EDO is pretty good. I can hear it's
not perfectly just, but to me it makes sense to call a type of
slightly tempered 4:5:6, from a purely intonational standpoint.

> I distinguish between dominant seventh chords and natural seventh chords. They are distinguished by function and tonal tendency, and these are tied to each other and to the absolute tuning of the chords.

If you sometimes hear a different function and tonal tendency, that's
fine, but I hope you can admit there are times when one can substitute
for the other.

> Surely you see the potential problems with these "practical subsets" of larger systems now? Just try it yourself and you will see that the simplest things will result in requiring clusters-and-gaps of intervals, the very thing that the elegantly spaced MOS scales avoid.

Yes, this is why I typically like to use EDOs. But, I think 22-EDO is
great in the 11-limit, because my tolerance for error is apparently
much higher than yours. How do you feel about 31-EDO for the 11 or
13-limit?

-Mike

🔗genewardsmith <genewardsmith@...>

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

> > 41-tET is close enough to Just for me, when using tall rational sonorities (up to the eleventh partial).
>
> OK, well I think the 5-limit in 41-EDO is pretty good. I can hear it's
> not perfectly just, but to me it makes sense to call a type of
> slightly tempered 4:5:6, from a purely intonational standpoint.

If 41 is close enough for you, then as Graham pointed out, you might consider Magic[19] or Magic[22].

http://xenharmonic.wikispaces.com/Chords+of+magic

Spectrum: 5/4, 9/7, 6/5, 4/3, 7/6, 11/8, 11/10, 10/9, 9/8, 7/5, 8/7, 12/11, 11/9, 14/11

🔗gbreed@...

Finding tempered scales with consecutive syntonic commas (81:80) is an interesting problem. (More general commas equal to one degree of 41 less so. Blackjack does it.)

For any rank two temperament, you can add 81:80 to the kernel. If 81:80 wasn't already tempered out, what you get will be an equal temperament. It will also be a meantone, or a contorted meantone.

Now, we want a scale of less than 24 notes to the octave. This means the syntonic comma must have a complexity less than twelve. That complexity equals the number of steps in the equal temperament above.

The upshot of all this is that the meantone ET that belongs to our hypothetical temperament class must have less than twelve notes. It's difficult to see how an accurate temperament can belong to such a class.

A notable exception is Porcupine. But it's still way less accurate than 41.

With roughly the TE error of 41 as a cutoff, the leading candidates are called Bunya, Hitchcock, Pluto, and Monkey.

Bunya is a 41&34

Graham

And I am not arguing against temperaments, where did get that idea? I am talking about the MOSs derived from them. I am talking about the practicalities of making music.

------------------------------------

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 6, 2012 at 7:04 AM, lobawad <lobawad@...> wrote:
> >
> > Mike, I think you rocket off onto Life, The Universe, and Everything tangents too quickly.
>
> No offense, but I think this statement is rude. And I'm not sure what
> specifically you think is a "tangent," because you didn't quote the
> thing you're claiming is tangential to your point.

If you are going to flag rudeness, do it consistently.

>
> > The question is, "why not use Blackjack or Wizard(22)?" and I am answering that.
> >
> > We are talking about practical music-making.
>
> I was hopefully talking about getting you to release a version of your
> example which "completed" the relevant JI chords, so we could all hear
> how they're not out of tune 5-limit things but are upper structures of
> other, more complete chords.

But those are complete JI chords. Maybe the timbre is throwing you off- if I do get around to extending the piece, I'll use smoother (but with plenty of partials) timbres.

>
> > 41-tET is close enough to Just for me, when using tall rational sonorities (up to the eleventh partial).
>
> OK, well I think the 5-limit in 41-EDO is pretty good. I can hear it's
> not perfectly just, but to me it makes sense to call a type of
> slightly tempered 4:5:6, from a purely intonational standpoint.

I think taller chords in 41 are pretty darn rational sounding- not perfect, but they pretty much "do that thing". Out here in real life my experience is that people recognize the similarity, assuming that I am correct in assessing some very consistent and similar associative descriptions people use as being specifically descriptive of rational intervals: ancient, old-fashioned, church/choir, sleepy, etc.

>
> > I distinguish between dominant seventh chords and natural seventh chords. They are distinguished by function and tonal tendency, and these are tied to each other and to the absolute tuning of the chords.
>
> If you sometimes hear a different function and tonal tendency, that's
> fine, but I hope you can admit there are times when one can substitute
> for the other.

:facepalm: I just got through explaining how I need so many pitches in 41 because I use the harmonic seventh in some places and the "5-limit" in others. And of course they can straight out substitute for one another across the board, in certain kinds of music that are eccentric of mainstream Western tonal music, I already said that.

>
> > Surely you see the potential problems with these "practical subsets" of larger systems now? Just try it yourself and you will see that the simplest things will result in requiring clusters-and-gaps of intervals, the very thing that the elegantly spaced MOS scales avoid.
>
> Yes, this is why I typically like to use EDOs. But, I think 22-EDO is
> great in the 11-limit, because my tolerance for error is apparently
> much higher than yours. How do you feel about 31-EDO for the 11 or
> 13-limit?

31-edo for the 11th and 13th partial? I don't know, have to check that out. I don't feel any "11-ness" to 22-edo at all, nor particularly 3 or 5 for that matter, it's pretty overwhelmingly 7th partial sounding to me. At least, the stuff I have heard.

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 6, 2012 at 5:47 PM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > No offense, but I think this statement is rude. And I'm not sure what
> > specifically you think is a "tangent," because you didn't quote the
> > thing you're claiming is tangential to your point.
>
> If you are going to flag rudeness, do it consistently.

I think I'm pretty consistent with that.

> > > The question is, "why not use Blackjack or Wizard(22)?" and I am answering that.
> > >
> > > We are talking about practical music-making.
> >
> > I was hopefully talking about getting you to release a version of your
> > example which "completed" the relevant JI chords, so we could all hear
> > how they're not out of tune 5-limit things but are upper structures of
> > other, more complete chords.
>
> But those are complete JI chords. Maybe the timbre is throwing you off- if I do get around to extending the piece, I'll use smoother (but with plenty of partials) timbres.

What do you mean complete JI chords? They're only 3 notes, I thought,
and a complete 11-limit otonal chord is 6 notes. What were the chords
you're using?

> > OK, well I think the 5-limit in 41-EDO is pretty good. I can hear it's
> > not perfectly just, but to me it makes sense to call a type of
> > slightly tempered 4:5:6, from a purely intonational standpoint.
>
> I think taller chords in 41 are pretty darn rational sounding- not perfect, but they pretty much "do that thing". Out here in real life my experience is that people recognize the similarity, assuming that I am correct in assessing some very consistent and similar associative descriptions people use as being specifically descriptive of rational intervals: ancient, old-fashioned, church/choir, sleepy, etc.

I hear that pretty well for just 4:5:6.

> > If you sometimes hear a different function and tonal tendency, that's
> > fine, but I hope you can admit there are times when one can substitute
> > for the other.
>
> :facepalm: I just got through explaining how I need so many pitches in 41 because I use the harmonic seventh in some places and the "5-limit" in others. And of course they can straight out substitute for one another across the board, in certain kinds of music that are eccentric of mainstream Western tonal music, I already said that.

It seemed like you were saying that 4:5:6:7 chords didn't have the
same tonal or dominant "function" as dominant 7 chords, and that this
was something you expected was heard naturally by everyone. If that's
not what you were saying, then I take it back.

> > Yes, this is why I typically like to use EDOs. But, I think 22-EDO is
> > great in the 11-limit, because my tolerance for error is apparently
> > much higher than yours. How do you feel about 31-EDO for the 11 or
> > 13-limit?
>
> 31-edo for the 11th and 13th partial? I don't know, have to check that out. I don't feel any "11-ness" to 22-edo at all, nor particularly 3 or 5 for that matter, it's pretty overwhelmingly 7th partial sounding to me. At least, the stuff I have heard.

-Mike

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> Finding tempered scales with consecutive syntonic commas (81:80) is an interesting problem. (More general commas equal to one degree of 41 less so. Blackjack does it.)
>
> For any rank two temperament, you can add 81:80 to the kernel. If 81:80 wasn't already tempered out, what you get will be an equal temperament. It will also be a meantone, or a contorted meantone.
>
> Now, we want a scale of less than 24 notes to the octave. This means the syntonic comma must have a complexity less than twelve. That complexity equals the number of steps in the equal temperament above.
>
> The upshot of all this is that the meantone ET that belongs to our hypothetical temperament class must have less than twelve notes. It's difficult to see how an accurate temperament can belong to such a class.
>
> A notable exception is Porcupine. But it's still way less accurate than 41.
>
> With roughly the TE error of 41 as a cutoff, the leading candidates are called Bunya, Hitchcock, Pluto, and Monkey.
>
> Bunya is a 41&34

Not rodan? Rodan[21] seems pretty great, and is significantly more accurate than 41.

It doesn't have any complete 11-limit hexads, but it has:
3 complete 9-limit pentads
4 8:9:10:12 chords
5 8:11:12:14 chords
and of course 2.3.7 harmony up the wazoo, because of 1029/1024.

And it has buttloads of 81/80 in a row.

Keenan

🔗lobawad <lobawad@...>

🔗gbreed@...

Yes, Rodan should have been there. I made a sign error. The true list is Rodan, Bunya, Hitchcock, Pluto, Monkey, Buzzard

Graham

------Original message------
From: Keenan Pepper <keenanpepper@...>
To: <tuning@yahoogroups.com>
Date: Wednesday, February 8, 2012 2:07:35 AM GMT-0000
Subject: [tuning] Re: Practical collections of tempered intervals

Not rodan? Rodan[21] seems pretty great, and is significantly more accurate than 41.

It doesn't have any complete 11-limit hexads, but it has:
3 complete 9-limit pentads
4 8:9:10:12 chords
5 8:11:12:14 chords
and of course 2.3.7 harmony up the wazoo, because of 1029/1024.

And it has buttloads of 81/80 in a row.

Keenan

------------------------------------

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> >
> > Not rodan? Rodan[21] seems pretty great, and is significantly more accurate than 41.
> >
> > It doesn't have any complete 11-limit hexads, but it has:
> > 3 complete 9-limit pentads
> > 4 8:9:10:12 chords
> > 5 8:11:12:14 chords
> > and of course 2.3.7 harmony up the wazoo, because of 1029/1024.
> >
> > And it has buttloads of 81/80 in a row.
> >
> > Keenan
> >
>
> "Rodan(26)" has many possibilities. But it would cause odd comma shifts for me, equating 290 cents with 314 for example.

I have no idea what you mean by this. Rodan does not equate "290 cents" with "314 cents". That doesn't even make sense to say.

Rodan equates certain JI intervals with each other, because it's a regular temperament. But "290 cents" is not an interval of a regular temperament at all, it's just a specific interval size.

Keenan

🔗lobawad <lobawad@...>

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

> >
> > "Rodan(26)" has many possibilities. But it would cause odd comma shifts for me, equating 290 cents with 314 for example.
>
> I have no idea what you mean by this. Rodan does not equate "290 cents" with "314 cents". That doesn't even make sense to say.
>
> Rodan equates certain JI intervals with each other, because it's a regular temperament. But "290 cents" is not an interval of a regular temperament at all, it's just a specific interval size.
>
> Keenan
>

I did not say Ronan. I said Ronan(26). "Ronan(26)" and "Ronan Temperament" are not the same thing.

Now, keeping in mind that I have been talking about altering "seventh chords" between harmonic form and "5-limit" form, make some music using one of these Rodan subsets and see what happens.

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > >
> > > "Rodan(26)" has many possibilities. But it would cause odd comma shifts for me, equating 290 cents with 314 for example.
> >
> > I have no idea what you mean by this. Rodan does not equate "290 cents" with "314 cents". That doesn't even make sense to say.
> >
> > Rodan equates certain JI intervals with each other, because it's a regular temperament. But "290 cents" is not an interval of a regular temperament at all, it's just a specific interval size.
> >
> > Keenan
> >
>
> I did not say Ronan. I said Ronan(26). "Ronan(26)" and "Ronan Temperament" are not the same thing.
>
> Now, keeping in mind that I have been talking about altering "seventh chords" between harmonic form and "5-limit" form, make some music using one of these Rodan subsets and see what happens.
>

That's Rodan, not Ronan, of course. I'm all jacked up on Wraith enzymes and tend to make these kinds of errors, LOL.

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> > Rodan equates certain JI intervals with each other, because it's a regular temperament. But "290 cents" is not an interval of a regular temperament at all, it's just a specific interval size.
> >
> > Keenan
> >
>
> I did not say Ronan. I said Ronan(26). "Ronan(26)" and "Ronan Temperament" are not the same thing.
>
> Now, keeping in mind that I have been talking about altering "seventh chords" between harmonic form and "5-limit" form, make some music using one of these Rodan subsets and see what happens.

I still don't get what you're talking about at all.

How does it make sense to say that any rodan scale equates "290 cents" with "314 cents"? 314 cents is 24 cents larger than 290 cents. They're always different.

Keenan

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> > > Rodan equates certain JI intervals with each other, because it's a regular temperament. But "290 cents" is not an interval of a regular temperament at all, it's just a specific interval size.
> > >
> > > Keenan
> > >
> >
> > I did not say Ronan. I said Ronan(26). "Ronan(26)" and "Ronan Temperament" are not the same thing.
> >
> > Now, keeping in mind that I have been talking about altering "seventh chords" between harmonic form and "5-limit" form, make some music using one of these Rodan subsets and see what happens.
>
> I still don't get what you're talking about at all.
>
> How does it make sense to say that any rodan scale equates "290 cents" with "314 cents"? 314 cents is 24 cents larger than 290 cents. They're always different.
>
> Keenan
>

Simply write in Rodan(26) using tetrads and imitative counterpoint and you will see what I mean. The collection of pitches offered, in terms of scale steps, conflates minor thirds with major and with the ditone- altering between different tetrads as I do, the real life effect is going to be that of minor thirds of 290 cents here and 314 cents there. That of course is what happens when I use this set of pitches. For anyone using Rodan(26), though, the set of pitches will create what sounds like commatic shifts. Unlike the commatic shifts I do with 41-edo for example, these will not sound purposeful, unless the composer surrenders themselves completely to the set of given pitches and goes with IT'S flow. Which is fine, but is backwards of the approach of those microtonalists who conceive of the music first, then find or make the tuning to fit.

🔗genewardsmith <genewardsmith@...>

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

> Simply write in Rodan(26) using tetrads and imitative counterpoint and you will see what I mean. The collection of pitches offered, in terms of scale steps, conflates minor thirds with major and with the ditone- altering between different tetrads as I do, the real life effect is going to be that of minor thirds of 290 cents here and 314 cents there.

It puts 317 cent minor thirds into the same class as 414 cent 14/11 style undecimal major thirds, and 290 cent 13/11 style tridecimal minor thirds into the same class as classic 386 cent major thirds. The first is a double circle, the second a complete circle, all of thirds. Rodan[26] is great; I recommend it.

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > Simply write in Rodan(26) using tetrads and imitative counterpoint and you will see what I mean. The collection of pitches offered, in terms of scale steps, conflates minor thirds with major and with the ditone- altering between different tetrads as I do, the real life effect is going to be that of minor thirds of 290 cents here and 314 cents there.
>
> It puts 317 cent minor thirds into the same class as 414 cent 14/11 style undecimal major thirds, and 290 cent 13/11 style tridecimal minor thirds into the same class as classic 386 cent major thirds. The first is a double circle, the second a complete circle, all of thirds. Rodan[26] is great; I recommend it.
>

If you roll with it, it is groovy- the harmonic tetrad is very good and the way the intervals alternate, which is the very flaw in light of the approach I was talking about before, becomes not a flaw but a feature. So it bombs according to one modality but that doesn't mean it's not good in another.

I think the obvious comparison, practically speaking, is 26 equal divisions of the octave. But that's a whole different ball of wax. After working with 26-edo a lot, I think 26-edo is all about the 7th partial, I even use a pure 8/7 as generator. By that I mean that whatever you do in 26-edo, it tends toward sounding like one big 7th partial languid twang.