Trying to figure out how microtonal music works is like early man trying to find patterns in the stars

Originally posted this on metatuning, but got a few offlist pm's to repost
it here, so here it is:

It's so frustrating. I've been a member of this list for like 3 years
now and I still don't understand what's going on at all - and that's after
reading tons of very insightful material generously referenced my way. I've
learned
a ton of math, a bunch about temperaments, tons about harmonic entropy
and psychoacoustics, how to map things into a paradigm regularly, and
so on and so forth -- but I have still yet to figure out how to just
write expressive, emotional music with anything other than 12-tet that
doesn't sound "weird."

If we have all of these "rules" to stop things from sounding "weird"
in 12-tet -- why can't we come up with them for microtonal music as
well? Is it just such a new movement that the big picture hasn't been
figured out yet, or is it that it has, and I just have missed it? Is there
some required reading

OK, the cliffnotes:
- I V IV I is a beautiful progression
- I ii bVII I is also
- In general, there are tons of amazing sounding 5-limit progressions
- My experiments to extend this and come up with intuitive, emotional,
aesthetically pleasing 7 and 11-limit progressions have basically
failed
- Does anyone see the big picture of all of this yet, and of how chord
progressions work in general?
- Did I miss something?

Sincerely,
A frustrated Mike Battaglia

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

> OK, the cliffnotes:
> - I V IV I is a beautiful progression
> - I ii bVII I is also
> - In general, there are tons of amazing sounding 5-limit
> progressions
> - My experiments to extend this and come up with intuitive,
> emotional, aesthetically pleasing 7 and 11-limit progressions
> have basically failed
> - Does anyone see the big picture of all of this yet, and of
> how chord progressions work in general?
> - Did I miss something?
>
> Sincerely,
> A frustrated Mike Battaglia

I don't remember this post from MMM, but probably I replied
with advice diametrically opposite what I'm about to say.

First of all, focus on 22. I would approach it the same
way you learned 12-ET. First learn to play (on a remapped
Halberstadt, or AXiS or Opal keyboard if you can afford it)
or score (in some notation system of your choice) all
inversions of the otonal and utonal 7th chords.

Then learn all 2-chord progressions between these which
involve a common dyad. Then all 2-chord progressions
between them involving a single common pitch.

Then learn to play or score the pentachordal major, minor,
and symmetrical major & minor decatonic scales. If playing,
play them ascending, descending, and in contrary motion.
If scoring, try writing contrary motion and then figuring
out which JI dyads are formed.

Then you should be able to string chord progressions
together and improvise decatonic melodies on top. And
practice SATB voicings in notation.

Give yourself a year in 22 and if it doesn't work, try a
different tuning. But I'm pretty sure it'll work.

-Carl

> I don't remember this post from MMM, but probably I replied
> with advice diametrically opposite what I'm about to say.

Hahaha! No, it was on metatuning, and only got a reply and a few offlist emails.

> First of all, focus on 22. I would approach it the same
> way you learned 12-ET. First learn to play (on a remapped
> Halberstadt, or AXiS or Opal keyboard if you can afford it)
> or score (in some notation system of your choice) all
> inversions of the otonal and utonal 7th chords.
>
> Then learn all 2-chord progressions between these which
> involve a common dyad. Then all 2-chord progressions
> between them involving a single common pitch.
>
> Then learn to play or score the pentachordal major, minor,
> and symmetrical major & minor decatonic scales. If playing,
> play them ascending, descending, and in contrary motion.
> If scoring, try writing contrary motion and then figuring
> out which JI dyads are formed.
>
> Then you should be able to string chord progressions
> together and improvise decatonic melodies on top. And
> practice SATB voicings in notation.
>
> Give yourself a year in 22 and if it doesn't work, try a
> different tuning. But I'm pretty sure it'll work.
>
> -Carl

22... Never thought about that. I've always been terrified of it
because the fifths are so far out, but what you say makes sense.
Hopefully I'll have more luck than with 31-tet and 72-tet.

I think I also need to figure out exactly how "temperament" works -
22-tet makes 16/9 and 7/4 the same thing, and I haven't quite sorted
out what exactly that means, musically.

Thanks for the advice,
Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> 22... Never thought about that. I've always been terrified of it
> because the fifths are so far out, but what you say makes sense.
> Hopefully I'll have more luck than with 31-tet and 72-tet.
>
> I think I also need to figure out exactly how "temperament" works -
> 22-tet makes 16/9 and 7/4 the same thing, and I haven't quite
> sorted out what exactly that means, musically.
>
> Thanks for the advice,
> Mike

I thought you read Paul's 22 paper

http://lumma.org/tuning/erlich/erlich-decatonic.pdf

?

It describes the decatonic scales I mentioned, and tells you
how the tetrads work in a way analogous to the triads of the
diatonic scale. It even shows how to do 11-limit extensions,
much like jazz extends the triads of the diatonic scale.

These decatonic scales belong to what we now call the pajara
temperament. It's definitely the best temperament for what
you're trying to do -- functional 7-limit harmony. Moreover,
12 is a pajara system, and it's been suggested that many
jazz standards are actually using it.

But there are other temperaments. In 31, there are 7-limit
meantone extensions that'll let you leverage the skills you
already have. In 72 there's miracle[10], the decatonic
miracle scale. And many others in 31 and 72. You just have
to know where to look. That's the point of the theory of
regular temperaments... otherwise these large scales can be
completely daunting.

-Carl

Hi Carl,

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

> It describes the decatonic scales I mentioned, and tells you
> how the tetrads work in a way analogous to the triads of the
> diatonic scale. It even shows how to do 11-limit extensions,
> much like jazz extends the triads of the diatonic scale.

Where does it show such a thing? 11-limit chords cannot be formed
from decatonic scales, some notes must be "chromatically" altered.

> These decatonic scales belong to what we now call the pajara
> temperament. It's definitely the best temperament for what
> you're trying to do -- functional 7-limit harmony. Moreover,
> 12 is a pajara system, and it's been suggested that many
> jazz standards are actually using it.

That's interesting! Who has suggested this?

Kalle Aho

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

> > It describes the decatonic scales I mentioned, and tells you
> > how the tetrads work in a way analogous to the triads of the
> > diatonic scale. It even shows how to do 11-limit extensions,
> > much like jazz extends the triads of the diatonic scale.
>
> Where does it show such a thing? 11-limit chords cannot be formed
> from decatonic scales, some notes must be "chromatically" altered.

Right. See pg.14 in this PDF

http://lumma.org/tuning/erlich/erlich-decatonic.pdf

> > These decatonic scales belong to what we now call the pajara
> > temperament. It's definitely the best temperament for what
> > you're trying to do -- functional 7-limit harmony. Moreover,
> > 12 is a pajara system, and it's been suggested that many
> > jazz standards are actually using it.
>
> That's interesting! Who has suggested this?

I forget. Was it George Secor or Keenan Pepper?

-Carl

I find Walter Mathieu's book Harmonic Experience provides a very helpful perspective on all this

Steve
 
 

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Mon, 8 February, 2010 3:55:34 PM
Subject: [tuning] Trying to figure out how microtonal music works is like early man trying to find patterns in the stars

 
Originally posted this on metatuning, but got a few offlist pm's to repost it here, so here it is:

It's so frustrating. I've been a member of this list for like 3 years
now and I still don't understand what's going on at all - and that's after
reading tons of very insightful material generously referenced my way. I've learned
a ton of math, a bunch about temperaments, tons about harmonic entropy
and psychoacoustics, how to map things into a paradigm regularly, and
so on and so forth -- but I have still yet to figure out how to just
write expressive, emotional music with anything other than 12-tet that
doesn't sound "weird."

If we have all of these "rules" to stop things from sounding "weird"
in 12-tet -- why can't we come up with them for microtonal music as
well? Is it just such a new movement that the big picture hasn't been
figured out yet, or is it that it has, and I just have missed it? Is there some required reading

OK, the cliffnotes:
- I V IV I is a beautiful progression
- I ii bVII I is also
- In general, there are tons of amazing sounding 5-limit progressions
- My experiments to extend this and come up with intuitive, emotional,
aesthetically pleasing 7 and 11-limit progressions have basically
failed
- Does anyone see the big picture of all of this yet, and of how chord
progressions work in general?
- Did I miss something?

Sincerely,
A frustrated Mike Battaglia

M

Send instant messages to your online friends http://au.messenger.yahoo.com

Hi Mike,

Originally posted this on metatuning, but got a few offlist pm's to repost
> it here, so here it is:
>
> I allready replied on metatuning but it was a short reply and perhaps not
very helpfull.
I'll try to give a better reply now.

> It's so frustrating. I've been a member of this list for like 3 years
> now and I still don't understand what's going on at all - and that's after
> reading tons of very insightful material generously referenced my way. I've
> learned
> a ton of math, a bunch about temperaments, tons about harmonic entropy
> and psychoacoustics, how to map things into a paradigm regularly, and
> so on and so forth -- but I have still yet to figure out how to just
> write expressive, emotional music with anything other than 12-tet that
> doesn't sound "weird."
>
> If we have all of these "rules" to stop things from sounding "weird"
> in 12-tet -- why can't we come up with them for microtonal music as
> well? Is it just such a new movement that the big picture hasn't been
> figured out yet, or is it that it has, and I just have missed it? Is there
> some required reading
>

I've figured out some JI rules aswell that prevent things from sounding
weird.

- 5-limit JI

- Stepsizes of melodies. The smallest step must be 16/15, 10/9, 9/8 or 75/64
(steps larger than this can be broken into these smaller steps)
Offcourse stepsizes like 25/24, 135/128 and 27/25 etc are ok too, but they
give chromatic music and can sound very weird (which when used right is a
good thing) so better leave these till later.

- No modulating because it can sound very weird too. Best to begin in a
single 12 tone JI scale. Will get to what constitutes modulating later.

- Avoid dissonant/wolf JI chords unless you're really sure what you're
doing.

- Build scales on 3 connected triads of either 1/1 5/4 3/2 or 1/1 6/5 3/2
(though 1/1 5/4 3/2 15/8 can be included aswell, I'll get to it later why)
For instance 1/1 5/4 3/2, 4/3 5/3 2/1 (connected in octave offcourse), 3/2
15/8 9/4, making major scale.
In the beginning mind stepsizes of melodies mentioned earlyer.
Then locate (could be 2 locations possible, investigate both) the scale
you just built in the 12tone 5-limit JI scale of 1/1 16/15 9/8 6/5 5/4 4/3
45/32 3/2 8/5 5/3 9/5 15/8 2/1
The scales you build using this method will allways fit.

> OK, the cliffnotes:
> - I V IV I is a beautiful progression
> - I ii bVII I is also
> - In general, there are tons of amazing sounding 5-limit progressions
> - My experiments to extend this and come up with intuitive, emotional,
> aesthetically pleasing 7 and 11-limit progressions have basically
> failed
>

I've succeeded in finding aestethically pleasing 7 and 11-limit like
progressions in 5-limit JI.
Take for instance what I believe to be used as the major scale in most music
extended to 12 tones:
1/1 25/24 9/8 75/64 5/4 4/3 45/32 3/2 25/16 5/3 225/128 15/8 2/1
(this is with the 1/1 at position "8/5" of the 5-limit JI scale I gave
before)

We find very 7-limit sounding minor triads as 75/64.
Play for instance:
15/16 5/4 3/2 15/8 9/4 45/16
1/1 5/4 3/2 225/128 9/4 45/16
2/3 4/3 5/3 2/1 75/32 6/1
How's that for a 7 - 11 limit chords :) It sounds great, like jazz, yet
there's one crucial difference between a real 11-limit chord... the 5-limit
version plays nice with all the other tones, allows inversions and allows so
many chord progressions without comma shifts, whereas 7-limiy doesn't do any
of these things.
I personally believe 7-limit has no place in music and that the 75/64
interval has allways been confused for a 7-limit interval.

- Does anyone see the big picture of all of this yet, and of how chord
> progressions work in general?
>

The big picture I've formed myself up till now has to do with permutations
of the harmonic series.
I'm sure you've read me talking about it before, but here it is in short
form ones again.

Take the harmonic series till the 5th harmonic.
Permutate these intervals any way you like / eg change the order of the 4
intervals.
If you see each of the 5 harmonics of the 5-limit harmonic series as an
anchor then the resulting scale of all the permutations is:
1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1
I see this scale as tonality, as potential for a chord.
One can also have the permutations run freely. Listen to the mp3 at the
bottom of my page for the result: www.develde.net
Then one modulates.
This harmonic permutation structure tells a lot of things. Like the harmonic
structure of the above 12tone scale, but also about modulations.
Like the following (by bach):
C (1/1) - G (3/1) - C (4/1) - E (5/1) -> tonic chord
E (5/4) - G (3/1) - C (4/1) - E (5/1)
G (3/2) - G (3/1) - C (4/1) - D (9/2)
G (3/4) - B (15/4) - D (9/2) - G (6/1) -> V chord
D (9/8) - A (10/3) - D (9/2) - G (6/1) -> II Chord
F (4/3) - A (10/3) - D (9/2) - F (16/3)
A (5/3) - A (10/3) - D (9/2) - E (5/1)
A (5/6) - C (4/1) - E (5/1) - A (20/3) -> A minor tonic chord

Harmonic permutation structure sais that it can't be played in a consonant
manner / without wolves. And that it must be the above.
Try as much as you like with harmonic permutations to find a solution to the
above progression but there isn't one (also no comma shifting one)
One really can't do anything wrong with harmonic permutation structure.

Here another progression example but this one is all consonant (both chords
and simple melodic stepsizes as I mentioned before):
1/1 6/5 3/2
16/15 4/3 8/5
5/4 3/2 15/8
4/3 5/3 2/1
3/2 15/8 9/4
8/5 2/1 12/5
15/8 9/4 45/16
2/1 12/5 3/1
15/8 9/4 45/16
8/5 2/1 12/5
3/2 9/5 9/4
4/3 8/5 2/1
5/4 3/2 15/8
16/15 4/3 8/5
1/1 5/4 3/2

As you can see it uses all 12 tones.
(but it doesn't use all triads possible, there are more + all major seventh
chords)

Ah long story. There's so much more to tell but I'd be typing too long, I
should put more work into making a proper website then I'll only have to
write everything once :)

But 5-limit JI can do it all.
Consonant music in one tonic with a fixed scale.
Consonant music that modulates all over the place.
Dissonant chords diatonic music in one tonic, dissonant diatonic music
modulating all over the place.
Consonat chormatic music, dissonant chormatic music.
Jazz / blues (75/64 etc)
Arabic music
Atonal music
etc

Btw once you accept 9/8 4/3 5/3 as a ii chord in major mode etc, the old
idea that JI can't do common practice music is gone!
It can do it.
And a lot of music with suprising ease.
My continued strugle with drei equale is not because it is impossible. It is
because I wish to have a good analisys technique that'll tell me exactly
when the modulations are in a consistent way. I'll get there eventualle.

Hope my post is of use to you.
And if not, then perhaps to someone else.

Good luck with your microtonal music in any case!

Marcel

Oh yes what I forgot to say against 7 or higher limit JI.

With 5-limit one allready gets sooo much music and musical structure.
Which works 100% of the time.
Perfect 12 tone scale from tonic. Perfect modulation structures etc. Atleast
in my opinion.
It can do everything.

Now 6-limit will give a 19-tone per octave scale tonality.
But it's not all that nice anymore, extremely chromatic, comma drifting
progressions become possible etc, and some of base chords in it don't sound
very nice to me and not musical.
Even counterpoint clearly says that outer fifths in chords should not move
parallel. This is exactly what 6-limit harmonic permutation does in it's
core.
6-limit is not very musical to me, or atleast at the very limit of it.

After that comes 7-limit. I have not calculated the number of tones per
octave for it's tonality scale but I suspect it's a lot. Perhaps 50 or so
per octave.
It's a comma gallore, chords in inversions that make no sense, progressions
that do nothing but shift and jump all over the place.
No man can recognise music in this.

Then comes 8-limi, 9-limit 10-limit, 11-limit.. well. In my opinion this has
nothing to do with musical structure anymore but is in the realm of
harmonics of sound.

So as far as I'm concerned music is 5-limit.

Disclaimer: I'm only stating my personal opinion here and my personal
research. Please no offtopic flames :)
No harm or disrespect ment to anybody.

Marcel

> I thought you read Paul's 22 paper
>
> http://lumma.org/tuning/erlich/erlich-decatonic.pdf
>
> ?
>
> It describes the decatonic scales I mentioned, and tells you
> how the tetrads work in a way analogous to the triads of the
> diatonic scale. It even shows how to do 11-limit extensions,
> much like jazz extends the triads of the diatonic scale.

I have read it, although I treated it mainly like a curiosity that was
out of the realm of what I was looking for. I think I was a bit put
off by Paul's assertion that many of the modes that I like aren't
valid scales to place over the I chord, which runs counter to my
entire compositional paradigm. I'll read it again though, because now
you have my curiosity piqued.

I think what I also need to do is reread Graham's work with my
elevated awareness of what's going on now.

> These decatonic scales belong to what we now call the pajara
> temperament. It's definitely the best temperament for what
> you're trying to do -- functional 7-limit harmony. Moreover,
> 12 is a pajara system, and it's been suggested that many
> jazz standards are actually using it.

Now that's fascinating. I really need to dig into this.

> But there are other temperaments. In 31, there are 7-limit
> meantone extensions that'll let you leverage the skills you
> already have. In 72 there's miracle[10], the decatonic
> miracle scale. And many others in 31 and 72. You just have
> to know where to look. That's the point of the theory of
> regular temperaments... otherwise these large scales can be
> completely daunting.

Well, I've been looking at 31 to extend meantone, thinking that I was
used to meantone - but perhaps I've been thinking more conceptually in
pajara. I have a much different take on harmony and such than most
classically oriented composers do, and it springs from my jazz ear
training at UM. Perhaps this means I've been using 12-tet to "think"
in another temperament rather than meantone all along - like I've been
thinking in pajara without realizing it.

I think what I need to do is figure out what the point of temperament
IS - I have always viewed it as a slight mistuning of the real
underlying reality of music (JI), for convenience's sake, and to limit
the amount of notes that someone has to think of. But when I listen to
comma pump-based chord progressions in 12-tet -- such as I vi ii V --
it seems clear that something else is going on.

Jeez, I should have written this thread 2 years ago! Thanks for the
insight. Can't you just write a book on this already, man?

-Mike

> I've figured out some JI rules aswell that prevent things from sounding weird.
>
> - 5-limit JI
>
> - Stepsizes of melodies. The smallest step must be 16/15, 10/9, 9/8 or 75/64 (steps larger than this can be broken into these smaller steps)
>   Offcourse stepsizes like 25/24, 135/128 and 27/25 etc are ok too, but they give chromatic music and can sound very weird (which when used right is a good thing) so better leave these till later.

I think you're on the right track with this, and this is the sort of
thing that I have realized too. The fact that you referred to it as
"chromatic music" shows that we're on the same page with this, except
I don't think that 135/128 would really be a "chromatic" interval. To
me, the characteristic "feel" of chromatic intervals seems to involve
two major thirds stacked on top of each other - like 25/16 being
involved somewhere or something. And on that note, I would say that
75/64 is a very "chromatic" sounding interval.

Put another way - most intervals that are labeled "chromatic" tend to
be two units out along the 5-axis in 5-limit pitch space. Whether this
is just a pattern I've noticed or some underlying tenet of reality,
I'm not sure. I think the word "chromatic" originally evolved more in
a pitch-class-labeling meantone sense.

> I've succeeded in finding aestethically pleasing 7 and 11-limit like progressions in 5-limit JI.
> Take for instance what I believe to be used as the major scale in most music extended to 12 tones:
> 1/1 25/24 9/8 75/64 5/4 4/3 45/32 3/2 25/16 5/3 225/128 15/8 2/1
> (this is with the 1/1 at position "8/5" of the 5-limit JI scale I gave before)
>
> We find very 7-limit sounding minor triads as 75/64.
> Play for instance:
> 15/16 5/4 3/2 15/8 9/4 45/16
> 1/1 5/4 3/2 225/128 9/4 45/16
> 2/3 4/3 5/3 2/1 75/32 6/1
> How's that for a 7 - 11 limit chords :) It sounds great, like jazz, yet there's one crucial difference between a real 11-limit chord... the 5-limit version plays nice with all the other tones, allows inversions and allows so many chord progressions without comma shifts, whereas 7-limiy doesn't do any of these things.
> I personally believe 7-limit has no place in music and that the 75/64 interval has allways been confused for a 7-limit interval.

So what's the name of the temperament eliminating the difference
between 75/64 and 7/6? That would be the septimal comma, right? Isn't
that pajara?

> Btw once you accept 9/8 4/3 5/3 as a ii chord in major mode etc, the old idea that JI can't do common practice music is gone!
> It can do it.
> And a lot of music with suprising ease.

Perhaps the idea is that if you temper out 81/80, you get the "mental
function" of 9/8 4/3 5/3, but the "harmonic resonance" of 10:12:15,
thus getting you the best of both worlds. But I'm completely useless
with temperament, my experiments having been confined to coming up
with novel isolated harmonic structures.

> My continued strugle with drei equale is not because it is impossible. It is because I wish to have a good analisys technique that'll tell me exactly when the modulations are in a consistent way. I'll get there eventualle.
>
> Hope my post is of use to you.
> And if not, then perhaps to someone else.
>
> Good luck with your microtonal music in any case!
>
> Marcel

Very useful, and thank you.

-Mike

> Oh yes what I forgot to say against 7 or higher limit JI.
>
> With 5-limit one allready gets sooo much music and musical structure.
> Which works 100% of the time.
> Perfect 12 tone scale from tonic. Perfect modulation structures etc. Atleast in my opinion.
> It can do everything.

OK, but the question is - why? I would like to believe it's because
nobody has figured out fluid 7-limit JI yet. Although, perhaps they
have, and perhaps it's expressed in this pajara temperament.

> Now 6-limit will give a 19-tone per octave scale tonality.
> But it's not all that nice anymore, extremely chromatic, comma drifting progressions become possible etc, and some of base chords in it don't sound very nice to me and not musical.
> Even counterpoint clearly says that outer fifths in chords should not move parallel. This is exactly what 6-limit harmonic permutation does in it's core.
> 6-limit is not very musical to me, or atleast at the very limit of it.

I wish you could come up with some musical examples to illustrate what
you mean. I do think you're onto something with your theory, but
sometimes it's hard to wrap my head around it.

> After that comes 7-limit. I have not calculated the number of tones per octave for it's tonality scale but I suspect it's a lot. Perhaps 50 or so per octave.
> It's a comma gallore, chords in inversions that make no sense, progressions that do nothing but shift and jump all over the place.
> No man can recognise music in this.
>
> Then comes 8-limi, 9-limit 10-limit, 11-limit.. well. In my opinion this has nothing to do with musical structure anymore but is in the realm of harmonics of sound.
>
> So as far as I'm concerned music is 5-limit.

But is there music to be recognized in it anyway? After a lifetime of
training, I am becoming much better in fluidly communicating ideas in
12-tet. But why is 12-tet so special? So then I moved into meantone.
But why is meantone so special? And why is 5-limit so special?

There's no reason why, except that that's the status quo for the moment.

-Mike

Dan,

--- In tuning@yahoogroups.com, "daniel_anthony_stearns" <daniel_anthony_stearns@...> wrote:
>
> --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@> wrote:
> > So as far as I'm concerned music is 5-limit.
> > Marcel
>
> kind of says it all, doesn't it?

In spades. I always thought of art as limitless.

> > So as far as I'm concerned music is 5-limit.
> > Marcel
>
> kind of says it all, doesn't it?

If you're goign to quote me, then why cut a speific part out?
My full text read:

So as far as I'm concerned music is 5-limit.

Disclaimer: I'm only stating my personal opinion here and my personal
research. Please no offtopic flames :)
No harm or disrespect ment to anybody.

Marcel

CAN YOU READ????

Read the disclaimer!!!
Which includes. Please no offtopic flames.

Now what are you doing? Exactly. You're starting yet another offtopic flame.
You are a real asshole.
I'm simply trying to help Mike and stated clearly that it's my personal
opinion etc etc.

It's not me that's the problem in starting offtopic flame threads. It's
idiots like you!

Marcel

> In spades. I always thought of art as limitless.
>

Sure throw more gas on the flames..
Idiot!
Read my disclaimer etc.

Marcel

well, let's see.....there's vanilla and there's Marcel's vanilla, right? okay, you win, vanilla's good !

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> > > So as far as I'm concerned music is 5-limit.
> > > Marcel
> >
> > kind of says it all, doesn't it?
>
>
> If you're goign to quote me, then why cut a speific part out?
> My full text read:
>
> So as far as I'm concerned music is 5-limit.
>
> Disclaimer: I'm only stating my personal opinion here and my personal
> research. Please no offtopic flames :)
> No harm or disrespect ment to anybody.
>
> Marcel
>
>
> CAN YOU READ????
>
> Read the disclaimer!!!
> Which includes. Please no offtopic flames.
>
> Now what are you doing? Exactly. You're starting yet another offtopic flame.
> You are a real asshole.
> I'm simply trying to help Mike and stated clearly that it's my personal
> opinion etc etc.
>
> It's not me that's the problem in starting offtopic flame threads. It's
> idiots like you!
>
> Marcel
>

Marcel,

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> Sure throw more gas on the flames..

I'm going to give allowances for the fact that English is not your native language, and I know that humor (and other inflections) might not translate well. I meant my above comment as a bit of a 'poke in the ribs', and not meant in a very harsh way.

That said... I still think that by placing the 'limits' that you have upon yourself, you've not only narrowed your own horizons, but it strongly colors your 'advice' to others. Yes, as with you, this is just my opinion, but you tend to be dismissive of a lot of music, much of which is valued by many of the members on these lists.

So, whether one takes *limits* in the intonation sense, or in the sense of boundaries, I'm all for loosening and raising the limits.

J

Hi Mike,

I think you're on the right track with this, and this is the sort of
> thing that I have realized too. The fact that you referred to it as
> "chromatic music" shows that we're on the same page with this, except
> I don't think that 135/128 would really be a "chromatic" interval. To
> me, the characteristic "feel" of chromatic intervals seems to involve
> two major thirds stacked on top of each other - like 25/16 being
> involved somewhere or something. And on that note, I would say that
> 75/64 is a very "chromatic" sounding interval.
>

75/64 one finds in the harmonic minor mode.
I'd still call that a diatonic mode.
And 135/128 I see as not beeing a normal step in a diatonic mode, a very
chromatic step.
But my use of the word diatonic and chromatic may not be textbook correct.

>
> Put another way - most intervals that are labeled "chromatic" tend to
> be two units out along the 5-axis in 5-limit pitch space. Whether this
> is just a pattern I've noticed or some underlying tenet of reality,
> I'm not sure. I think the word "chromatic" originally evolved more in
> a pitch-class-labeling meantone sense.
>
>
> > I've succeeded in finding aestethically pleasing 7 and 11-limit like
> progressions in 5-limit JI.
> > Take for instance what I believe to be used as the major scale in most
> music extended to 12 tones:
> > 1/1 25/24 9/8 75/64 5/4 4/3 45/32 3/2 25/16 5/3 225/128 15/8 2/1
> > (this is with the 1/1 at position "8/5" of the 5-limit JI scale I gave
> before)
> >
> > We find very 7-limit sounding minor triads as 75/64.
> > Play for instance:
> > 15/16 5/4 3/2 15/8 9/4 45/16
> > 1/1 5/4 3/2 225/128 9/4 45/16
> > 2/3 4/3 5/3 2/1 75/32 6/1
> > How's that for a 7 - 11 limit chords :) It sounds great, like jazz, yet
> there's one crucial difference between a real 11-limit chord... the 5-limit
> version plays nice with all the other tones, allows inversions and allows so
> many chord progressions without comma shifts, whereas 7-limiy doesn't do any
> of these things.
> > I personally believe 7-limit has no place in music and that the 75/64
> interval has allways been confused for a 7-limit interval.
>
> So what's the name of the temperament eliminating the difference
> between 75/64 and 7/6? That would be the septimal comma, right? Isn't
> that pajara?
>

I don't know much about temperaments.
But to temper this interval would mean you have to temper for instance the
major third in a major triad.
Besides this I see no reason for tempering it.
Everybody like the number 7 but is it actually better?
I think not. Try playing the above progression in 7-limit, it will sound
weird and require comma shifts etc.
Also 75/64 has it's own "ring". Try playing 1/1 2/1 75/32 or 75/16 to hear
it. Sounds perfectly in tune to me, 7/6 doesn't. It rings strong, but in the
wrong way to me.

>
>
> > Btw once you accept 9/8 4/3 5/3 as a ii chord in major mode etc, the old
> idea that JI can't do common practice music is gone!
> > It can do it.
> > And a lot of music with suprising ease.
>
> Perhaps the idea is that if you temper out 81/80, you get the "mental
> function" of 9/8 4/3 5/3, but the "harmonic resonance" of 10:12:15,
> thus getting you the best of both worlds. But I'm completely useless
> with temperament, my experiments having been confined to coming up
> with novel isolated harmonic structures.
>

Yes that's how I see it too :)
Mental function of 9/8 4/3 5/3 but harmonic resonance/ring/consonance
resembling 10:12:15
But after repeated listening and getting used to 9/8 4/3 5/3 I really really
like it and personally wouldn't have it any other way anymore.
And besides this, to temper this interval has a domino effect and means
other intervals get tempered aswell, like a major chord becoming tempered.

>
> > My continued strugle with drei equale is not because it is impossible. It
> is because I wish to have a good analisys technique that'll tell me exactly
> when the modulations are in a consistent way. I'll get there eventualle.
> >
> > Hope my post is of use to you.
> > And if not, then perhaps to someone else.
> >
> > Good luck with your microtonal music in any case!
> >
> > Marcel
>
> Very useful, and thank you.
>

I'm glad you found it usefull :)

Cheers,
Marcel

Hi John,

I'm going to give allowances for the fact that English is not your native
> language, and I know that humor (and other inflections) might not translate
> well. I meant my above comment as a bit of a 'poke in the ribs', and not
> meant in a very harsh way.
>

Ohhh sorry then :(
I'm the idiot now. Sorry again.
I've gotten too on edge.

>
> That said... I still think that by placing the 'limits' that you have upon
> yourself, you've not only narrowed your own horizons, but it strongly colors
> your 'advice' to others. Yes, as with you, this is just my opinion, but you
> tend to be dismissive of a lot of music, much of which is valued by many of
> the members on these lists.
>

That's a fair view.
And it's true. I don't like tunings other than JI.
But I do still enjoy good music in any tuning :)
But it's just a personal opinion and preference that the music I heard
posted on these lists so far doesn't really trigger much in me.
But since much music here is about certain tunings which I don't find
interesting that's not surprising I guess.
There's a lot of experimenting on these lists and that's great offcourse.
But in my view it's apparently pretty hard to get all the parts together
that are required to make great music.
But that's just my taste.
I don't have high apreciation for commercial music either. Though this has
the advantage that it's professionally produced. Music on these lists isn't.
Anyhow these are just my opinions. Not ment in a disrespectfull way.
Ahh it's a long story to explain what I ment and why I said it and how it's
related to people commenting negatively on my research.
But it was ment as let me do my thing in piece even if you don't agree. I
let eveybody else do their thing in piece even if I don't agree.

>
> So, whether one takes *limits* in the intonation sense, or in the sense of
> boundaries, I'm all for loosening and raising the limits.
>
> J
>

Perfectly allright with me :)
All I ask for is it beeing ok too that I'm doing my thing. And can talk
about it to interested people without beeing flamed.
Though I don't mean this to you after my misreading cleared, but people like
Dan and about a dozen others.

Kind regards,
Marcel

Marcel, just one more thing, and to echo the assertions of others here:

You are of the opinion that only 5-limit music is "valid," and that
7-limit or 11-music is not. I think you are using the term "7-limit"
differently than most here -- I can't think of a time otherwise
someone has referred to a "6-limit chord" on here, for example.

I and many others are of the opinion that 5-limit music is just the
status quo, and 7-limit music and beyond represents the "next step"
which we have not yet figured out. The thing is that although you
assert that only 5-limit music sounds good to you -- keep in mind that
we have the benefit of centuries of research that have helped us
figure out how 5-limit music works.

But without arguing over the matter, let's put it this way: there may
very well be some neurological or psychological reason why 5-limit
music is "optimal" in one way or another. However, there would have to
be some explanation WHY it's optimal, why it's better than 3-limit
music, why it can't be expanded to 7-limit music, etc.

Your assertion that 5-limit JI is basically the best there can be
doesn't have much logical backing without some explanation as to why.
Otherwise, one might ask if it's simply the best there is so far. Many
would even contest the fact that it's the best so far as well. All of
my favorite pieces of music in the world are written in 12-tet -- is
that the best that can be done?

-Mike

On Mon, Feb 8, 2010 at 10:41 PM, Marcel de Velde <m.develde@...m> wrote:
>
>
>
> Hi Mike,
>
>> I think you're on the right track with this, and this is the sort of
>> thing that I have realized too. The fact that you referred to it as
>> "chromatic music" shows that we're on the same page with this, except
>> I don't think that 135/128 would really be a "chromatic" interval. To
>> me, the characteristic "feel" of chromatic intervals seems to involve
>> two major thirds stacked on top of each other - like 25/16 being
>> involved somewhere or something. And on that note, I would say that
>> 75/64 is a very "chromatic" sounding interval.
>
> 75/64 one finds in the harmonic minor mode.
> I'd still call that a diatonic mode.
> And 135/128 I see as not beeing a normal step in a diatonic mode, a very chromatic step.
> But my use of the word diatonic and chromatic may not be textbook correct.
>
>
>>
>> Put another way - most intervals that are labeled "chromatic" tend to
>> be two units out along the 5-axis in 5-limit pitch space. Whether this
>> is just a pattern I've noticed or some underlying tenet of reality,
>> I'm not sure. I think the word "chromatic" originally evolved more in
>> a pitch-class-labeling meantone sense.
>>
>> > I've succeeded in finding aestethically pleasing 7 and 11-limit like progressions in 5-limit JI.
>> > Take for instance what I believe to be used as the major scale in most music extended to 12 tones:
>> > 1/1 25/24 9/8 75/64 5/4 4/3 45/32 3/2 25/16 5/3 225/128 15/8 2/1
>> > (this is with the 1/1 at position "8/5" of the 5-limit JI scale I gave before)
>> >
>> > We find very 7-limit sounding minor triads as 75/64.
>> > Play for instance:
>> > 15/16 5/4 3/2 15/8 9/4 45/16
>> > 1/1 5/4 3/2 225/128 9/4 45/16
>> > 2/3 4/3 5/3 2/1 75/32 6/1
>> > How's that for a 7 - 11 limit chords :) It sounds great, like jazz, yet there's one crucial difference between a real 11-limit chord... the 5-limit version plays nice with all the other tones, allows inversions and allows so many chord progressions without comma shifts, whereas 7-limiy doesn't do any of these things.
>> > I personally believe 7-limit has no place in music and that the 75/64 interval has allways been confused for a 7-limit interval.
>>
>> So what's the name of the temperament eliminating the difference
>> between 75/64 and 7/6? That would be the septimal comma, right? Isn't
>> that pajara?
>
> I don't know much about temperaments.
> But to temper this interval would mean you have to temper for instance the major third in a major triad.
> Besides this I see no reason for tempering it.
> Everybody like the number 7 but is it actually better?
> I think not. Try playing the above progression in 7-limit, it will sound weird and require comma shifts etc.
> Also 75/64 has it's own "ring". Try playing 1/1 2/1 75/32 or 75/16 to hear it. Sounds perfectly in tune to me, 7/6 doesn't. It rings strong, but in the wrong way to me.
>
>>
>>
>> > Btw once you accept 9/8 4/3 5/3 as a ii chord in major mode etc, the old idea that JI can't do common practice music is gone!
>> > It can do it.
>> > And a lot of music with suprising ease.
>>
>> Perhaps the idea is that if you temper out 81/80, you get the "mental
>> function" of 9/8 4/3 5/3, but the "harmonic resonance" of 10:12:15,
>> thus getting you the best of both worlds. But I'm completely useless
>> with temperament, my experiments having been confined to coming up
>> with novel isolated harmonic structures.
>
> Yes that's how I see it too :)
> Mental function of 9/8 4/3 5/3 but harmonic resonance/ring/consonance resembling 10:12:15
> But after repeated listening and getting used to 9/8 4/3 5/3 I really really like it and personally wouldn't have it any other way anymore.
> And besides this, to temper this interval has a domino effect and means other intervals get tempered aswell, like a major chord becoming tempered.
>
>>
>>
>> > My continued strugle with drei equale is not because it is impossible. It is because I wish to have a good analisys technique that'll tell me exactly when the modulations are in a consistent way. I'll get there eventualle.
>> >
>> > Hope my post is of use to you.
>> > And if not, then perhaps to someone else.
>> >
>> > Good luck with your microtonal music in any case!
>> >
>> > Marcel
>>
>> Very useful, and thank you.
>
> I'm glad you found it usefull :)
>
> Cheers,
> Marcel
>

Hi Mike,

Marcel, just one more thing, and to echo the assertions of others here:
>
> You are of the opinion that only 5-limit music is "valid," and that
> 7-limit or 11-music is not. I think you are using the term "7-limit"
> differently than most here -- I can't think of a time otherwise
> someone has referred to a "6-limit chord" on here, for example.
>

Ah yes that's true I use 5- 6- 7- limit also as harmonic permutation limit.
But when I refer to 7-limit I usually mean prime 7-limit as is usually meant
on this list.

>
> I and many others are of the opinion that 5-limit music is just the
> status quo, and 7-limit music and beyond represents the "next step"
> which we have not yet figured out.
>

Well the thing is, that 5-limit isn't yet figured out. By anybody, including
me.
Nobody can tell how normal common practice music should be tuned and how
5-limit really works.

> The thing is that although you
> assert that only 5-limit music sounds good to you -- keep in mind that
> we have the benefit of centuries of research that have helped us
> figure out how 5-limit music works.
>

Agreed that 12tet music is 5-limit JI.
But I think that once 5-limit JI is well enough understood that it'll help
make great new music.
Harmonize arabic scales etc.
And for instance some jazz finally uses 75/64 to good effect, something that
was missed in classical music.
I think there are many many many more things missed like this waiting to be
discovered.
5-limit seems inexhaustive to me.

>
> But without arguing over the matter, let's put it this way: there may
> very well be some neurological or psychological reason why 5-limit
> music is "optimal" in one way or another. However, there would have to
> be some explanation WHY it's optimal, why it's better than 3-limit
> music, why it can't be expanded to 7-limit music, etc.
>

I've tried to explain this with harmonic permutations in part.
With the after harmonic 5-limit and all it's permutations, there comes
harmonic 6-limit which is allready crazy but perhaps some sensible music can
be made with it along the lines of Partch or something, but 7-limit is
atleast in permutation structure it's too crazy for musical use (which I
personally belief to be of great importance in music, it's why chords can be
inversed and mirrored etc).
Btw I read Rameau said something similar about 7-limit. I should have
listened back then, would've saved me a lot of extended JI research. I
wanted to believe in 7-limit.

> Your assertion that 5-limit JI is basically the best there can be
> doesn't have much logical backing without some explanation as to why.
> Otherwise, one might ask if it's simply the best there is so far. Many
> would even contest the fact that it's the best so far as well. All of
> my favorite pieces of music in the world are written in 12-tet -- is
> that the best that can be done?
>
> -Mike
>

What it boild down to for me is that 5-limit works, and I'm not missing
anything in 5-limit (with for instance 225/128), and 7-limit so completely
not works for me.
But it's just a personal opinion, and I'm stating it as such.
I really don't expect anybody to just say oh Marcel says it is so so I'll
believe him.
But perhaps some people will remember my line of though and it'll help them
somewhere in the future.

Marcel

Hi Daniel,

the impact of ones music is the ultimate arbiter of the means used to get
> there.....things like tuning are at most something like number 6.66 on the
> list.and even then, they're only of residual, lasting interest to failed
> artists with too much time on their hands, hopeless sycophants, and Dungeon
> and Dragon minutia-like geekery specialists.
> The music (art) you make is where it's at, IMo-----and hell, that might
> even be nothing more than a given tuning theory, given its ummph and overall
> resonance.
>

For the most part I agree.
And I'd be happy if I compose one day and my music is played in near 12tet
by an orchestra, or in 12tet on a piano etc.
I bet some people are surprised I'm saying this :)
Even though I care a lot about correct JI tuning.
It's the musical insight JI gives that I'm after.
Like music is math kind of thing :) Don't mean music by computer but the
insight into chords and their functions, melodic movements, modulations etc
that'll hopefully allow me and perhaps other to compose great new music
somewhere in the future.
That's what I'm doing it for.
If that music can translate in 12tet with some loss, so be it. It's not
really about that.

and not to be a pain in the ass, but mike....is your music (art) anywhere i
> can check........Marcel? i'm just curious
> daniel
>

I've not composed a single thing in my life (well except once when I was 8
or so, 20 second mathematic counterpoint / canon for piano lol).
I do improvise a lot, but never recorded anything or written it down.
I do plan do begin doing so in the not too distant future.
So far the only thing that is sort of comming from my hand is a simplified
part of my harmonic permutation theory generated by computer sung by midi
choir available at www.develde.net bottom of the page.

Marcel

If 7-limit is too crazy then how come the Ptolemy Homalon scale (which reduces to x/18) of

1. (1/1)
2. (10/9)
3. (11/9)
4. (4/3)
5. (3/2)
6. (5/3)
7. (11/6)
8. (2/1)

....sounds so smooth (at least to me)?
If I have it right, that scale is 11-limit: the only thing(s) are many of the 11-limit ratios aren't that noticeably far tempered off lower limit ones that form "perfect" low-limit chords and the notes are fairly well spaced apart to avoid roughness.

I am pretty sure that a large majority of how any limit music "really works" is that it successfully balances between goals of maximizing periodicity and minimizing roughness. The real problem I see in theories that keep coming up here is they throw roughness pretty much out the door for the sake of
1) Preserving "low-limit" periodicity and
2) The related concepts of exact "virtual pitch" tonality that follows from it (IMVHO the false assumption that a chord must be reduced to exactly one virtual root tone and not, say, a few very close to root tones or a few seperate virtual root tones that are highly periodic...both very legal in my book).

I'm not saying I have the answer...but that at least I'm pretty sure I'm attacking the right problems with the right balance between them. Let me put it this way...if 7+ limit is truly "crazy and beyond human comprehension"...
A) Why does the above scale work? (if you try it and agree it works)
B) If not, how would the above scale be best converted to 5-limit, do you believe the 5-limit version sounds better, and why so?

Hi Michael,

If 7-limit is too crazy then how come the Ptolemy Homalon scale (which
> reduces to x/18) of
>
> 1. (1/1)
> 2. (10/9)
> 3. (11/9)
> 4. (4/3)
> 5. (3/2)
> 6. (5/3)
> 7. (11/6)
> 8. (2/1)
>
> ....sounds so smooth (at least to me)?
>

It sounds not so good to me.
If I hold 1/1 and play the scale above that I think I'm hearing it as 1/1
9/8 6/5 4/3 3/2 5/3 9/5 2/1, though not sure.
Perhaps the 27/25 is between 10/9 and 6/5.
Ah there are many options. I can't say without harmony.
I don't like the sound of the neutral third of 11/9, it sounds like a bad
6/5 to me, not at all neutral as could also be a 5/4.
I do like the 150 cents stepsize from 5/3 to 11/6, but i feel it is better
captured by 27/25

Btw there are much closer matches cents wise in a 6-limit permutation scale,
and also in 5-limit permutation scales based on an allready permutated chord
(long story what that means, and it's one of the things I'm still
investigating).
But actually the above scale I gave seems to do it allready for me.
I'm surprised myself that it does given the large difference with yours
cents wise.

Btw as for arabic music and intervals like these. They seem to me to be
exadurated.
It's like they're screaming, hear me I'm a chromatic interval. But they're
never backed up by proper harmony.
And something like 11/9 11/6 won't work in harmony, they're too far out of
tune it seems to me.
See my above example for 11-limit like chords in 5-limit and how those do
work out.

Again disclaimer, these are personal views, no disrespect ment.

Marcel

> I have still yet to figure out how to just
> write expressive, emotional music with anything other than 12-tet that
> doesn't sound "weird."

I highly recommend checking out the TransFormSynth, or TFS, a free dynamic tonality synthesizer. It turns your computer keyboard into an isomorphic keyboard with the same fingering in every key and tuning (within a given temperament). On this interface you can play in 12-, 17-, 19-, 31-, and 53- equal divisions of the octave with the SAME FINGERING :D
This way you don't have to spend a year learning the basic patterns of a single tuning just to find out you don't love it. Instead, you spend that time learning the patterns of a given temperament and learn how to apply them to every tuning within that temperament.

While providing you with an ergonomic interface through which you can play every tuning with the same fingering, the program also modifies the harmonic structure of the timbres you use to maximize sensory consonance. It is the harmonic structure that determines sensory consonance experienced from intervals, both harmonic and melodic, played with complex tones, and the TFS changes the partial structure of the tones you use to make sure they match up closest to your current tuning. This, though altering the timbre of your sounds slightly, provides consonance in many tunings so that they don't sound NEAR as "weird".
For instance, 22-edo the major third gets pretty darn sharp. Instead of just dealing with the clash, the TFS remaps the partials of your given tone so that it is this "sharp" third that is the one that is MOST consonant for that timbre. This sharp third no longer sounds sharp, just different.
Here is a short video demonstrating dynamic tonality:
http://www.youtube.com/watch?v=Nd4h8vmEsQM

And you can download it (for free) at the bottom of this page:
http://www.dynamictonality.com/spectools.htm

Hope this helps you find your way =)

John Moriarty

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> I highly recommend checking out the TransFormSynth,
[snip]
> And you can download it (for free) at the bottom of this page:
> http://www.dynamictonality.com/spectools.htm
>
> Hope this helps you find your way =)
>
> John Moriarty

I think my head just exploded. I downloaded The Viking

http://www.dynamictonality.com/viking.htm

The UI has a dropdown of "continuums" which offers
"syntonic", "hanson", and "magic" for choices. And for
each of these, a slider that lets you change the generator
size in realtime, along with "tuning presets" that include
compatible ETs and "Tenney optimal".

See what I mean about regular mapping reaching critical mass?
All these concepts were developed here and tuning-math.

The synth combines all of this with spectral synthesis ala
Sethares! I have no idea how to use the UI yet, but I'm
already playing it from my MIDI keyboard.

How does TFS compare to The Viking? Is it newer?

!!!!

-Carl

Nothing microtonal is up yet, except for a short pseudo-72 improvisation up
here: http://www.michaelbattagliamusic.com/DartmouthApp/ObliqueMotion.mp3

As for my other music, it isn't collected in one place. I have the
recordings from my senior recital online at:
http://rabbit.eng.miami.edu/students/mbattaglia/Senior_Recital/

Of those, I think the best example was an improvisation that I did over the
Beatles' "Eleanor Rigby" with my friend Steve Brickman, who is a very
talented emerging composer. It can be found here:
http://rabbit.eng.miami.edu/students/mbattaglia/Senior_Recital/1-05%20Eleanor%20Rigby.mp3

The whole thing was improvised live - I'm on piano and he's on sax.

-Mike

On Mon, Feb 8, 2010 at 11:20 PM, daniel_anthony_stearns <
daniel_anthony_stearns@...> wrote:

>
>
> the impact of ones music is the ultimate arbiter of the means used to get
> there.....things like tuning are at most something like number 6.66 on the
> list.and even then, they're only of residual, lasting interest to failed
> artists with too much time on their hands, hopeless sycophants, and Dungeon
> and Dragon minutia-like geekery specialists.
> The music (art) you make is where it's at, IMo-----and hell, that might
> even be nothing more than a given tuning theory, given its ummph and overall
> resonance.
> and not to be a pain in the ass, but mike....is your music (art) anywhere i
> can check........Marcel? i'm just curious
> daniel
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Mike Battaglia
> <battaglia01@...> wrote:
> >
> > Marcel, just one more thing, and to echo the assertions of others here:
> >
> > You are of the opinion that only 5-limit music is "valid," and that
> > 7-limit or 11-music is not. I think you are using the term "7-limit"
> > differently than most here -- I can't think of a time otherwise
> > someone has referred to a "6-limit chord" on here, for example.
> >
> > I and many others are of the opinion that 5-limit music is just the
> > status quo, and 7-limit music and beyond represents the "next step"
> > which we have not yet figured out. The thing is that although you
> > assert that only 5-limit music sounds good to you -- keep in mind that
> > we have the benefit of centuries of research that have helped us
> > figure out how 5-limit music works.
> >
> > But without arguing over the matter, let's put it this way: there may
> > very well be some neurological or psychological reason why 5-limit
> > music is "optimal" in one way or another. However, there would have to
> > be some explanation WHY it's optimal, why it's better than 3-limit
> > music, why it can't be expanded to 7-limit music, etc.
> >
> > Your assertion that 5-limit JI is basically the best there can be
> > doesn't have much logical backing without some explanation as to why.
> > Otherwise, one might ask if it's simply the best there is so far. Many
> > would even contest the fact that it's the best so far as well. All of
> > my favorite pieces of music in the world are written in 12-tet -- is
> > that the best that can be done?
> >
> > -Mike
> >
> >
> > On Mon, Feb 8, 2010 at 10:41 PM, Marcel de Velde <m.develde@...> wrote:
> > >
> > >
> > >
> > > Hi Mike,
> > >
> > >> I think you're on the right track with this, and this is the sort of
> > >> thing that I have realized too. The fact that you referred to it as
> > >> "chromatic music" shows that we're on the same page with this, except
> > >> I don't think that 135/128 would really be a "chromatic" interval. To
> > >> me, the characteristic "feel" of chromatic intervals seems to involve
> > >> two major thirds stacked on top of each other - like 25/16 being
> > >> involved somewhere or something. And on that note, I would say that
> > >> 75/64 is a very "chromatic" sounding interval.
> > >
> > > 75/64 one finds in the harmonic minor mode.
> > > I'd still call that a diatonic mode.
> > > And 135/128 I see as not beeing a normal step in a diatonic mode, a
> very chromatic step.
> > > But my use of the word diatonic and chromatic may not be textbook
> correct.
> > >
> > >
> > >>
> > >> Put another way - most intervals that are labeled "chromatic" tend to
> > >> be two units out along the 5-axis in 5-limit pitch space. Whether this
> > >> is just a pattern I've noticed or some underlying tenet of reality,
> > >> I'm not sure. I think the word "chromatic" originally evolved more in
> > >> a pitch-class-labeling meantone sense.
> > >>
> > >> > I've succeeded in finding aestethically pleasing 7 and 11-limit like
> progressions in 5-limit JI.
> > >> > Take for instance what I believe to be used as the major scale in
> most music extended to 12 tones:
> > >> > 1/1 25/24 9/8 75/64 5/4 4/3 45/32 3/2 25/16 5/3 225/128 15/8 2/1
> > >> > (this is with the 1/1 at position "8/5" of the 5-limit JI scale I
> gave before)
> > >> >
> > >> > We find very 7-limit sounding minor triads as 75/64.
> > >> > Play for instance:
> > >> > 15/16 5/4 3/2 15/8 9/4 45/16
> > >> > 1/1 5/4 3/2 225/128 9/4 45/16
> > >> > 2/3 4/3 5/3 2/1 75/32 6/1
> > >> > How's that for a 7 - 11 limit chords :) It sounds great, like jazz,
> yet there's one crucial difference between a real 11-limit chord... the
> 5-limit version plays nice with all the other tones, allows inversions and
> allows so many chord progressions without comma shifts, whereas 7-limiy
> doesn't do any of these things.
> > >> > I personally believe 7-limit has no place in music and that the
> 75/64 interval has allways been confused for a 7-limit interval.
> > >>
> > >> So what's the name of the temperament eliminating the difference
> > >> between 75/64 and 7/6? That would be the septimal comma, right? Isn't
> > >> that pajara?
> > >
> > > I don't know much about temperaments.
> > > But to temper this interval would mean you have to temper for instance
> the major third in a major triad.
> > > Besides this I see no reason for tempering it.
> > > Everybody like the number 7 but is it actually better?
> > > I think not. Try playing the above progression in 7-limit, it will
> sound weird and require comma shifts etc.
> > > Also 75/64 has it's own "ring". Try playing 1/1 2/1 75/32 or 75/16 to
> hear it. Sounds perfectly in tune to me, 7/6 doesn't. It rings strong, but
> in the wrong way to me.
> > >
> > >>
> > >>
> > >> > Btw once you accept 9/8 4/3 5/3 as a ii chord in major mode etc, the
> old idea that JI can't do common practice music is gone!
> > >> > It can do it.
> > >> > And a lot of music with suprising ease.
> > >>
> > >> Perhaps the idea is that if you temper out 81/80, you get the "mental
> > >> function" of 9/8 4/3 5/3, but the "harmonic resonance" of 10:12:15,
> > >> thus getting you the best of both worlds. But I'm completely useless
> > >> with temperament, my experiments having been confined to coming up
> > >> with novel isolated harmonic structures.
> > >
> > > Yes that's how I see it too :)
> > > Mental function of 9/8 4/3 5/3 but harmonic resonance/ring/consonance
> resembling 10:12:15
> > > But after repeated listening and getting used to 9/8 4/3 5/3 I really
> really like it and personally wouldn't have it any other way anymore.
> > > And besides this, to temper this interval has a domino effect and means
> other intervals get tempered aswell, like a major chord becoming tempered.
> > >
> > >>
> > >>
> > >> > My continued strugle with drei equale is not because it is
> impossible. It is because I wish to have a good analisys technique that'll
> tell me exactly when the modulations are in a consistent way. I'll get there
> eventualle.
> > >> >
> > >> > Hope my post is of use to you.
> > >> > And if not, then perhaps to someone else.
> > >> >
> > >> > Good luck with your microtonal music in any case!
> > >> >
> > >> > Marcel
> > >>
> > >> Very useful, and thank you.
> > >
> > > I'm glad you found it usefull :)
> > >
> > > Cheers,
> > > Marcel
> > >
> >
>
>
>

Dear John,

Holy crap!

Sincerely,
Mike

PS: thanks for ensuring that I will never do anything productive outside of
music ever again

On Tue, Feb 9, 2010 at 12:29 AM, jlmoriart <JlMoriart@...> wrote:

>
>
> > I have still yet to figure out how to just
> > write expressive, emotional music with anything other than 12-tet that
> > doesn't sound "weird."
>
> I highly recommend checking out the TransFormSynth, or TFS, a free dynamic
> tonality synthesizer. It turns your computer keyboard into an isomorphic
> keyboard with the same fingering in every key and tuning (within a given
> temperament). On this interface you can play in 12-, 17-, 19-, 31-, and 53-
> equal divisions of the octave with the SAME FINGERING :D
> This way you don't have to spend a year learning the basic patterns of a
> single tuning just to find out you don't love it. Instead, you spend that
> time learning the patterns of a given temperament and learn how to apply
> them to every tuning within that temperament.
>
> While providing you with an ergonomic interface through which you can play
> every tuning with the same fingering, the program also modifies the harmonic
> structure of the timbres you use to maximize sensory consonance. It is the
> harmonic structure that determines sensory consonance experienced from
> intervals, both harmonic and melodic, played with complex tones, and the TFS
> changes the partial structure of the tones you use to make sure they match
> up closest to your current tuning. This, though altering the timbre of your
> sounds slightly, provides consonance in many tunings so that they don't
> sound NEAR as "weird".
> For instance, 22-edo the major third gets pretty darn sharp. Instead of
> just dealing with the clash, the TFS remaps the partials of your given tone
> so that it is this "sharp" third that is the one that is MOST consonant for
> that timbre. This sharp third no longer sounds sharp, just different.
> Here is a short video demonstrating dynamic tonality:
> http://www.youtube.com/watch?v=Nd4h8vmEsQM
>
> And you can download it (for free) at the bottom of this page:
> http://www.dynamictonality.com/spectools.htm
>
> Hope this helps you find your way =)
>
> John Moriarty
>
>
>

> I think my head just exploded. I downloaded The Viking

Hahahahahahaha!

-Mike

>
"I don't like the sound of the neutral third of 11/9, it sounds like a bad 6/5 to me, not at all neutral as could also be a 5/4."

One question...you seem to rate everything in stability when played as a dyad from the root tone IE "the sound of 1/1 and 6/5 together". I, of course, agree that maximizing stability of each note with the root is great for chord starting from the root. However, realistically a large majority of music is based on mostly chords beside ones that originate from the root "C".

>"Ah there are many options. I can't say without harmony."
Exactly (otherwise, IMVHO, we would be playing a game of creating to most pure dyads from the root and/or a very limited subset of notes in the scale). Here's a test...
A) Try making all the possible triads in this scale you think sound at least good (though not perfect). For example 5/3 to 11/6 may be part of one of the triads.
B) Try making as many triads in your own scale and note, out of the ones with very similar mood, which sound better

>"I do like the 150 cents stepsize from 5/3 to 11/6, but i feel it is better captured by 27/25"
But what would that optimization do to, say, the relationship between 5/3 * 27/25 = 135/75 = 27/15 and other notes like your suggested 9/8? My guess is while 27/25 would sound fine and slightly optimized as an interval by itself, it would clash with several of the other notes.

>"Again disclaimer, these are personal views, no disrespect ment."
No offense taken...we're both trying to actually get something done & not arguing jus for sake of arguing, IMVHO.

-Michael
_._,___

Hi Michael,

One question...you seem to rate everything in stability when played as a
> dyad from the root tone IE "the sound of 1/1 and 6/5 together". I, of
> course, agree that maximizing stability of each note with the root is great
> for chord starting from the root. However, realistically a large majority
> of music is based on mostly chords beside ones that originate from the root
> "C".
>

In my system I'm not rating intervals based on root stability.
But in "translating" your scale I did it by ear, and indeed by root note.

>
> >"Ah there are many options. I can't say without harmony."
> Exactly (otherwise, IMVHO, we would be playing a game of creating to
> most pure dyads from the root and/or a very limited subset of notes in the
> scale). Here's a test...
> A) Try making all the possible triads in this scale you think sound at
> least good (though not perfect). For example 5/3 to 11/6 may be part of one
> of the triads.
> B) Try making as many triads in your own scale and note, out of the ones
> with very similar mood, which sound better
>

There are the greatest number of "consontant" 5-limit major and minor triads
possible in 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1
To tune any other way will be loosing triadic consonance if you rate major
triad more consonant than minor triad (even mirroring won't work)

>
>
> >"I do like the 150 cents stepsize from 5/3 to 11/6, but i feel it is
> better captured by 27/25"
> But what would that optimization do to, say, the relationship between 5/3
> * 27/25 = 135/75 = 27/15 and other notes like your suggested 9/8? My guess
> is while 27/25 would sound fine and slightly optimized as an interval by
> itself, it would clash with several of the other notes.
>

27/15 /3 = 9/5 :)
9/5 will form 5/4 with 9/4
9/5 will form 27/20 with 4/3
Making possible in this scale the wolf major triad of 9/5 9/4 8/3.
It is only under very specific circumstances a correct chord in my opinion
(but usually not, so best consider it unusable)
Btw for the most consonant 7-note scale I'd rate 1/1 9/8 5/4 4/3 3/2 5/3
15/8 2/1 much higher, and consider the 9/8 4/3 5/3 minor triad in very
functional.
But these are only subset of a full 12 tone JI scale, and even that 12 tone
JI scale changes as modulations happen.
I do not have a system for maximum consonance in a fixed scale for all music
or anything like that.

Marcel

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

> I think what I need to do is figure out what the point of
> temperament IS - I have always viewed it as a slight mistuning of
> the real underlying reality of music (JI), for convenience's sake,
> and to limit the amount of notes that someone has to think of. But
> when I listen to comma pump-based chord progressions in 12-tet --
> such as I vi ii V -- it seems clear that something else is going on.

Mike,

to put it a bit vaguely the point of temperament is to acoustically
realize what was already there as a way of hearing. Let me show what I
mean...

Let's imagine you were working in strict JI and notating the notes in
the key of C. Acoustically C would be the 1/1. Now, let's think about
the E above C. If your notation was based on a circle of fifths the
E would be acoustically an 81/64 while you might notate 5/4 above C
as E- for example. Alternatively, if the notation was based like Ben
Johnston's on just major diatonic scale, 5/4 would be notated as E
and 81/64 as E+. The important thing to realize about both of these
notations is that both of those notes are some kind of E. This
implies that they are also heard as versions of the same thing. So
the essential spirit that leads to tempering already exists in the
minds of many strict JI composers too.

Temperament just makes these different versions of the same thing also
acoustically identical. The point of this is to have chords
reasonably close to their ideal JI versions while avoiding commatic
melodic movement which many find unpleasant. But of course there are
other ways to handle this than fixed-pitch temperament, some kind of
adaptive tuning for example.

Kalle Aho

Mike B> "I have always viewed it as a slight mistuning of

the real underlying reality of music (JI), for convenience' s sake,

and to limit the amount of notes that someone has to think of."

Oddly enough, to a fair extent, so have I. At least, among the people who I see "prophetizing" their use of JI: the idea seems to be simply to temper to acheive better "average dyadic purity" rather than to, say, increase the degree of tonal color or number of chords available.

Kalle>"5/4 would be notated as E and 81/64 as E+."
Right, so in this example (and many others) different versions of a note are established, each to harmonize more purely with particular other notes forming perfect dyads. And all adaptive JI does is determine that selections while avoiding commatic melodic movement so much as possible, correct?

>"If your notation was based on a circle of fifths the
E would be acoustically an 81/64 while you might notate 5/4 above C
as E- for example.
Temperament just makes these different versions of the same thing also
acoustically identical."

Right. You could say I consider a loophole in many people's though process is the idea that everything must aim for the ideal of being more or less "acoustically identical" to 12TET tones. For example 11/9: when I made a scale with it I was posed the question (paraphrased) "is this supposed to be an E or a D#?!"

>"So the essential spirit that leads to tempering already exists in the minds of many strict JI composers too. "
Then again, of course, 11/9 can be considered JI, but many people would avoid tones like that as they are of "high limit" (11, to be exact).
I guess you could say that's what I mean in a sense by "strict-JI" as well...the quest to keep low limits and the idea that only the lowest limits (particular 7 and under) consistute enough consonance to form "resolved sounding" chords.

A flip question becomes: why argue about a single "fixed" JI scale
when you can just use adaptive JI to do "perfect JI purity tempering"? I sure hope few people view adaptive
JI with unnoticably small commatic melody movement as the "Holy Grail" of tuning though... Because then I fear once the "purity equation" problem is solved few of us would experiment with anything more complex than, say, a 7:8:9 chord IE other chords that yield more complex tonal colors.

-Michael

Oh I have reaaaally reaaaally good tip for working with 5-limit JI!! :)

I can't beleive I missed the importance of this before!!
I had half found and realised this trick before but had so many things to
worry about I had put this on in the back of my mind.
It is so much nicer to work with than working out permutation possibilities!
:)

Ok here it is.
To determine wether a minor triad is the consonant 1/1 6/5 3/2 or one of the
more dissonant variants like 1/1 32/27 40/27 or 1/1 75/64 3/2 (I don't know
yet about 1/1 32/27 1024/675, perhaps it is never allowed. and these are all
major triad possibilities in 5-limit permutation JI).
There is the following trick:
Every single instance of 1/1 6/5 3/2 can also be played as 8/5 2/1 12/5 3/2.
In other words a major 7th chord of 1/1 5/4 3/2 15/8, with the minor triad
as 5/4 3/2 15/8!!
This will make clearly audible the true structure of the permutation.

Now take for instance the I-vi-ii-V example:
I -> C-E-G clearly major chord.
vi -> C-E-A minor chord, but which one? play F-A-C-E, does it sound right?
it does, then yes it's a 1/1 6/5 3/2 minor.
ii -> D-F-A minor chord, but which one? play Bb-D-F-A, does it sound right?
well... hmmm this does sound nice, but it doesn't sound at all like the
chord we ment does it!! It sounds like we've left C major and are now in F
major or something, modulated.
But just to be sure lets check it going into the V chord.
V -> D-G-B clear major chord. But oeh that sounds awfull and very wrong
after comming from Bb-D-F-A!!
So the ii chord defenately isn't a 1/1 6/5 3/2 triad.
So it must be a 1/1 75/64 3/2 or 1/1 32/27 3/2 chord.
Luckily these 2 are pretty audibly different and identifiable :-)
Quick check tells it's the 1/1 32/27 3/2 chord. Making it 9/8 4/3 5/3 and
staying nicely in c major mode :-)

And yes this ALLWAYS works. There is not a single 1/1 6/5 3/2 chord that
escapes this method :)
Oh this makes 5-limit JI a pleaaaasure to work with :)
I'm all smiles now :) haha

Cheers,
Marcel

C (1/1) - G (3/1) - C (4/1) - E (5/1) -> tonic chord
> E (5/4) - G (3/1) - C (4/1) - E (5/1)
> G (3/2) - G (3/1) - C (4/1) - D (9/2)
> G (3/4) - B (15/4) - D (9/2) - G (6/1) -> V chord
> D (9/8) - A (10/3) - D (9/2) - G (6/1) -> II Chord
> F (4/3) - A (10/3) - D (9/2) - F (16/3)
> A (5/3) - A (10/3) - D (9/2) - E (5/1)
> A (5/6) - C (4/1) - E (5/1) - A (20/3) -> A minor tonic chord
>
> Harmonic permutation structure sais that it can't be played in a consonant
> manner / without wolves. And that it must be the above.
> Try as much as you like with harmonic permutations to find a solution to
> the above progression but there isn't one (also no comma shifting one)
> One really can't do anything wrong with harmonic permutation structure.
>

> Quick check tells it's the 1/1 32/27 3/2 chord. Making it 9/8 4/3 5/3 and
> staying nicely in c major mode :-)
>

Sorry, quick correction to avoid possible confusion. That should offcourse
be 1/1 32/27 40/27, not 1/1 32/27 3/2 which is never possible.

>"There are the greatest number of "consontant" 5-limit major and minor
triads possible in 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8
2/1
To tune any other way will be loosing triadic consonance if you
rate major triad more consonant than minor triad (even mirroring won't
work)"

Such as 16/15 6/5 4/3 AKA 16:18:20 and 9/8 5/4 45/32 AKA 36:40:45. Funny thing is the latter triad (even) sounds a bit off to me: not periodic enough I guess you could say. But it seems to me in your scale you really have the sub-scales of

1/1-16/15 6/5 4/3 8/5-5/3 9/5 AKA 15:16:18:20:25:27

1/1 9/8 5/4 45/32-3/2 15/8 AKA 32:36:40:45:48:60 (IMVHO, this one isn't quite periodic enough to work...but to some people it may be OK)

1/1 5/4-4/3 3/2 5/3 AKA 12:15:16:18:20

Now make any chord of any of the above sub-scales and you should be fine.
But try to create alternative triads like 45/32 3/2 8/5 or 3/2 8/5 5/3...I think you'll agree you just can't make it happen "legally" as you run into too many periodicity issues. Again you run smack into the usual "no half steps work in resolved chords" issue.

I can understand how your above scale could optimize major triads (assuming a major third followed by a minor third)...but can imagine it falls to pieces when reproducing things like add2 chords and 7th,9th...chords that use minor followed by major thirds.
Not to mention trying to make chords with new structures that are smaller than a whole step (IE 5/4 to 11/6).

>"9/5 will form 5/4 with 9/4
9/5 will form 27/20 with 4/3"

Sounds good...the only problem is, again, to make that chord work you have to make other chords impossible.

>"Making possible in this scale the wolf major triad of 9/5 9/4 8/3."
Exactly. So, sadly...it seems you're not gaining extra possibilities for chords, but merely trading purity from certain chords to others. IMVHO an ideal scale will have no "wolf" chords, but chords in a range of consonance from "passable in use as being resolved" to "completely resolved".
------------------------------------------------

Taking your scale of
1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8
2/1

I can simplify that IMVHO pretty closely to the x/15 harmonic series IE
1/1 16/15 17/15 18/15 19/15 20/15 21/15 23/15 24/15 25/15 27/15 28/15
AKA
15:16:17:18: 19:20:21:23: 24:25:27:28
------------------------------------------------------------------------------------------
For sake of avoiding close notes with very hard beating I could eliminate certain notes to get the 7-note scale of
1) 15:17:19:21:23:25:27
.....which has it's smallest interval as 1.08 AKA 27:25...very close to 13/12.

Your suggested 7-note subset scale of
2) 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1

would translate to the lower-periodicity structure of
1/1 27/24 30/24 32/24 36/24 40/24 45/24 =
24:27:30:32:36:40:45
....which has it's smallest interval as 32/30 and 48/45 (both 16/15) which = 1.06666666 (considerably rougher than 1.08)

Try to see how many chords (and not just triads) you can make with both of the above scales.
I think you'll find many more are available under the former scale. Far as maximizing purity of standard triads (rather than adding new moods)...my question to you is what does your scale system have to offer over adaptive JI?

-Michael

One quick addendum:

C-E-G
C-E-A
D-F-A
D-G-B
will by this method be tuned to c major as
1/1 - 5/4 - 3/2
1/1 - 5/4 - 5/3
9/8 - 4/3 - 5/3
9/8 - 3/2 - 15/8

But the question is sure to arrise in some of you what actually happens if
we do play the ii chord as a major 7th and then still go to V.
Just because it sounds wrong that surely doesn't mean that it's impossible,
since it can be played nontheless.
Well offcourse it can be played in 5-limit JI. And 5-limit will show you why
it sounds so wrong:
There are 2 main ways to play it.
One in C major, one in F major.
In C major:
1/1 - 5/4 - 3/2
1/1 - 5/4 - 5/3
225/256 - 9/8 - 4/3 - 5/3 aah here is the 1/1 5/4 1024/675 chord. There is
only one such chord in the whole 12 tone scale. Yes it sounds bad.
9/8 - 3/2 - 15/8

In F major:
C 1/1 - 5/4 - 3/2
1/1 - 5/4 - 5/3
8/9 - 10/9 - 4/3 - 5/3 yes here a nice major fifth chord, defenately not a
ii chord in C major.
10/9 - 3/2 - 15/8 aah here the reason why it sounds terrible when seen as
this way aswell. a 1/1 5/4 40/27 major chord.

So it sounds bad in 12tet, and JI shows why :)

One other note:
While all 1/1 6/5 3/2 chords can be made into major 7th chords, this does
NOT mean that all 1/1 5/4 3/2 chords can be turned into 1/1 5/4 3/2 15/8
major 7th chords.
6 out of 8 major chords can be turned into major 7th chords, but 2 cannot!

Marcel

On 9 February 2010 17:02, Marcel de Velde <m.develde@...> wrote:

> Oh I have reaaaally reaaaally good tip for working with 5-limit JI!! :)
>
> I can't beleive I missed the importance of this before!!
> I had half found and realised this trick before but had so many things to
> worry about I had put this on in the back of my mind.
> It is so much nicer to work with than working out permutation
> possibilities! :)
>
> Ok here it is.
> To determine wether a minor triad is the consonant 1/1 6/5 3/2 or one of
> the more dissonant variants like 1/1 32/27 40/27 or 1/1 75/64 3/2 (I don't
> know yet about 1/1 32/27 1024/675, perhaps it is never allowed. and these
> are all major triad possibilities in 5-limit permutation JI).
> There is the following trick:
> Every single instance of 1/1 6/5 3/2 can also be played as 8/5 2/1 12/5
> 3/2.
> In other words a major 7th chord of 1/1 5/4 3/2 15/8, with the minor triad
> as 5/4 3/2 15/8!!
> This will make clearly audible the true structure of the permutation.
>
> Now take for instance the I-vi-ii-V example:
> I -> C-E-G clearly major chord.
> vi -> C-E-A minor chord, but which one? play F-A-C-E, does it sound right?
> it does, then yes it's a 1/1 6/5 3/2 minor.
> ii -> D-F-A minor chord, but which one? play Bb-D-F-A, does it sound right?
> well... hmmm this does sound nice, but it doesn't sound at all like the
> chord we ment does it!! It sounds like we've left C major and are now in F
> major or something, modulated.
> But just to be sure lets check it going into the V chord.
> V -> D-G-B clear major chord. But oeh that sounds awfull and very wrong
> after comming from Bb-D-F-A!!
> So the ii chord defenately isn't a 1/1 6/5 3/2 triad.
> So it must be a 1/1 75/64 3/2 or 1/1 32/27 3/2 chord.
> Luckily these 2 are pretty audibly different and identifiable :-)
> Quick check tells it's the 1/1 32/27 3/2 chord. Making it 9/8 4/3 5/3 and
> staying nicely in c major mode :-)
>
> And yes this ALLWAYS works. There is not a single 1/1 6/5 3/2 chord that
> escapes this method :)
> Oh this makes 5-limit JI a pleaaaasure to work with :)
> I'm all smiles now :) haha
>
> Cheers,
> Marcel
>

Hi Michael,

I can understand how your above scale could optimize major triads
> (assuming a major third followed by a minor third)...but can imagine it
> falls to pieces when reproducing things like add2 chords and
> 7th,9th...chords that use minor followed by major thirds.
>

No it does quite the opposite.
I shines like no other tuning system with chords like these.

> Not to mention trying to make chords with new structures that are smaller
> than a whole step (IE 5/4 to 11/6).
>

The smallest step is 25/24, or about 70.7 cents.
To get smaller steps you'd have to go to harmonic 6-limit 19 tone per octave
tonality permutation scale.

About adaptive-ji.
I can't seriously comment on that, I've made clear many times before what I
think of that hidious tuning system and don't consider it JI at all.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> Sorry, quick correction to avoid possible confusion. That should
> offcourse be 1/1 32/27 40/27, not 1/1 32/27 3/2 which is never
> possible.

I'm curious (and I bet I'm not the only one) about these kinds of
statements:

"...not 1/1 32/27 3/2 which is never possible."

"I don't know yet about 1/1 32/27 1024/675, perhaps it is never
allowed."

You obviously think that your take on JI exists objectively and is
"out there" to be discovered. But where is it?

The "knowledge" about it is obviously not like knowledge of logical
or mathematical truths. It's also not empirically testable like the
statements of science. Rather, it is based on intuition like moral
and aesthetic understanding but differs from them in being based
only on the intuition of one person (you Marcel). That makes it
revelatory/religious "knowledge". Enough said.

Kalle Aho

I'm curious as to if these statements are based on math or hearing.

Chris

On Tue, Feb 9, 2010 at 11:40 AM, Kalle <kalleaho@...> wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Marcel de Velde
> <m.develde@...> wrote:
>
> > Sorry, quick correction to avoid possible confusion. That should
> > offcourse be 1/1 32/27 40/27, not 1/1 32/27 3/2 which is never
> > possible.
>
> I'm curious (and I bet I'm not the only one) about these kinds of
> statements:
>
> "...not 1/1 32/27 3/2 which is never possible."
>
> "I don't know yet about 1/1 32/27 1024/675, perhaps it is never
> allowed."
>
> You obviously think that your take on JI exists objectively and is
> "out there" to be discovered. But where is it?
>
> The "knowledge" about it is obviously not like knowledge of logical
> or mathematical truths. It's also not empirically testable like the
> statements of science. Rather, it is based on intuition like moral
> and aesthetic understanding but differs from them in being based
> only on the intuition of one person (you Marcel). That makes it
> revelatory/religious "knowledge". Enough said.
>
> Kalle Aho
>
>
>

Marcel>"No it does quite the opposite.
I shines like no other tuning system with chords like these."
>"The smallest step is 25/24, or about 70.7 cents"
Hmm...that's essentially heard to the ear as 1/1 AKA the same tone rather than two separate ones.
I'm taking about chords formed from notes at least a half step but at least a 1/8th tone less than a whole step apart...that are obviously far enough apart to be heard as two separate tones when played together.

Could you have me an example from your scale of such chords?

>"About adaptive-ji.I can't seriously comment on that, I've made
clear many times before what I think of that hidious tuning system and
don't consider it JI at all."

I will agree there. From what I've heard it sounds like a wobbly/indecisive version (both physically and mood-wise) of whatever scale it's trying to purify and the wobbly-ness (melodic comma shift?) often bugs me more than the purity gain is worth. Or let me put it this way: what's your view about why adaptive JI isn't so great?

> You obviously think that your take on JI exists objectively and is
> "out there" to be discovered. But where is it?
>

It's scattered around in posts I made to this list in about a year time I
think :)
I'm going to set up a webpage where I explain everything in detail.

>
> The "knowledge" about it is obviously not like knowledge of logical
> or mathematical truths. It's also not empirically testable like the
> statements of science. Rather, it is based on intuition like moral
> and aesthetic understanding but differs from them in being based
> only on the intuition of one person (you Marcel). That makes it
> revelatory/religious "knowledge". Enough said.
>

No you're wrong here.
It's based purely on math and logic.
It's also a consistent system. I'm not interested in fooling myself.

But I'm not ready to start such a discussion like I see comming on this
subject.
So you can think of it like you will for now.
I'll post a message to the list when I have a website ready so you can all
scrutinise things in detail after reading the full theory and all the math
and logic.

Marcel

:

> Hmm...that's essentially heard to the ear as 1/1 AKA the same tone rather
> than two separate ones.
>

I hear 25/24 as a distinct cromatic semitone.

> I'm taking about chords formed from notes at least a half step but at least
> a 1/8th tone less than a whole step apart...that are obviously far enough
> apart to be heard as two separate tones when played together.
>

Well there's 27/25 and 10/9
Take your pick and see in the scale I gave before where they exist and form
a chord :)

>
> I will agree there. From what I've heard it sounds like a
> wobbly/indecisive version (both physically and mood-wise) of whatever scale
> it's trying to purify and the wobbly-ness (melodic comma shift?) often bugs
> me more than the purity gain is worth. Or let me put it this way: what's
> your view about why adaptive JI isn't so great?
>

Sorry but not feel like again posting a negative tirade on adaptive-ji. I'll
just say I agree with your words and would add a few more of my own ;)

Marcel

Chris (concerning Marcel's theories)>I'm curious as to if these statements are based on math or hearing.

I am betting on math. But we have to remember even math can be viewed subjectively within music. In fact even the so-called objective theories such as roughness/critical-band and periodicity can be viewed as subjective as different people stress those two to different amounts. An extreme example some just need periodicity and don't care about roughness and actually love the sound of harmonic distortion (even for a dyad of 15/14 AKA a "half step") while others can't stand roughness of two notes less than a full two whole steps apart. Also some the critical band roughness of overtones matters a lot and
Setharesian timbres can make even the most un-periodic and rough scales sound pure to these people. Not to mention the issue of the mood of chords: some people may like a 7:8:10 chord more than a 2:3:4 just because of its mood without regard to roughness, timbre, or periodicity.

And of course, many people think somewhere inbetween...taking a bit of each theory and weighing how much each well-established theory matters by their own personal preference. To me any theory where 80%+ of people think it increases musicality/sound-makes-you-feel-good-ness is worth holding as objective and a good rule of thumb is try to maximize all of the above so much as you can in a balanced fashion..

Marcel>"...not 1/1 32/27 3/2 which is never possible."
I'll say this much, it's generally agreed upon by many (and thus fairly objective) that tones very high up on the harmonic series AKA tones lacking much periodicity at all....generally sound unresolved (unless they are within, say, 12 cents of a JI ratio that has good/short periodicity).
Thus 1/1 32/27 3/2 becomes 54:64:81...so far from periodic I'd be surprised if anyone considered it consonant: I think that's what Marcel is trying to say.

>"I don't know yet about 1/1 32/27 1024/675, perhaps it is never
allowed."
This just sounds weird to me. True 1024 is within a few cents of 34/27...but is the x/27 harmonic series partial really close enough to the center to be OK? This is very subjective ground, IMVHO. To me around harmonic 18+ is where things get too un-periodic (having a very long period, kind of like my...(LOL)) while Marcel, I'm guessing, thinks that happens around more like harmonic #30. And I know some people won't touch anything over about x/10 and consider it "terribly dissonant".

I think where Marcel is getting trouble is instead of saying "it sounds too un-periodic to me" he'll say things like "it isn't allowed" that seem to indirectly imply his opinion is the exclusive answer. I try my best (as I'm sure many of you do) to say things in the form of "this is my opinion and I believe it could help of X issue in tuning math or at least reveal a good direction to go when searching for answers".

-Michael

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> > You obviously think that your take on JI exists objectively and is
> > "out there" to be discovered. But where is it?
> >
>
> It's scattered around in posts I made to this list in about a year
> time I think :)
> I'm going to set up a webpage where I explain everything in detail.

That's not at all what I asked, but funnily, your answer is
completely in line with what I said about revelatory knowledge.

> > The "knowledge" about it is obviously not like knowledge of
> > logical or mathematical truths. It's also not empirically
> > testable like the statements of science. Rather, it is based on
> > intuition like moral and aesthetic understanding but differs from
> > them in being based only on the intuition of one person (you
> > Marcel). That makes it revelatory/religious "knowledge". Enough
> > said.
> >
>
> No you're wrong here.
> It's based purely on math and logic.

Of course it is based on math and logic (although "purely" is
debatable). That doesn't make it math or logic. Of course you could
arrange the system in an axiomatic way, see

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

but your axioms would have to be justified somehow. And the only
justification I can see here is your personal intuition.

> It's also a consistent system. I'm not interested in fooling myself.

That's not the impression I get. It is constantly changing and thus
contradicting itself.

> But I'm not ready to start such a discussion like I see comming on
> this subject.
> So you can think of it like you will for now.

I'll do that in any case.

> I'll post a message to the list when I have a website ready so you
> can all scrutinise things in detail after reading the full theory
> and all the math and logic.

OK.

Kalle Aho

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Kalle" <kalleaho@> wrote:
>
> > > It describes the decatonic scales I mentioned, and tells you
> > > how the tetrads work in a way analogous to the triads of the
> > > diatonic scale. It even shows how to do 11-limit extensions,
> > > much like jazz extends the triads of the diatonic scale.
> >
> > Where does it show such a thing? 11-limit chords cannot be formed
> > from decatonic scales, some notes must be "chromatically" altered.
>
> Right. See pg.14 in this PDF
>
> http://lumma.org/tuning/erlich/erlich-decatonic.pdf
>
> > > These decatonic scales belong to what we now call the pajara
> > > temperament. It's definitely the best temperament for what
> > > you're trying to do -- functional 7-limit harmony. Moreover,
> > > 12 is a pajara system, and it's been suggested that many
> > > jazz standards are actually using it.
> >
> > That's interesting! Who has suggested this?
>
> I forget. Was it George Secor or Keenan Pepper?
>
> -Carl

No, try Ray Perlner:

/tuning-math/message/15953

--George

I've already addressed this. I sent a message to the tuning list some time
ago announcing "Battaglia-JI." Battaglia-JI is an expansion of its
predecessor, DeVelde-JI. Although triads like 1/1 32/27 3/2 aren't allowed
in DeVelde-JI, they are considered valid in Battaglia-JI.

I highly recommend people upgrade to the new system :)

-Mike

On Tue, Feb 9, 2010 at 11:40 AM, Kalle <kalleaho@...> wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Marcel de Velde
> <m.develde@...> wrote:
>
> > Sorry, quick correction to avoid possible confusion. That should
> > offcourse be 1/1 32/27 40/27, not 1/1 32/27 3/2 which is never
> > possible.
>
> I'm curious (and I bet I'm not the only one) about these kinds of
> statements:
>
> "...not 1/1 32/27 3/2 which is never possible."
>
> "I don't know yet about 1/1 32/27 1024/675, perhaps it is never
> allowed."
>
> You obviously think that your take on JI exists objectively and is
> "out there" to be discovered. But where is it?
>
> The "knowledge" about it is obviously not like knowledge of logical
> or mathematical truths. It's also not empirically testable like the
> statements of science. Rather, it is based on intuition like moral
> and aesthetic understanding but differs from them in being based
> only on the intuition of one person (you Marcel). That makes it
> revelatory/religious "knowledge". Enough said.
>
> Kalle Aho
>
>
>

> The important thing to realize about both of these
> notations is that both of those notes are some kind of E. This
> implies that they are also heard as versions of the same thing. So
> the essential spirit that leads to tempering already exists in the
> minds of many strict JI composers too.

Yes, but the question is -- why? Eb is also an E with an accidental,
why is that different?

For the last few months my approach has been to try to "separate"
those things in my mind. That being said -- the chord C-E-F#-B-D#
doesn't have the same harmonic properties as C-Eb-G, even though in
12-tet the D# and the Eb are identical. Because in the first chord,
you hear the C-D# as a major third on top of a fifth on top of a major
third -- or 75/32 -- but in the second chord, you hear the C-Eb as a
minor third, or 6/5 (or 19/16 or whatever you'd like).

What's the difference? Well, one's called D#, and one's called Eb. But
there is no diesis in 12-tet -- does that not reflect that people also
hear those notes as the "same thing?" If not, where do you draw the
line?

So I think that even in temperament you can distinguish underlying
perceptual changes happening with the same notes... or discover new
ways that existing notes can harmonically function.

Of course, this personal view of mine makes perfect sense until you
consider 12-tet comma pumps that sound perfectly natural, and I'm not
sure what's going on with that. Perhaps your brain switches its mode
of placement for some tempered intervals around in retrospect, as the
progression completes. Or perhaps it merges them together. I'm not
sure.

I think the truth is reflected somewhere in what you said, but the
question is -- why? Is there some inherent psychoacoustic reason for
this, or is it just a matter of conditioning? Psychoacoustically and
psychologically -- what's really going on?

-Mike

> Reply to sender | Reply to group
> Messages in this topic (34)
> Recent Activity:
>
> New Members 3
> New Links 1
>
> Visit Your Group Start a New Topic
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
>   tuning-subscribe@yahoogroups.com - join the tuning group.
>   tuning-unsubscribe@yahoogroups.com - leave the group.
>   tuning-nomail@yahoogroups.com - turn off mail from the group.
>   tuning-digest@yahoogroups.com - set group to send daily digests.
>   tuning-normal@yahoogroups.com - set group to send individual emails.
>   tuning-help@yahoogroups.com - receive general help information.
> Switch to: Text-Only, Daily Digest • Unsubscribe • Terms of Use
> .
>

>    A flip question becomes: why argue about a single "fixed" JI scale when you can just use adaptive JI to do "perfect JI purity tempering"?   I sure hope few people view adaptive JI with unnoticably small commatic melody movement as the "Holy Grail" of tuning though...  Because then I fear once the "purity equation" problem is solved few of us would experiment with anything more complex than, say, a 7:8:9 chord IE other chords that yield more complex tonal colors.
>
> -Michael

Yes, but my goal is to figure out why any of this happens to begin
with. I want to figure out the psychoacoustic, or psychological, or
just some kind of tangible basis for everything. Why is there an
inconsistency between JI purity and tonalness to begin with?

-Mike

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

> > > That's interesting! Who has suggested this?
> >
> > I forget. Was it George Secor or Keenan Pepper?
> >
> > -Carl
>
> No, try Ray Perlner:
>
> /tuning-math/message/15953

Thanks George! You have such an excellent memory.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The important thing to realize about both of these
> > notations is that both of those notes are some kind of E. This
> > implies that they are also heard as versions of the same thing.
> > So the essential spirit that leads to tempering already exists
> > in the minds of many strict JI composers too.
>
> Yes, but the question is -- why? Eb is also an E with an
> accidental, why is that different?

Eb is apart from E by 25/24, whereas E and E+ are apart
by 81/80. As to why we heed one and ignore the other, it
is cultural. Traditional Thai music is based on pentatonic
scales in 7-ET, where 25/24 vanishes. And presumably one
day the Bach of xenharmony will arrive, and we will get a
genre where 81/80 (or some other comma that vanishes in 12)
becomes commonly heard as chromatic.

-Carl

The TransFormSynth has been around for a few years now; folks
here may remember the early version in 2007 demonstrated by
Jim Plamondon on YouTube (a very cheesy video which gave no
credit to its actual creator, the person who wrote all the Java
classes for it: Dr. William Sethares; give him some credit, please!!)

TFS is fantastic! And I appreciate very much that it's free and
the people promoting it are scholars who are behaving like
scholars instead of making ridiculous hyperbolic claims.

Still, without allowing something beyond subsets of non-12
tunings, in its current form the TFS is unnecessarily limiting
to my mind, tacitly suggesting the idea that traditional
patterns (read diatonic) of a given temperament are all the
only patterns that make any musical sense; so, while it's very
practical, I think it's also extremely conservative, at this point.

Cheers,
AAH
=====

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> > I have still yet to figure out how to just
> > write expressive, emotional music with anything other than 12-tet that
> > doesn't sound "weird."
>
> I highly recommend checking out the TransFormSynth, or TFS, a free dynamic tonality synthesizer. It turns your computer keyboard into an isomorphic keyboard with the same fingering in every key and tuning (within a given temperament). On this interface you can play in 12-, 17-, 19-, 31-, and 53- equal divisions of the octave with the SAME FINGERING :D
> This way you don't have to spend a year learning the basic patterns of a single tuning just to find out you don't love it. Instead, you spend that time learning the patterns of a given temperament and learn how to apply them to every tuning within that temperament.
>
> While providing you with an ergonomic interface through which you can play every tuning with the same fingering, the program also modifies the harmonic structure of the timbres you use to maximize sensory consonance. It is the harmonic structure that determines sensory consonance experienced from intervals, both harmonic and melodic, played with complex tones, and the TFS changes the partial structure of the tones you use to make sure they match up closest to your current tuning. This, though altering the timbre of your sounds slightly, provides consonance in many tunings so that they don't sound NEAR as "weird".
> For instance, 22-edo the major third gets pretty darn sharp. Instead of just dealing with the clash, the TFS remaps the partials of your given tone so that it is this "sharp" third that is the one that is MOST consonant for that timbre. This sharp third no longer sounds sharp, just different.
> Here is a short video demonstrating dynamic tonality:
> http://www.youtube.com/watch?v=Nd4h8vmEsQM
>
> And you can download it (for free) at the bottom of this page:
> http://www.dynamictonality.com/spectools.htm
>
> Hope this helps you find your way =)
>
> John Moriarty
>

I wish I had joined this list 3 years earlier.

> As it turns out, decatonic scales HAVE been used extensively in Jazz.
> One of the most common bebop scales is a major scale with added blue
> 3rd, 5th and 7th: C D Eb E F F# G A Bb B. Note, 8 short steps and two
> long ones. This scale is featured prominently in everything from Blue
> Monk to Purple Haze. Not all jazz works with this temperament ("I've
> got rhythm" is comma pump city,) but a surprising amount does,
> especially the bluesier stuff.

That was the first scale that I thought of as well. Modern guys are
starting to move towards a different decatonic scale though - C C# D
D# E F# G G# A B C - this is basically a lydian scale with a "#15"
thrown in, and giving the option between lydian and lydian augmented.
It's a mixture of lydian, lydian augmented, lydian #2, and lydian aug
#2 -- which are all modes of the 4 usual parent scales of western
music - with the option of the #1 thrown in as well, which is related
to the other extensions by fifth, as well as to the root directly via
17/16, and to the D# by a major second, and to the A by a major third,
etc. There are all sorts of 17- and 19- limit intervals being tempered
out here. Sometimes an A# can be used as well, making it an 11 note
scale.

And if you throw in an F (which merges lydian augmented with ionian
augmented), you get the full 12 note scale, but conceived of as a far
cry from it being a "chromatic" scale, with every note having a
possible harmonic function. Perhaps this is what Bartok was also doing
with his polymodal chromatic scales. Perhaps once I finally figure out
what's going on with temperament in general, I'll try to reverse
engineer some linear or planar temperament making use of this fact.

For those curious as to what this scale sounds like, you can hear my
piece "Sand Prism" here:
http://rabbit.eng.miami.edu/students/mbattaglia/Senior_Recital/1-01%20Sand%20Prism.mp3

It's a bit long, but demonstrates the harmonic concept.

> Anyway, my feeling is paultone/twintone is in fact the second most
> common linear temperament in western music after meantone, and
> therefore warrants more study.

I have often noticed that my harmonic ideas differ quite a bit from
the usual "classical" approach -- perhaps it's that I tend to think
naturally in a pajara or dominant context, and the classical folks
tend to think in meantone.

What temperament was Debussy thinking in? How about Ravel?

This has been a very inspiring day.

-Mike

On Tue, Feb 9, 2010 at 1:49 PM, gdsecor <gdsecor@yahoo.com> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "Kalle" <kalleaho@> wrote:
> >
> > > > It describes the decatonic scales I mentioned, and tells you
> > > > how the tetrads work in a way analogous to the triads of the
> > > > diatonic scale. It even shows how to do 11-limit extensions,
> > > > much like jazz extends the triads of the diatonic scale.
> > >
> > > Where does it show such a thing? 11-limit chords cannot be formed
> > > from decatonic scales, some notes must be "chromatically" altered.
> >
> > Right. See pg.14 in this PDF
> >
> > http://lumma.org/tuning/erlich/erlich-decatonic.pdf
> >
> > > > These decatonic scales belong to what we now call the pajara
> > > > temperament. It's definitely the best temperament for what
> > > > you're trying to do -- functional 7-limit harmony. Moreover,
> > > > 12 is a pajara system, and it's been suggested that many
> > > > jazz standards are actually using it.
> > >
> > > That's interesting! Who has suggested this?
> >
> > I forget. Was it George Secor or Keenan Pepper?
> >
> > -Carl
>
> No, try Ray Perlner:
>
> /tuning-math/message/15953
>
> --George
>
>

I remember the YouTube video, but didn't know the software
was available. I'm still wondering whether it is considered
to supercede The Viking or compliment it or...

Certainly I see nothing in The Viking which "tacitly
suggest[s] ... that traditional patterns (read diatonic) of
a given temperament are all the only patterns that make any
musical sense".

-Carl

--- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@...> wrote:
>
> The TransFormSynth has been around for a few years now; folks
> here may remember the early version in 2007 demonstrated by
> Jim Plamondon on YouTube (a very cheesy video which gave no
> credit to its actual creator, the person who wrote all the Java
> classes for it: Dr. William Sethares; give him some credit,
> please!!)
>
> TFS is fantastic! And I appreciate very much that it's free
> and the people promoting it are scholars who are behaving like
> scholars instead of making ridiculous hyperbolic claims.
>
> Still, without allowing something beyond subsets of non-12
> tunings, in its current form the TFS is unnecessarily limiting
> to my mind, tacitly suggesting the idea that traditional
> patterns (read diatonic) of a given temperament are all the
> only patterns that make any musical sense; so, while it's very
> practical, I think it's also extremely conservative, at this
> point.
>
> Cheers,
> AAH
> =====

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Certainly I see nothing in The Viking which "tacitly
> suggest[s] ... that traditional patterns (read diatonic) of
> a given temperament are all the only patterns that make any
> musical sense".

OK, maybe I wasn't clear there. I mean, the whole premise of
dynamic tonality implies that 12 tone subsets of other tunings
are all that are musically useful, and the keyboard patterns
suggested for use with dynamic tonality seem to be those that
favor diatonicism.

So, 12-tone subsets and diatonicism as implied by the core
concept as it's being presented currently - that is what I am
calling a tacit suggestion, that I find limiting from the
standpoint of creative resources for making music.

Cheers,
AAH
=====

> > The important thing to realize about both of these
> > notations is that both of those notes are some kind of E. This
> > implies that they are also heard as versions of the same thing. So
> > the essential spirit that leads to tempering already exists in the
> > minds of many strict JI composers too.
>

Are you suggesting that we hear such an E as different JI ratios at the same
instance?
I don't think so. There's a lot that points to a decision in interpreting a
tempered interval.
Sorry if I misunderstood.

> Yes, but the question is -- why? Eb is also an E with an accidental,
> why is that different?
>
> For the last few months my approach has been to try to "separate"
> those things in my mind. That being said -- the chord C-E-F#-B-D#
> doesn't have the same harmonic properties as C-Eb-G, even though in
> 12-tet the D# and the Eb are identical. Because in the first chord,
> you hear the C-D# as a major third on top of a fifth on top of a major
> third -- or 75/32 -- but in the second chord, you hear the C-Eb as a
> minor third, or 6/5 (or 19/16 or whatever you'd like).
>

Yes agreed. C (1/1) - E (5/4) - F# (45/32) - B (15/8) - D# (75/32)
Although I think this D# is also very frequently spelled as Eb. Can't trust
notation at all.
As for 1/1 6/5 3/2. It can also be 1/1 75/64 3/2. A very nice chord in my
opinion.
1/1 75/64 3/2 15/8 75/32 when comming from your previous chord (or also drop
15/8 to 5/3 for instance)(resolve to somthing like 15/8 75/32 45/16)

> What's the difference? Well, one's called D#, and one's called Eb. But
> there is no diesis in 12-tet -- does that not reflect that people also
> hear those notes as the "same thing?" If not, where do you draw the
> line?
>
> So I think that even in temperament you can distinguish underlying
> perceptual changes happening with the same notes... or discover new
> ways that existing notes can harmonically function.
>
> Of course, this personal view of mine makes perfect sense until you
> consider 12-tet comma pumps that sound perfectly natural, and I'm not
> sure what's going on with that. Perhaps your brain switches its mode
> of placement for some tempered intervals around in retrospect, as the
> progression completes. Or perhaps it merges them together. I'm not
> sure.
>

I agree with your perfect sense view :)

But I don't understand which comma pumps you're referring to?
You mean for instance I-vi-ii-V etc? Do you not find 9/8 4/3 5/3 a
satisfactory solution?

>
> I think the truth is reflected somewhere in what you said, but the
> question is -- why? Is there some inherent psychoacoustic reason for
> this, or is it just a matter of conditioning? Psychoacoustically and
> psychologically -- what's really going on?

Yes indeed.
This question is puzzling me too.
I'm calling it brain math :) I don't see how psychoacoustical things can
fully explain it.
It must be atleast partly deeper in the brain.
Perhaps music can even teach us about the brain.
On a very far out speculation, there are hints thoughts etc are waves too.
Perhaps the brain partially works inside in a JI way too.
The brain must be doing some serious math somewhere in some ways in any
case. Perhaps the way the brain does this is related to JI.
I've allways seen it as a sort of universal truth. Music in JI will hold
throughout the universe. Things like comma pumps don't all of a sudden not
pump on another planet lol
It's such beautifull math and such a beautifull system, who knows maybe
mother nature / evolution found use for it.
/end of far out brain math speculation ;)

Marcel

--- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > Certainly I see nothing in The Viking which "tacitly
> > suggest[s] ... that traditional patterns (read diatonic) of
> > a given temperament are all the only patterns that make any
> > musical sense".
>
> OK, maybe I wasn't clear there. I mean, the whole premise of
> dynamic tonality implies that 12 tone subsets of other tunings
> are all that are musically useful, and the keyboard patterns
> suggested for use with dynamic tonality seem to be those that
> favor diatonicism.
>
> So, 12-tone subsets and diatonicism as implied by the core
> concept as it's being presented currently - that is what I am
> calling a tacit suggestion, that I find limiting from the
> standpoint of creative resources for making music.

Well, I've only played with it 30 seconds so far, but I'd
say diatonicism corresponds to their "syntonic continuum"
setting, whereas the other settings are other worlds --
scales based on generators other than the 5th, which,
controlled from my MIDI keyboard, immediately produced
out-of-order scales with apparently > 12/oct. I know from
their 'isomorphic mappings' paper, their equations are
fully general, and they intend to support the thummer
with 19, etc etc.

On another point, yes, Bill deserves lots of credit, as
does Milne. And it's a most-welcome development. They do
cite Gene, Paul, and even in a draft, me. But it would
have been nice to get a little more recognition that this
work is essentially lifted from these mailing lists. Or
even better, some direct contribution from the authors here,
instead of lurking.

That said, we couldn't get our stuff together enough to
craft a paper -- we tried, but it died amid constant
bickering over minutia. Perhaps that's to do with the
nature of mailing lists and long-distance collaboration.
Or perhaps we're all just jerks. So anyway, I'm very glad
these guys rose and did the exceptional job they did to
move these things closer to reality. And that includes
Jim, bless him.

-Carl

I wrote:
> That said, we couldn't get our stuff together enough to
> craft a paper -- we tried, but it died amid constant
> bickering over minutia. Perhaps that's to do with the
> nature of mailing lists and long-distance collaboration.
> Or perhaps we're all just jerks. So anyway, I'm very glad
> these guys rose and did the exceptional job they did to
> move these things closer to reality. And that includes
> Jim, bless him.

To be fair, several of us were sent drafts offlist, but we
were asked to keep quiet, presumably because of a publishing
embargo. And I suppose had the authors engaged on
tuning-math, they would have risked getting dragged down
into the bickering. So be it. -Carl

Well, most of those scales with "apparently > 12/oct"
don't have more than twelve tones per octave. Choosing
19ET gives apparent 19ET, but the keyboard mapping
becomes strange, at least to me, presumably having to
do with the diatonic bias I was talking about, but how
the mapping makes sense might just not be evident
unless one has something like an Axis keyboard to use
with it. The computer keyboard option in The Viking
comes from synth maker and doesn't do the Wicki/Hayden
layout that would be like the Thummer... at least I
couldn't get that to work.

Another way I found to get something really microtonal was
to type something other than 1200 for the "Oct. Width",
and once that's done, the keyboard mappings again are
strange.

The remarks made about 19ET and the Thummer have always
struck me as pretty incoherent, though the paper does address
it, it's rather abstract. Considering that Thumtronics
is bankrupt (although the website is still there) I wouldn't
expect to see a Thummer playing 19ET available anytime
soon, unless the device becomes open source, which was what
Plamondon had intended to do when his company dissolved.
Anyway, there really are not enough keys on it to explore
19. And who wants to stop at 19 anyway? It's all way too
limiting in my opinion.

Again, I love these synths; the work is great, so please
don't think I'm bashing anything or anyone. All I'm saying
is that in their present forms, for me, they're too biased
and too limiting. I'm much more interested in applying
spectral mapping principles to the Tonal Plexus (big
surprise!)

Cheers,
AAH
=====

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > > Certainly I see nothing in The Viking which "tacitly
> > > suggest[s] ... that traditional patterns (read diatonic) of
> > > a given temperament are all the only patterns that make any
> > > musical sense".
> >
> > OK, maybe I wasn't clear there. I mean, the whole premise of
> > dynamic tonality implies that 12 tone subsets of other tunings
> > are all that are musically useful, and the keyboard patterns
> > suggested for use with dynamic tonality seem to be those that
> > favor diatonicism.
> >
> > So, 12-tone subsets and diatonicism as implied by the core
> > concept as it's being presented currently - that is what I am
> > calling a tacit suggestion, that I find limiting from the
> > standpoint of creative resources for making music.
>
> Well, I've only played with it 30 seconds so far, but I'd
> say diatonicism corresponds to their "syntonic continuum"
> setting, whereas the other settings are other worlds --
> scales based on generators other than the 5th, which,
> controlled from my MIDI keyboard, immediately produced
> out-of-order scales with apparently > 12/oct. I know from
> their 'isomorphic mappings' paper, their equations are
> fully general, and they intend to support the thummer
> with 19, etc etc.
>
> On another point, yes, Bill deserves lots of credit, as
> does Milne. And it's a most-welcome development. They do
> cite Gene, Paul, and even in a draft, me. But it would
> have been nice to get a little more recognition that this
> work is essentially lifted from these mailing lists. Or
> even better, some direct contribution from the authors here,
> instead of lurking.
>
> That said, we couldn't get our stuff together enough to
> craft a paper -- we tried, but it died amid constant
> bickering over minutia. Perhaps that's to do with the
> nature of mailing lists and long-distance collaboration.
> Or perhaps we're all just jerks. So anyway, I'm very glad
> these guys rose and did the exceptional job they did to
> move these things closer to reality. And that includes
> Jim, bless him.
>
> -Carl
>

On 10 Feb 2010, at 5:58 AM, Mike Battaglia wrote:

>> The important thing to realize about both of these
>> notations is that both of those notes are some kind of E. This
>> implies that they are also heard as versions of the same thing. So
>> the essential spirit that leads to tempering already exists in the
>> minds of many strict JI composers too.
>
> Yes, but the question is -- why? Eb is also an E with an accidental,
> why is that different?

This is just a name convention which has historical background. If music is developped in a different way, maybe we would have different note names, different notation system and no accidentals in the case that each of 12 chromatic notes will have its individual name and graphical sign.

>
> For the last few months my approach has been to try to "separate"
> those things in my mind. That being said -- the chord C-E-F#-B-D#
> doesn't have the same harmonic properties as C-Eb-G, even though in
> 12-tet the D# and the Eb are identical. Because in the first chord,
> you hear the C-D# as a major third on top of a fifth on top of a major
> third -- or 75/32 -- but in the second chord, you hear the C-Eb as a
> minor third, or 6/5 (or 19/16 or whatever you'd like).
>
> What's the difference? Well, one's called D#, and one's called Eb. But
> there is no diesis in 12-tet -- does that not reflect that people also
> hear those notes as the "same thing?" If not, where do you draw the
> line?
>

Answer is: the context.

Daniel Forro

Dear All,
Would anyone like to submit a track to be added to this binaural peice I am creating?
 
Please download from:
(right click on down arrow in the task bar of the play widget and listen on headphones as the piece is binaural)
 
http://soundcloud.com/our-common-ground/soft-fire
 
This peice 'soft fire' is a dozen or so sine waves which form a two chord progression.  Evolving polyrhythms are created by the binaural beating of similar and harmonically related intervals, one played in L channel and one played in the right channell.
 
The idea is that vast harmonic space can be created by resonating at the sweet spots in the stillness of the harmonic nodes. i am trying to create space rather than fill it with melody, though their is some travelling betweeen harmonic nodes via glissandos, some almost imperceptible.
 
The tonal centres of this peice are 128 hz, 320hz and 83.33 hz.
 
I want to weave many voices into the mix as mine is a bit boring and meaningless when not in community. I would appreciate some ebullient percussion that I could 'dub' into the far distance a la King Tubby. I would also appreciate some frugal but surprising higher pitched resonances (thinking of Vaughn Williams) to create that sense of vast height.
 
Thanks
Steve

__________________________________________________________________________________
Yahoo!7: Catch-up on your favourite Channel 7 TV shows easily, legally, and for free at PLUS7. www.tv.yahoo.com.au/plus7

On 10 Feb 2010, at 6:36 AM, Mike Battaglia wrote:

>>
>> As it turns out, decatonic scales HAVE been used extensively in Jazz.
>> One of the most common bebop scales is a major scale with added blue
>> 3rd, 5th and 7th: C D Eb E F F# G A Bb B. Note, 8 short steps and two
>> long ones. This scale is featured prominently in everything from Blue
>> Monk to Purple Haze. Not all jazz works with this temperament ("I've
>> got rhythm" is comma pump city,) but a surprising amount does,
>> especially the bluesier stuff.

I don't think this was used as a scale by itself, more like
overlapping subsets (minor pentatonics or blues scale for melody,
major chords for harmony}. But from my listening and analysing
experience bebop used more chromatic approach, patterns and licks
chromatically shifted and transposed (besides minor pentatonic, blues
scale, common 7-tone scales and 8-tone diminished symmetric scales -
which is common to all jazz styles). And it must be said that scales
are not always used as scales in jazz (scale passages), because
melodies are not done only from seconds, more often from thirds and
other intervals. Jazz uses also lot of broken (arpeggiated) chords as
melodic material.

>
> That was the first scale that I thought of as well. Modern guys

For example who?

> are
> starting to move towards a different decatonic scale though - C C# D
> D# E F# G G# A B C - this is basically a lydian scale with a "#15"
> thrown in, and giving the option between lydian and lydian augmented.
> It's a mixture of lydian, lydian augmented, lydian #2, and lydian aug
> #2 -- which are all modes of the 4 usual parent scales of western
> music - with the option of the #1 thrown in as well, which is related
> to the other extensions by fifth, as well as to the root directly via
> 17/16, and to the D# by a major second, and to the A by a major third,
> etc. There are all sorts of 17- and 19- limit intervals being tempered
> out here. Sometimes an A# can be used as well, making it an 11 note

I don't think there is such tendency. Yes, maybe somebody in 50's
after reading Chromatic Lydian Concept... Nowadays everything
possible is used and mixed, even in jazz. There's not possible to see
some clear and distinctive "schools" or compositional or
improvisational tendencies. From your description it looks like this
is main, easily recognizable tendency. I don't think so.

And what has jazz to do with microtones? Maybe you hear there
something which is not there :-)

> scale.
>
> And if you throw in an F (which merges lydian augmented with ionian
> augmented), you get the full 12 note scale, but conceived of as a far
> cry from it being a "chromatic" scale, with every note having a
> possible harmonic function.

I'm sorry but I know only one chromatic scale, and of course it's
possible to create chords on all its notes.

> Perhaps this is what Bartok was also doing
> with his polymodal chromatic scales.

Polymodal has nothing to do with chromatic. Yes, it's possible to
combine modes in such way that their notes mixed together makes a
chromatic scale, but if they are not used as chromatic scales, we
can't talk about chromaticism.

I woudn't say Bartók's chromaticism was derived from polymodality.
He used more sophisticated principles on border of dodecaphony,
symmetric axis, interval groups... And not only chromaticism.

Daniel Forro

> I don't think this was used as a scale by itself, more like
> overlapping subsets (minor pentatonics or blues scale for melody,
> major chords for harmony}. But from my listening and analysing
> experience bebop used more chromatic approach, patterns and licks
> chromatically shifted and transposed (besides minor pentatonic, blues
> scale, common 7-tone scales and 8-tone diminished symmetric scales -
> which is common to all jazz styles). And it must be said that scales
> are not always used as scales in jazz (scale passages), because
> melodies are not done only from seconds, more often from thirds and
> other intervals. Jazz uses also lot of broken (arpeggiated) chords as
> melodic material.

Yes, it's more of a newer sound. Not used too much in bebop.

> >
> > That was the first scale that I thought of as well. Modern guys
>
> For example who?

Aaron Parks, Kurt Rosenwinkel, Brad Mehldau, Jim Black, Aisha Duo,
Ralph Alessi, etc. That whole crowd

> I don't think there is such tendency. Yes, maybe somebody in 50's
> after reading Chromatic Lydian Concept... Nowadays everything
> possible is used and mixed, even in jazz. There's not possible to see
> some clear and distinctive "schools" or compositional or
> improvisational tendencies. From your description it looks like this
> is main, easily recognizable tendency. I don't think so.

This is simply a tendency I have noticed, and the scale that I
outlined is just my way of categorizing a harmonic trend that I
notice. For starters, it's something that -I- use :) And I didn't make
up the idea by myself. It was a sound in my head that I just fleshed
out with that scale.

Perhaps a more accurate way of terming it is that it's a polymodal
setup I hear going on - over a chord like C, I might hear B mixolydian
played over it (or even B ionian).

> And what has jazz to do with microtones? Maybe you hear there
> something which is not there :-)

Well, if I hear it... :)

> Polymodal has nothing to do with chromatic. Yes, it's possible to
> combine modes in such way that their notes mixed together makes a
> chromatic scale, but if they are not used as chromatic scales, we
> can't talk about chromaticism.

> I woudn't say Bartók's chromaticism was derived from polymodality.
> He used more sophisticated principles on border of dodecaphony,
> symmetric axis, interval groups... And not only chromaticism.

I got the term from
http://en.wikipedia.org/wiki/Polymodal_chromaticism. Perhaps the
article itself is wrong and demands a rewrite.

-Mike

On 10 Feb 2010, at 12:32 PM, Mike Battaglia wrote:

Thanks for the names of jazz musicians, I will check...

> I got the term from
> http://en.wikipedia.org/wiki/Polymodal_chromaticism. Perhaps the
> article itself is wrong and demands a rewrite.
>
> -Mike

Hm, wikipedia... Written by a certain person named Anonymus, and full
of errors and strange statements. Only trustful sources are some
facts, but explanations and interpretations not always...

I see it like this:

- Polymodal chromaticism doesn't exist, both terms just describe two
different approaches to music.

- Of course if we superimpose, combine two or more modes or scales
which have less tones then 12, we can get the chromatic scale in the
result. But in such polymodal works composer doesn't use
chromaticism, he works with modes. Chromaticism is more or less
latent and can be avoided. Even dissonances and chromatic seconds can
be avoided with careful composing method. I wouldn't talk in this
case about chromaticism.

- Chromatic scale is a chromatic scale. Nothing else. To describe it
as "12-tone polymode" just because it was a result from combining two
or mode modes is really unnecessary.

Just my opinion.

Daniel Forró

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Mike B> "I have always viewed it as a slight mistuning of
>
> the real underlying reality of music (JI), for convenience' s sake,
>
> and to limit the amount of notes that someone has to think of."
>
> Oddly enough, to a fair extent, so have I. At least, among the
> people who I see "prophetizing" their use of JI: the idea seems to
> be simply to temper to acheive better "average dyadic purity"
> rather than to, say, increase the degree of tonal color or number
> of chords available.

It depends what you take as chords. If any kind of subset is a chord
then any scale, tempered or not, with the same number of notes has
the same number of chords. On the other hand, if chords have to be
consonant, then tempering can increase the number of chords
available.

> Kalle>"5/4 would be notated as E and 81/64 as E+."
> Right, so in this example (and many others) different versions
> of a note are established, each to harmonize more purely with
> particular other notes forming perfect dyads. And all adaptive JI
> does is determine that selections while avoiding commatic melodic
> movement so much as possible, correct?

This is basically correct although the kind of adaptive tuning I
advocate doesn't try to avoid inflections but minimizes the pitch
range of a note (that also keeps inflections small).

> >"If your notation was based on a circle of fifths the E would be
> acoustically an 81/64 while you might notate 5/4 above C as E- for
> example. Temperament just makes these different versions of the
> same thing also acoustically identical."
>
> Right. You could say I consider a loophole in many people's
> though process is the idea that everything must aim for the ideal
> of being more or less "acoustically identical" to 12TET tones. For
> example 11/9: when I made a scale with it I was posed the question
> (paraphrased) "is this supposed to be an E or a D#?!"

I'm not sure what you mean. The only thing that is acoustically
identical to 12TET is 12TET itself.

> >"So the essential spirit that leads to tempering already exists in
> the minds of many strict JI composers too."
> Then again, of course, 11/9 can be considered JI, but many
> people would avoid tones like that as they are of "high limit" (11,
> to be exact).
> I guess you could say that's what I mean in a sense by "strict-
> JI" as well...the quest to keep low limits and the idea that only
> the lowest limits (particular 7 and under) consistute enough
> consonance to form "resolved sounding" chords.

What I mean by "strict-JI" is the practice that both melodic and
harmonic intervals are derived from low-limit whole number ratios.
But what is considered low-limit may vary, even from piece to piece
by the same composer. In adaptive JI chords are just but melodic
intervals may be tempered.

> A flip question becomes: why argue about a single "fixed" JI
> scale when you can just use adaptive JI to do "perfect JI purity
> tempering"? I sure hope few people view adaptive JI with
> unnoticably small commatic melody movement as the "Holy Grail" of
> tuning though... Because then I fear once the "purity equation"
> problem is solved few of us would experiment with anything more
> complex than, say, a 7:8:9 chord IE other chords that yield more
> complex tonal colors.

I think we should separate the intonation and scale/structural
issues. Now they are both under the broad category of tuning. I don't
know if anyone disputes the datum that a scale and its'
intonation/tuning can be understood as different things. Some people
here are only interested in the intonation of existing music like for
example some of the 12-tone well temperament people, some are
interested in new possible scales and structures that don't exist in
12-tone tunings and some (like me) are interested about both in
varying degrees.

Kalle Aho

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The important thing to realize about both of these
> > notations is that both of those notes are some kind of E. This
> > implies that they are also heard as versions of the same thing. So
> > the essential spirit that leads to tempering already exists in the
> > minds of many strict JI composers too.
>
> Yes, but the question is -- why? Eb is also an E with an accidental,
> why is that different?

Standard notation doesn't distinguish between E, E- and E+.
Accidentals are a feature of standard notation which is based on
diatonic scale as naturals. No one thinks that E and Eb are somehow
same. On the other hand, it is a defining feature of diatonic scale
that four fifths makes a major third + two octaves. This is true in
pythagorean tuning. This thinking was inherited when triads started
to be used. One thing that may also explain why we hear discriminable
pitches as versions of the same note is that in diatonic context the
syntonic comma is much smaller than seconds. If notes separated by
syntonic comma were included in the scale separately as "seconds" the
resulting scale would be improper. See

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

So if a scale is strictly proper, all thirds are larger than seconds,
all fourths are larger than thirds and so on. I don't know how it is
explained but supposedly some notes in improper scales are more
likely heard as inflections than separate notes.

> For the last few months my approach has been to try to "separate"
> those things in my mind. That being said -- the chord C-E-F#-B-D#
> doesn't have the same harmonic properties as C-Eb-G, even though in
> 12-tet the D# and the Eb are identical. Because in the first chord,
> you hear the C-D# as a major third on top of a fifth on top of a
> major third -- or 75/32 -- but in the second chord, you hear the C-
> Eb as a minor third, or 6/5 (or 19/16 or whatever you'd like).
>
> What's the difference? Well, one's called D#, and one's called Eb.
> But there is no diesis in 12-tet -- does that not reflect that
> people also hear those notes as the "same thing?" If not, where do
> you draw the line?

They have different names because notation is based on pythagorean
and meantone, not 12-equal. I actually think that D# and Eb are
melodically the same in 12-equal but the same note can have different
harmonic functions in different contexts.

> So I think that even in temperament you can distinguish underlying
> perceptual changes happening with the same notes... or discover new
> ways that existing notes can harmonically function.

Yes.

> Of course, this personal view of mine makes perfect sense until you
> consider 12-tet comma pumps that sound perfectly natural, and I'm
> not sure what's going on with that. Perhaps your brain switches its
> mode of placement for some tempered intervals around in retrospect,
> as the progression completes. Or perhaps it merges them together.
> I'm not sure.

I think they sound perfectly natural because, contra Marcel, our
brain doesn't analyze music in terms of JI. Our mind doesn't
recognize a tempered scale or some extra harmonic relation not
existing in its' JI version as some kind of unnatural perversion or
illusion even if tempered intervals gain their resonance from their
proximity to just intervals.

Kalle Aho

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> > > The important thing to realize about both of these
> > > notations is that both of those notes are some kind of E. This
> > > implies that they are also heard as versions of the same thing.
> > > So the essential spirit that leads to tempering already exists
> > > in the minds of many strict JI composers too.
> >
>
> Are you suggesting that we hear such an E as different JI ratios at
> the same instance? I don't think so. There's a lot that points to a
> decision in interpreting a tempered interval.
> Sorry if I misunderstood.

No, I think we don't hear that E as a ratio, that is: (tempered)
intervals are not interpreted as ratios at all. Sure, there is an
interval of major third between C and E but major third is not the
same thing as 4:5. 4:5 is a frequency ratio while major third is a
diatonic interval that can be and has been tuned in many different
ways. I don't understand where people get this idea that JI is a
theory of perception. It is not, it is a tuning system.

Kalle Aho

Mike B>
"I want to figure out the psychoacoustic, or psychological, or just some kind of tangible basis for everything. Why is there an
inconsistency between JI purity and tonalness to begin with?"

I don't think there is an inconsistency and I think we already know a lot if not most of the "whys" behind human hearing but not how they connect and rate in importance vis-a-vis each other.

IMVHO, the real problem is that people keep trying to view the theories as seperate or say there's only one way to create the effect (IE saying perfect periodicity and the harmonic series (and standard scales built around that idea) is the only way while virtually ignoring roughness: easy example; "perfectly periodic" harmonic distortion is often very high on roughness).
--------------------------------------------
If someone were to ask me why tonality, periodicity, difference tones, and virtual pitch work I'd summarize

"These all relate to ways of optimizing the phenomenon in physics AKA periodicity. Not-very-periodic waveforms take a long time to repeat and if that length is greater than a 20th of a second or so (time resolution of human hearing, as exploited in the mp3 format) the brain requires extra effort to process it."
I could also add "JI purity is 'tonal-ness' because it insist all tones in a chord point to a root tone in a straight harmonic series, thus sharing difference tones that point to the root tone and make the consecutive dyads in the harmonic series beat at the same rate against each other."
///////////////////////////////////
That the "easy answer", in my book. The hard question then becomes how much lack of periodicity really causes the brain to struggle...and in the same way how much roughness does...and, ultimately, what quantitative combinations of Periodicity+Roughness are possible in chords and scales while still feeling "resolved". I'd add the sensation of roughness is caused by the resolution of the basilar membrane in your ears.

We have Plomp and Llevelt for roughness graphs and perhaps periodicity covered by Paul Erlich...it's about time someone made "human tolerance for periodicity + roughness" graphs that record the result of "sum of the two theories" and "human tolerance for varying parameters of periodicity + roughness". If there is already one...I sure haven't seen it.
------------------------------------------------------------------
One you have that continuum fairly solved...I figure you can try different methods to make timbres, tunings, scale, and chords that meet said above standards, teetering on the edge of "resolved-ness" while adding more flexibility to music that comes from having more relaxed standards.
Would you agree we have more than enough theories about possible psychoacoustic standards to follow...and need to start working more on how to connect them and ultimately just more creative ways to apply them?

-Michael

Mike's question about microtonal music has inspired me to write a longer piece of text. At first, I intended to include it right in the body of the message. But then I thought it would be better to have the document stored separately.
For people who are familiar with various 2D temperaments, maybe they find some statements too "introductory". But I'm not sure how to explain my view in an understandable way without touching on these things.
Anyway, whether you find it useful to read or not, you can find it as an RTF document in this folder:
/tuning/files/PetrParizek

Petr

Kalle>"On the other hand, if chords have to be
consonant, then tempering can increase the number of chords
available."
Exactly, "tempering can increase the number of chords
available"...and that was the assumption I was making: that a set of note must meet a standard for consonance to qualify as a chord.

> Right. You could say I consider a loophole in many people's
> though process is the idea that everything must aim for the ideal
> of being more or less "acoustically identical" to 12TET tones. For
> example 11/9: when I made a scale with it I was posed the question
> (paraphrased) "is this supposed to be an E or a D#?!"

Exactly...I think it's frustrating that micro-tonality so often pushes people in the direction of making these "new" intervals for the purpose of sounding like old ones. It seems to me to make the whole art-form just go in circles so far as creating options the average Joe would hear and say "now that sounds fresh". Maybe you could give a good justification for this...what's the ultimate point (for you and perhaps others) about doing what looks on the surface like proving something already proved?

>"Some people here are only interested in the intonation of existing music like for
example some of the 12-tone well temperament people"
Right...I guess my question here becomes why said people don't accept adaptive JI as their final answer...

>"some are interested in new possible scales and structures that don't exist in 12-tone tunings"
Obviously, I'm in that boat. It sometimes amazes me how much people from the two groups spend arguing with each other or complaining that the other group is making too many posts exclusive to their one of the two topic. Perhaps we should consider splitting the group into two sections (historically-based microtonality and alternative-microtonality)? I'm just wondering b/c I think it could solve a lot of problems here.

The brain is automatically looking for order and
recognizable patterns. The patterns of a chain of pure
fifths can sound correct, the patterns of pure JI can sound
correct, and the patterns of an ET can sound correct, each
one sounding correct for different reasons.

The fifths-chain sounds correct mostly for melodic
structures. JI sounds correct mostly for harmonic
structures. ETs can bridge between these and sound
correct for having an overall structure that is
consistent. None shares a correctness with the
others.

Each thing has a simplicity about it that is
automatically recognizable as 'correct': pure fifths
are built from 1 interval, the first most basic interval
after the octave. JI intervals are strictly harmonic,
representing purity beyond the fifths chain. ETs
have 1 step size. None shares a simplicity with the
others.

Each one also has things about it that sound 'wrong'.
Fifths start sounding wrong harmonically, JI starts
sounding wrong melodically, and ETs sound wrong
because they are impure. None shares a wrongness
with the others.

Each of these three things competes with the others,
and each complements the others. The fifths chain
defines the deepest melodic structures of diatonicism,
pulling harmonic roots towards a pentatonic center
like a gravity well. JI defines the harmonic structures
of diatonicism and beyond, breaking the structure of
the fifths chain by different sizes of commas, pulling
polyphonic vertical structures like another gravity well.
ETs force both the fifths chain and JI harmonies into a
one-size-fits-all mold, like putting on a pair of glasses
that makes everything a little out of focus, but one
can quickly get used to it, and all the discrepancies
and constant shifts of sharpening in focus required for
JI vanish, and all the competition between JI and the
fifths chain vanishes, and everything gets glossed
with a mood peculiar to the step size of that ET.

As for comma-shifted letter names versus chromatically
inflected letter names, this has to do with all of the above,
in view of average limits of perception. I give a complete
explanation from this point of view here:
<http://www.h-pi.com/theory/foreword.html>

Yours,
AAH
====

--- In tuning@yahoogroups.com, "Kalle" <kalleaho@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > The important thing to realize about both of these
> > > notations is that both of those notes are some kind of E. This
> > > implies that they are also heard as versions of the same thing. So
> > > the essential spirit that leads to tempering already exists in the
> > > minds of many strict JI composers too.
> >
> > Yes, but the question is -- why? Eb is also an E with an accidental,
> > why is that different?
>
> Standard notation doesn't distinguish between E, E- and E+.
> Accidentals are a feature of standard notation which is based on
> diatonic scale as naturals. No one thinks that E and Eb are somehow
> same. On the other hand, it is a defining feature of diatonic scale
> that four fifths makes a major third + two octaves. This is true in
> pythagorean tuning. This thinking was inherited when triads started
> to be used. One thing that may also explain why we hear discriminable
> pitches as versions of the same note is that in diatonic context the
> syntonic comma is much smaller than seconds. If notes separated by
> syntonic comma were included in the scale separately as "seconds" the
> resulting scale would be improper. See
>
> http://en.wikipedia.org/wiki/Rothenberg_propriety
>
> So if a scale is strictly proper, all thirds are larger than seconds,
> all fourths are larger than thirds and so on. I don't know how it is
> explained but supposedly some notes in improper scales are more
> likely heard as inflections than separate notes.
>
> > For the last few months my approach has been to try to "separate"
> > those things in my mind. That being said -- the chord C-E-F#-B-D#
> > doesn't have the same harmonic properties as C-Eb-G, even though in
> > 12-tet the D# and the Eb are identical. Because in the first chord,
> > you hear the C-D# as a major third on top of a fifth on top of a
> > major third -- or 75/32 -- but in the second chord, you hear the C-
> > Eb as a minor third, or 6/5 (or 19/16 or whatever you'd like).
> >
> > What's the difference? Well, one's called D#, and one's called Eb.
> > But there is no diesis in 12-tet -- does that not reflect that
> > people also hear those notes as the "same thing?" If not, where do
> > you draw the line?
>
> They have different names because notation is based on pythagorean
> and meantone, not 12-equal. I actually think that D# and Eb are
> melodically the same in 12-equal but the same note can have different
> harmonic functions in different contexts.
>
> > So I think that even in temperament you can distinguish underlying
> > perceptual changes happening with the same notes... or discover new
> > ways that existing notes can harmonically function.
>
> Yes.
>
> > Of course, this personal view of mine makes perfect sense until you
> > consider 12-tet comma pumps that sound perfectly natural, and I'm
> > not sure what's going on with that. Perhaps your brain switches its
> > mode of placement for some tempered intervals around in retrospect,
> > as the progression completes. Or perhaps it merges them together.
> > I'm not sure.
>
> I think they sound perfectly natural because, contra Marcel, our
> brain doesn't analyze music in terms of JI. Our mind doesn't
> recognize a tempered scale or some extra harmonic relation not
> existing in its' JI version as some kind of unnatural perversion or
> illusion even if tempered intervals gain their resonance from their
> proximity to just intervals.
>
> Kalle Aho
>

I like what I hear. Very ambient and tranquil.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Feb 10, 2010, at 4:11 AM, Steven Grainger wrote:

>
>
> Dear All,
> Would anyone like to submit a track to be added to this binaural
> peice I am creating?
>
> Please download from:
> (right click on down arrow in the task bar of the play widget and
> listen on headphones as the piece is binaural)
>
> http://soundcloud.com/our-common-ground/soft-fire
>
> This peice 'soft fire' is a dozen or so sine waves which form a two
> chord progression. Evolving polyrhythms are created by the binaural
> beating of similar and harmonically related intervals, one played in
> L channel and one played in the right channell.
>
>
> The idea is that vast harmonic space can be created by resonating at
> the sweet spots in the stillness of the harmonic nodes. i am trying
> to create space rather than fill it with melody, though their is
> some travelling betweeen harmonic nodes via glissandos, some almost
> imperceptible.
>
>
> The tonal centres of this peice are 128 hz, 320hz and 83.33 hz.
>
>
> I want to weave many voices into the mix as mine is a bit boring and
> meaningless when not in community. I would appreciate some ebullient
> percussion that I could 'dub' into the far distance a la King Tubby.
> I would also appreciate some frugal but surprising higher pitched
> resonances (thinking of Vaughn Williams) to create that sense of
> vast height.
>
>
> Thanks
>
> Steve
>

"ETs have 1 step size. None shares a simplicity with the
others."
IMVHO a hole in this theory is the inability to, say, put half steps into a consonant chord.
Another thing is, >>at least with sine waves<<, I believe there is a psychoacoustic basis for the use of TET scale.
That basis would be akin to "12TET more-or-less optimizes the lowest average dissonance (based on the roughness theory ALA Plomp and Llevelt) heard between all possible dyads with the 2/1 octave for a 12-tone scale".
Odd fact...7TET optimizes that same thing for 7 tones...and the standard diatonic scale has 7-tones: it all begs the question why people haven't experimented more with trying to make a scale within, say, 12 cents of all 7TET tones that has many possible JI-compliant chords.

>"JI sounds correct mostly for harmonic structures. "
It does but, for example, Sethares experiments with 10TET also sound fairly correct and have nothing to do with harmonic structures as they use warped timbres/"spectral mapping". I'm pretty sure there are multiple ways to be "correct" in this sense.

>"Each thing has a simplicity about it that is automatically recognizable as 'correct':"
Again I doubt it is that simple. Make scales out of 1+(1/PHI)^n and 1+(1/sqrt(2))^n. These both follow very high levels of symmetry and simpilicity (Golden and Silver Sections), yet one sounds significantly better than the other.

>"Fifths start sounding wrong harmonically, JI starts sounding wrong melodically, and ETs sound wrong because they are impure."
The question then seems to become "how wrong is too wrong" and "why are each of these more wrong or less wrong"?
The obvious answers to me are
A) Psychoacoustics and the physiology of the human ear
B) A certain degree of personal taste / psychology: some people may in fact find JI a bit less harmonically attractive than ET...be it by cultural conditioning or otherwise.

>"JI defines the harmonic structures of diatonicism and beyond"
I'd restate that as "periodicity, often enforced by harmonic structures and forming the basis for many existing and future scale systems, is one way to optimize consonance in music"...implying that roughness optimization ALA Sethares and other types of optimization are also possible for future scale systems.

Here again we have the typical list conflicts between people who champion optimizing scales with standard intervals (ALA 12TET, well temperment, and historical music) and those who could care less about compliance to standard intervals so long as their new scale works well psychoacoustically. I'll leave it at this: I agree with many of the statements above, but believe they are incomplete parts of a larger picture defined by abstract psycho-acoustics and a certain degree of personal taste.

-Michael

Each premise begins with small numbers. When
number get large for each, the structures start
overlapping and sharing correctness. The equations
you give sound more or less correct for their
properties of sharing correctness with basic
structures as stated previously.

The tricks of the trade are to exploit each thing
for its correctness and build structures that tend
towards correctness and minimize wrongness.
Large numbers accomplish this, and the trick
is to find reasonable limits for a system that
includes all the properties one wants to exploit.

Of course my other post was incomplete, as is
this one. I gave a link to 30+ webpages of text,
graphics, and audio examples which elaborate
the ideas. I'll leave it at that.

Yours,
AAH
=====

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> "ETs have 1 step size. None shares a simplicity with the
> others."
> IMVHO a hole in this theory is the inability to, say, put half steps into a consonant chord.
> Another thing is, >>at least with sine waves<<, I believe there is a psychoacoustic basis for the use of TET scale.
> That basis would be akin to "12TET more-or-less optimizes the lowest average dissonance (based on the roughness theory ALA Plomp and Llevelt) heard between all possible dyads with the 2/1 octave for a 12-tone scale".
> Odd fact...7TET optimizes that same thing for 7 tones...and the standard diatonic scale has 7-tones: it all begs the question why people haven't experimented more with trying to make a scale within, say, 12 cents of all 7TET tones that has many possible JI-compliant chords.
>
>
> >"JI sounds correct mostly for harmonic structures. "
> It does but, for example, Sethares experiments with 10TET also sound fairly correct and have nothing to do with harmonic structures as they use warped timbres/"spectral mapping". I'm pretty sure there are multiple ways to be "correct" in this sense.
>
>
> >"Each thing has a simplicity about it that is automatically recognizable as 'correct':"
> Again I doubt it is that simple. Make scales out of 1+(1/PHI)^n and 1+(1/sqrt(2))^n. These both follow very high levels of symmetry and simpilicity (Golden and Silver Sections), yet one sounds significantly better than the other.
>
>
> >"Fifths start sounding wrong harmonically, JI starts sounding wrong melodically, and ETs sound wrong because they are impure."
> The question then seems to become "how wrong is too wrong" and "why are each of these more wrong or less wrong"?
> The obvious answers to me are
> A) Psychoacoustics and the physiology of the human ear
> B) A certain degree of personal taste / psychology: some people may in fact find JI a bit less harmonically attractive than ET...be it by cultural conditioning or otherwise.
>
>
> >"JI defines the harmonic structures of diatonicism and beyond"
> I'd restate that as "periodicity, often enforced by harmonic structures and forming the basis for many existing and future scale systems, is one way to optimize consonance in music"...implying that roughness optimization ALA Sethares and other types of optimization are also possible for future scale systems.
>
>
> Here again we have the typical list conflicts between people who champion optimizing scales with standard intervals (ALA 12TET, well temperment, and historical music) and those who could care less about compliance to standard intervals so long as their new scale works well psychoacoustically. I'll leave it at this: I agree with many of the statements above, but believe they are incomplete parts of a larger picture defined by abstract psycho-acoustics and a certain degree of personal taste.
>
> -Michael
>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Kalle>"On the other hand, if chords have to be
> consonant, then tempering can increase the number of chords
> available."
> Exactly, "tempering can increase the number of chords
> available"...and that was the assumption I was making: that a set
of note must meet a standard for consonance to qualify as a chord.

Haven't you ever heard of dissonant chords?

> > Right. You could say I consider a loophole in many people's
> > though process is the idea that everything must aim for the ideal
> > of being more or less "acoustically identical" to 12TET tones. For
> > example 11/9: when I made a scale with it I was posed the question
> > (paraphrased) "is this supposed to be an E or a D#?!"
>
> Exactly...I think it's frustrating that micro-tonality so often
pushes people in the direction of making these "new" intervals for
the purpose of sounding like old ones. It seems to me to make the
whole art-form just go in circles so far as creating options the
average Joe would hear and say "now that sounds fresh". Maybe you
could give a good justification for this...what's the ultimate point
(for you and perhaps others) about doing what looks on the surface
like proving something already proved?

Your editing makes it appear that I wrote the upper paragraph here
but you are actually answering to yourself. :D

> >"Some people here are only interested in the intonation of
existing music like for
> example some of the 12-tone well temperament people"
> Right...I guess my question here becomes why said people don't
accept adaptive JI as their final answer...

Well, I'll let them answer that. One reason might be that they play
acoustic instruments like harpsichords.

> >"some are interested in new possible scales and structures that
don't exist in 12-tone tunings"
> Obviously, I'm in that boat. It sometimes amazes me how much
people from the two groups spend arguing with each other or
complaining that the other group is making too many posts exclusive
to their one of the two topic. Perhaps we should consider splitting
the group into two sections (historically-based microtonality and
alternative-microtonality)? I'm just wondering b/c I think it could
solve a lot of problems here.

I don't advocate splitting. There is a common theoretical ground to
both groups. Considering the label "historically-based microtonality":
there is nothing particularly microtonal or xenharmonic about 12-tone
well-temperaments.

Kalle Aho

P.S. changing spectra to fit a tuning is an example of
using a principle of harmonic correctness from JI. If you
look at anything that seems to conflict with the basic
premises I outlined previously, you'll see that whatever
it is simply culls an underlying principle of one or another
of those things, adapts and exploits it for some other
aim of obtaining correctness. What is correct is a matter
of cultural bias and personal judgement, for sure. If
you don't like the word 'correct', then substitute
'simple', 'straightforward', 'comprehensible',
'preattentively acceptible', etc.

AAH
=====

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> "ETs have 1 step size. None shares a simplicity with the
> others."
> IMVHO a hole in this theory is the inability to, say, put half steps into a consonant chord.
> Another thing is, >>at least with sine waves<<, I believe there is a psychoacoustic basis for the use of TET scale.
> That basis would be akin to "12TET more-or-less optimizes the lowest average dissonance (based on the roughness theory ALA Plomp and Llevelt) heard between all possible dyads with the 2/1 octave for a 12-tone scale".
> Odd fact...7TET optimizes that same thing for 7 tones...and the standard diatonic scale has 7-tones: it all begs the question why people haven't experimented more with trying to make a scale within, say, 12 cents of all 7TET tones that has many possible JI-compliant chords.
>
>
> >"JI sounds correct mostly for harmonic structures. "
> It does but, for example, Sethares experiments with 10TET also sound fairly correct and have nothing to do with harmonic structures as they use warped timbres/"spectral mapping". I'm pretty sure there are multiple ways to be "correct" in this sense.
>
>
> >"Each thing has a simplicity about it that is automatically recognizable as 'correct':"
> Again I doubt it is that simple. Make scales out of 1+(1/PHI)^n and 1+(1/sqrt(2))^n. These both follow very high levels of symmetry and simpilicity (Golden and Silver Sections), yet one sounds significantly better than the other.
>
>
> >"Fifths start sounding wrong harmonically, JI starts sounding wrong melodically, and ETs sound wrong because they are impure."
> The question then seems to become "how wrong is too wrong" and "why are each of these more wrong or less wrong"?
> The obvious answers to me are
> A) Psychoacoustics and the physiology of the human ear
> B) A certain degree of personal taste / psychology: some people may in fact find JI a bit less harmonically attractive than ET...be it by cultural conditioning or otherwise.
>
>
> >"JI defines the harmonic structures of diatonicism and beyond"
> I'd restate that as "periodicity, often enforced by harmonic structures and forming the basis for many existing and future scale systems, is one way to optimize consonance in music"...implying that roughness optimization ALA Sethares and other types of optimization are also possible for future scale systems.
>
>
> Here again we have the typical list conflicts between people who champion optimizing scales with standard intervals (ALA 12TET, well temperment, and historical music) and those who could care less about compliance to standard intervals so long as their new scale works well psychoacoustically. I'll leave it at this: I agree with many of the statements above, but believe they are incomplete parts of a larger picture defined by abstract psycho-acoustics and a certain degree of personal taste.
>
> -Michael
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
>
> > > > That's interesting! Who has suggested this?
> > >
> > > I forget. Was it George Secor or Keenan Pepper?
> > >
> > > -Carl
> >
> > No, try Ray Perlner:
> >
> > /tuning-math/message/15953
>
> Thanks George! You have such an excellent memory.
>
> -Carl

My memory isn't really that good. I paste copies of most of the messages that I send into document files, including the date & message # of each msg., which makes these readily searchable. This happened to be a message to which I replied, so I also had Ray's name, msg. #, & msg. date in my file.

--George

Kalle>"Haven't you ever heard of dissonant chords?"
Of course...but it is relatively easy to create many of such (dissonant) chords within a scale....hence IMVHO the challenge becomes making a scale with many
consonant chords. Also (in general) if we want more people to join the revolution of micro-tonality...we need to be able to deal in consonant chords to convince them we aren't just making random noise tied together by a bunch of confusing equations.

>"I don't advocate splitting. There is a common theoretical ground to
both groups."
>" Considering the label "historically- based microtonality" :
there is nothing particularly microtonal or xenharmonic about 12-tone
well-temperaments."

And yet we get these huge threads about enharmonic equivalents, why 12TET works well, JI and Beethoven, commatic tempering, use of different diatonic modes (often within 12TET), and such...which are all counted as being on-topic. And how many times do people from said group honestly talk about things like "critical band roughness" or try to argue there may be another reason for identification of a root note beside the classically accepted idea of "virtual pitch"?
I don't see what's so inaccurate about the "historically based" label...although I realize "historic tunings" would be a mis-label as people in the above group often make slight strategic deviations (IE temperaments and such) from the historical tuning they are trying to optimize.

The only real common grounds I see are
A) That we deal in scales
and interval sizes other than 12TET (both larger IE marco-tonal and smaller IE micro-tonal).
However, I see one group almost exclusively
insisting on having all notes staying within 10 cents or so of any given historical tuning
(12TET, mean-tone, etc.) to optimize it and the other group almost exclusively tries
not to stay within those limits (and in fact strives to avoid them: easy example is Sethares making usually dissonant as dirt 10TET sound fairly consonant in "Ten Strings"). And one group focusses mostly on developing tunings for new songs while the other tries to re-tune existing ones.
B) That some of us deal in making or designing micro-tonal instruments for both ET and non-ET scale...which is a similar mathematical challenge regardless of the tuning.

Feel free to give counter-examples, but I get the impression there is not much overlap and relatively few people from either of the two groups interested in much of
what the other group has to say (which often degenerates into dogmatic arguments where each side "knows they are right" from the get go). I figure maybe many of us should just agree to disagree).

-Michael

>"P.S. changing spectra to fit a tuning is an example of
using a principle of harmonic correctness from JI."
How so? As I recall the equations Sethares used were based on the minimum points in roughness curves which cause overtones of multiple tones in the scale to align the best on average...nothing to do with JI-style periodicity. Also, how can Sethares timbre-matching be "harmonic correctness" if the timbre looks nothing like the harmonic series so fundamental to JI?

My point is (at least as for now) that I still believe that creating a scale ideal for both harmony and melody is not so simply as balancing between the "symmetry" virtue of 12TET and the harmonic-balancing of JI (or that to get more symmetry you need to sacrifice harmonic-balancing). IE the chord 2:3:4 is very well "harmonically balanced" as it is very close to the root of the harmonic series.

Heck, even my own perspective that creating an ideal scale involves minimizing root-tone roughness via imitating 7TET and maximizing "harmonic balance" by using ratios of 13/12 or lower to represent distances between consecutive notes I don't think covers the whole system.
I'm convinced something that would cover the entire gammut would explain
A) where consonance becomes dissonance (roughness wise...for example with regard to consecutive sine tones played in TET tunings)
B) where consonance becomes dissonance (periodicity/"JI" wise)
C) If a chord meets A and B (is consonant according to A and B) yet somehow sounds dissonant, why does it?

BTW, where is that 30-page explanation link you supposedly sent? I never received it...

To Michael:

I would never properly understand how temperaments like hanson or semisixths work (or even Bohlen-Pierce) if I hadn't, prior to that, understood how meantone works.
I would never properly understand how meantone works if I hadn't understood how 31-EDO or 19-EDO works.
I would never properly understand how 31-EDO works if I hadn't understood what JI means.
I would never properly understand what JI means if I hadn't tried to synthesize harmonic and inharmonic spectra and examined the intervals in their overtones.
... And you want to tell me that the two groups of "microtonalists" have nothing in common? Hey, I just can't imagine talking about one side without knowing anything about the other ... There are so many links there ...

Petr

--- In tuning@yahoogroups.com, Michael
<djtrancendance@...> wrote:
> >"P.S. changing spectra to fit a tuning is an
> > example of using a principle of harmonic
> > correctness from JI."
> How so? As I recall the equations Sethares
>used were based on the minimum points in
>roughness curves which cause overtones of
>multiple tones in the scale to align the best
>on average...nothing to do with JI-style periodicity.
>Also, how can Sethares timbre-matching be
>"harmonic correctness" if the timbre looks
>nothing like the harmonic series so fundamental to JI?

But that is making things much more complicated
than necessary. Don't overlook the obvious:

- JI intervals fit into a harmonic series
- mapped spectral intervals fit into a warped spectrum

The principle is exactly the same:

- intervals : overtones

You get your intervals from a system of overtones.
In one case, the overtones are whole number multiples
of a fundamental, in the other, they related to the
fundamental by a mapping principle or formula
applied to a scale.

> Heck, even my own perspective that creating
> an ideal scale involves minimizing root-tone
> roughness via imitating 7TET and maximizing
> "harmonic balance" by using ratios of 13/12
> or lower to represent distances between
> consecutive notes I don't think covers the
> whole system.

That's fine, but you seem to miss my point:

- chain of pure fifths
- JI intervals
- ETs

See how these relate to whatever you are doing,
and you'll find the simple obviousness of whatever
it is can be characterized as adaptations of the
correctness or obviousness each of those things.

> I'm convinced something that would cover the
> entire gammut would explain
> A) where consonance becomes dissonance
> (roughness wise...for example with regard to
> consecutive sine tones played in TET tunings)
> B) where consonance becomes dissonance
> (periodicity/"JI" wise)
> C) If a chord meets A and B (is consonant
> according to A and B) yet somehow sounds
> dissonant, why does it?

All valid questions that can inform the creation
of musical systems, but there is no need to get
bogged down in such gory details that will
never have general solutions in order to
validate the simple premises I've stated.

> BTW, where is that 30-page explanation link you
> supposedly sent? I never received it...

It is at the end of my first post.

Yours,
AAH
=====

Responding to Michael:

> I'm convinced something that would cover the

> entire gammut would explain

> A) where consonance becomes dissonance

> (roughness wise...for example with regard to

> consecutive sine tones played in TET tunings)

> B) where consonance becomes dissonance

> (periodicity/ "JI" wise)

> C) If a chord meets A and B (is consonant

> according to A and B) yet somehow sounds

> dissonant, why does it?

One of the problems I see in this is that it leaves harmonic/contrapuntal function and historical changes in perception of consonance/dissonance out of the equation. In common practice music one of Hindemith's most consonant chords, an 027 (say, [low to high] G C D) is is always a dissonance and must resolve, with the C always resolving downwards.  Any chord with tritones and half steps in Hindemiths system is automatically more dissonant that a chord lacking these intervals, yet a V m9 chord in minor, one of the most important chords in the harmonic syntax of late Romantic music. What is more, one can weave all sorts of non-chord tones that are more consonant with the bass than the m7 and m9, yet these will feel dissonant to this very dissonant chord.  This is owing to the harmonic syntax and to contrapuntal expectations (the m9 will eventually resolve down by half step, but if the m9 is clearly the chord tone,  a neighbor-tone M9 against the bass
[i.e., a more consonant interval] will clearly be a non-chord tone).  Another interesting case involves borrowed chords--bVI in a clearly-established major key is more consonant than the diatonic vi or diatonic ii7, etc., but will always sound somewhat foreign and connote the minor tonality (owing to the b3 and the b6-5 tendency). The Neapolitan chord in a minor key gives a little island of major, but it clearly sounds foreign to the key, especially in the older tunings.  The  historical derivations for the Np6 chord are from the minor iv chord, with the 5th raised to a m6.  This was a standard tactic in figured bass practice, in which a triad (minor iv) was always considered more consonant than a sixth chord (Np6).  Ergo, the Np6 was more dissonant than the minor iv; in addition, it required chromatic voice leading (b2-1-l.t.).  So there are a lot more factors than harmonic sonority in play.

Some of you probably know Tenney's little book, A History of Consonance' and
'Dissonance'
.  It's a bit superficial, but it does show nicely how perceptions of consonance and dissonance have changed over the centuries.

Franklin

Dr. Franklin Cox

1107 Xenia Ave.

Yellow Springs, OH 45387

(937) 767-1165

franklincox@...

--- On Wed, 2/10/10, hpiinstruments <aaronhunt@...> wrote:

From: hpiinstruments <aaronhunt@...>
Subject: [tuning] Re: The point of temperament
To: tuning@yahoogroups.com
Date: Wednesday, February 10, 2010, 9:39 PM

--- In tuning@yahoogroups. com, Michael

<djtrancendance@ ...> wrote:

> >"P.S. changing spectra to fit a tuning is an

> > example of using a principle of harmonic

> > correctness from JI."

> How so? As I recall the equations Sethares

>used were based on the minimum points in

>roughness curves which cause overtones of

>multiple tones in the scale to align the best

>on average...nothing to do with JI-style periodicity.

>Also, how can Sethares timbre-matching be

>"harmonic correctness" if the timbre looks

>nothing like the harmonic series so fundamental to JI?

But that is making things much more complicated

than necessary. Don't overlook the obvious:

- JI intervals fit into a harmonic series

- mapped spectral intervals fit into a warped spectrum

The principle is exactly the same:

- intervals : overtones

You get your intervals from a system of overtones.

In one case, the overtones are whole number multiples

of a fundamental, in the other, they related to the

fundamental by a mapping principle or formula

applied to a scale.

> Heck, even my own perspective that creating

> an ideal scale involves minimizing root-tone

> roughness via imitating 7TET and maximizing

> "harmonic balance" by using ratios of 13/12

> or lower to represent distances between

> consecutive notes I don't think covers the

> whole system.

That's fine, but you seem to miss my point:

- chain of pure fifths

- JI intervals

- ETs

See how these relate to whatever you are doing,

and you'll find the simple obviousness of whatever

it is can be characterized as adaptations of the

correctness or obviousness each of those things.

> I'm convinced something that would cover the

> entire gammut would explain

> A) where consonance becomes dissonance

> (roughness wise...for example with regard to

> consecutive sine tones played in TET tunings)

> B) where consonance becomes dissonance

> (periodicity/ "JI" wise)

> C) If a chord meets A and B (is consonant

> according to A and B) yet somehow sounds

> dissonant, why does it?

All valid questions that can inform the creation

of musical systems, but there is no need to get

bogged down in such gory details that will

never have general solutions in order to

validate the simple premises I've stated.

> BTW, where is that 30-page explanation link you

> supposedly sent? I never received it...

It is at the end of my first post.

Yours,

AAH

=====

Petr,

Of course 31EDO is a mean-tone temperament and (at least so far as I know) many of not most of all historical tunings (at least the non-ethnic ones) revolve around mean-tone....with only more recent research showing how mean-tone is really pushing for JI (even if those who created it didn't realize it since JI wasn't acknowledged back then).

Meanwhile (at least so far as I know) JI simply explains the kind of intervals likely to form pure-sounding chords within any tuning. When I look at

"I would never properly understand how meantone
works if I hadn't understood how 31-EDO or 19-EDO works.
I would never properly understand how 31-EDO works
if I hadn't understood what JI means.
I would never properly understand what JI means if
I hadn't tried to synthesize harmonic and inharmonic spectra and examined the
intervals in their overtones."

....I see them as all joined together, rather than forming a progressive hierarchy of learning. Couldn't someone have just as well learned, for example, that mean-tone is created by taking 1.5^x and then dividing by multiples of the octave and then learned JI to find the chords?

>"I would never properly understand how temperaments
like hanson or semisixths work (or even Bohlen-Pierce) if I hadn't, prior to
that, understood how mean-tone works."

Let's start with BP since I haven't tried the other two temperaments yet. I know BP uses the octave * a fifth AKA the "tri-tave" as it's period, aims to foremost align the odd harmonics rather than the even ones, and uses the 3/5/7 chord (rather than the 6/5/4 chord (noting 6/4 = 3/2) as with meantone) to generate itself and thus produces very pure "thirds and fifths". To me it seems like just a variation on meantone with the triad shifted to odd harmonics: very connected to history, but not really showing anything new far as psychoacoustics, higher-limit intervals...at least on the surface. What is there that makes BP, Hanson...and other temperaments you say you learned well "only" because you learned meantone well first so special and new (at least so far...I'm unconvinced you're doing much more than connecting historical tuning to only-slightly-less historical tuning)?

>"... And you want to tell me that the two groups of
"microtonalists" have nothing in common?"
I never said they had nothing in common...just very little. Especially when it comes to how they go about making new scales or viewing why certain intervals "work" and psychoacoustics. From what I've heard from you in this e-mail, it sounds like you are focused mostly toward preserving the type of chords prominent in mean-tone (IE those with strong thirds and fifths) and slight variants of them such as those in BP.

Part of it might be personallity too...to me BP is a historic scale and if it indeed has its roots in mean-tone that only seems to prove it moreso. To me Just Intonation is modern, but only when used to create scale that break traditional scale limits IE have more than 2 step sizes, differ more than 10 cents from traditional mean-tone intervals, etc. ...otherwise it seems to always end up becoming some sort of Pythagorean tuning.

One other observation...it seems those interested more in historical tunings obsess a bit about maintaining the purity of thirds and fifths (with Magic temperament, for example, concentrating on keeping the purity of thirds). What are your favorite counter-examples to this?

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Kalle>"Haven't you ever heard of dissonant chords?"
> Of course...but it is relatively easy to create many of such
> (dissonant) chords within a scale....hence IMVHO the challenge
> becomes making a scale with many
> consonant chords. Also (in general) if we want more people to join
> the revolution of micro-tonality...we need to be able to deal in
> consonant chords to convince them we aren't just making random
> noise tied together by a bunch of confusing equations.

I asked "Haven't you ever heard of dissonant chords?" because YOU
said:

"...and that was the assumption I was making: that a set of note must
meet a standard for consonance to qualify as a chord."

Prima facie that seems to imply that chords can't be dissonant.

Anyway, the xenharmonic temperaments discussed in these lists are
doing just what you described: scales with many consonant chords.
They just don't fit your idiosyncratic need to have scales where any
combination of tones produces a consonant chord. I understand your
frustration but keep in mind that almost no one else is so single-
mindedly interested in such scales. And for a millionth time: for
harmonic sounds these scales must be harmonic series segments. As far
as we know, there is no other way, so no need to complain about
"tonal color", what is that anyway?

> >"I don't advocate splitting. There is a common theoretical ground
> > to both groups."
> >" Considering the label "historically- based microtonality":
> > there is nothing particularly microtonal or xenharmonic about
> > 12-tone well-temperaments."
>
> And yet we get these huge threads about enharmonic equivalents,
> why 12TET works well, JI and Beethoven, commatic tempering, use of
> different diatonic modes (often within 12TET), and such...which are
> all counted as being on-topic. And how many times do people from
> said group honestly talk about things like "critical band
> roughness"

You obviously have a huge obsession with critical band roughness, why
should we be talking about it? You are repeating that there is some
conflict between periodicity and roughness. Newsflash! There isn't:
for harmonic sounds JI intervals minimize roughness.

> or try to argue there may be another reason for identification of a
> root note beside the classically accepted idea of "virtual pitch"?

I believe the consensus is that the perception of chord roots is
a by-product of pitch perception. Combination tones are a separate
phenomenon, there is no need to confuse the two phenomena.

> I don't see what's so inaccurate about the "historically
> based" label...although I realize "historic tunings" would be a
> mis-label as people in the above group often make slight strategic
> deviations (IE temperaments and such) from the historical tuning
> they are trying to optimize.

It is the "microtonality" in your "historically- based microtonality"
that is mis-labeling, not the "historically based".

> The only real common grounds I see are
> A) That we deal in scales
> and interval sizes other than 12TET (both larger IE marco-tonal and
> smaller IE micro-tonal).
> However, I see one group almost exclusively
> insisting on having all notes staying within 10 cents or so of any
> given historical tuning
> (12TET, mean-tone, etc.) to optimize it and the other group almost
> exclusively tries
> not to stay within those limits (and in fact strives to avoid them:
> easy example is Sethares making usually dissonant as dirt 10TET
> sound fairly consonant in "Ten Strings"). And one group focusses
> mostly on developing tunings for new songs while the other tries to
> re-tune existing ones.
> B) That some of us deal in making or designing micro-tonal
> instruments for both ET and non-ET scale...which is a similar
> mathematical challenge regardless of the tuning.
> Feel free to give counter-examples, but I get the impression
> there is not much overlap and relatively few people from either of
> the two groups interested in much of what the other group has to
> say (which often degenerates into dogmatic arguments where each
> side "knows they are right" from the get go). I figure maybe many
> of us should just agree to disagree).

There is a centuries old continuum of tuning lore that is
interconnected in endless ways. That is the common ground here.
Feel free to start your own group where you can sensor any discussions
that don't cater to your singular interests.

Kalle Aho

Aaron Hunt>"The principle is exactly the same: - intervals : overtones"
I had said "which cause overtones of multiple tones in the scale to align the best on average"...which, if I understand you, is saying the same thing you are saying: they align the two. The term "harmonic correctness" confused me, if you'd said something like "harmonic alignment" I would have likely gotten it the first time.

You're right though...JI aligns with the harmonic series spectrum in a similar manner odd scales like 10TET align with Sethares warped timbres. And it turns out if you use his equations on the harmonic series you obtain JI diatonic by taking the minima of the graph. Still, you can't use JI to solve his alignment equation for non-harmonic-series scales...hence why I still am siding with the opinion "it's not so simple as JI..."

>"That's fine, but you seem to miss my point:
1) - chain of pure fifths
2) - JI intervals
3) - ETs"

I get your point, but I still don't believe it's anywhere near all-inclusive.
What I'm doing does somewhat relate to ET's and JI intervals...but has little to do with the chain of pure 5ths. The only way it relates to ET, though, is that it uses ET to estimate the curve of tones that best follows the critical band and avoids roughness. And it doesn't even obey JI so much as it lets itself go to higher limits of JI...just enough to maintain IMVHO a decent (but not "super-pure") level of periodicity.

So it's really more a case of:
-Periodicity (yes, uses JI, but often with mid to fairly high limit JI Intervals...not very strict JI)
-Critical band following (happens to be not too far from 7TET, but approximates the critical band to a similar degree mean-tone intervals can approximate JI)

>"See how these relate to whatever you are doing, and you'll find the simple obviousness of whatever it is can be characterized as adaptations of the
correctness or obviousness each of those things."
Again I see some similarities...but by no means an exclusive balancing between the three. The chain of pure-fifths seems to be a common and IMVHO a bit over-stated goal on this list...it seems to promote meantone as an ideal type/goal of tuning. Someone, I'm betting, could just as easily argue that a chain of pure thirds IE Magic Temperament should be used instead...
Another interesting link is http://en.wikipedia.org/wiki/Ptolemy where Ptolemy says "However, Pythagoras believed that the mathematics of music
should be based on the specific ratio of 3:2 whereas Ptolemy merely
believed that it should just generally involve tetrachords and octaves". Given the importance of tetrachords and more possibilities without the "circle of 5ths" limitation, maybe we should give Ptolemy a second chance...

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> > "That's fine, but you seem to miss my point:
> > 1) - chain of pure fifths
> > 2) - JI intervals
> > 3) - ETs"
>
> I get your point, but I still don't believe it's
> anywhere near all-inclusive.
> What I'm doing does somewhat relate to ET's
> and JI intervals...but has little to do with the chain
> of pure 5ths. The only way it relates to ET, though,
> is that it uses ET to estimate the curve of tones that
> best follows the critical band and avoids roughness.
> And it doesn't even obey JI so much as it lets itself
> go to higher limits of JI...just enough to maintain
> IMVHO a decent (but not "super-pure") level of periodicity.
>
> So it's really more a case of:
> -Periodicity (yes, uses JI, but often with mid to fairly
> high limit JI Intervals...not very strict JI)
> -Critical band following (happens to be not too far
> from 7TET, but approximates the critical band to a
> similar degree mean-tone intervals can approximate JI)

7ET certainly is related to a chain of pure fifths;
a chain of pure fifths is at its heart - 3 tones its axis,
5 tones approximating pentatonic give a default scale
in 7ET. 7 moreover is directly related to the pure fifths
diatonic set. You can't get much more grounded in the
chain of fifths than that. You are missing the forest
for the trees.

> >"See how these relate to whatever you are doing,
> > and you'll find the simple obviousness of whatever
> > it is can be characterized as adaptations of the
> > correctness or obviousness each of those things."
> Again I see some similarities...but by no means an
> exclusive balancing between the three. The chain of
> pure-fifths seems to be a common and IMVHO a bit
> over-stated goal on this list...

It's not a goal. It's a basic structure.

> it seems to promote
> meantone as an ideal type/goal of tuning. Someone,
> I'm betting, could just as easily argue that a chain of
> pure thirds IE Magic Temperament should be used instead...

Sure, that's a structure too, but a *less basic one* than
the chain of fifths, unless you want to argue that 5 is less
than 3?

> Another interesting link is http://en.wikipedia.org/
> wiki/Ptolemy where Ptolemy says "However, Pythagoras
> believed that the mathematics of music should be based
> on the specific ratio of 3:2 whereas Ptolemy merely
> believed that it should just generally involve tetrachords
> and octaves". Given the importance of tetrachords and
> more possibilities without the "circle of 5ths" limitation,
> maybe we should give Ptolemy a second chance...

Well, in that case, one could consult better sources
than Wikipedia. Andrew Baker's book: "Greek Musical
Writings, Volume II, Harmonic and Acoustic Theory" is a
good place to start.

Ask yourself the question: what is a tetrachord? Your
answer points you back to the number 3. You can't
escape these things. They seem to be too simple for you...
you are coming up with challenges for yourself and that's
fine, but don't overlook simple facts; they will inform you
more securely than chasing chimeras in endless details.

Yours,
AAH
=====

Kalle>"They just don't fit your idiosyncratic need to have scales where any
combination of tones produces a consonant chord."

Doesn't have to be any combination of tones (though indeed that's one of the things I've been trying for).
However I will beg the question that while we have temperaments that concentrate on pure thirds (magic), fifths (mean-tone), odd harmonics and tritaves (BP), etc.
....why do I see so little work going on with respect to things like purifying different types of seconds (or intervals between them)?

I will admit though I am somewhat obsessed with the idea of turning an interval in that area into something that can be used in chords within a scale. That and experimenting with timbre matching and getting fairly good periodicity even from scales with higher-limit fractions. I used to be more "obsessed" with PHI and Silver Ratio based scales. At one point in time, I was "obsessed" with scales derived from subsets of the x/16 harmonic series (as opposed to the diatonic JI scale, based on x/24). And before that, I was obsessed with Sethares' work. Man...isn't that a lot of obsessions for someone who's supposedly "single-minded"? In a few months who knows...it might be something else. And yes, they all have somewhat of a common thread of "minimizing roughness", but what's so hideous about that?
***************************************************
>"but keep in mind that almost no one else is so single-mindedly interested in such scales.
Well, would someone really be so bored if they found out they could play chords like c c# d# and still have them sound resolved enough to "rest" on...wouldn't it open a bunch of new compositional possibilities?

>"And for a millionth time: for harmonic sounds these scales must be harmonic series segments. "
I wouldn't go that far...there can be a certain degree of temperament around those. Now for you...how many posts have I used with examples of chords like 2:3:4 and 6:7:9? You should know...that I well know what you're getting at here.

>"As far as we know, there is no other way, so no need to complain about "tonal color", what is that anyway?"
One way I think of it is that a 2:3:4 chord can sound vastly different depending on a different root pitch or even just a little bit of "bending" of any tone in the chord. I don't believe in "a chord is perfectly pure or it's just a poor imitation of perfectly pure"...though I will agree too far from pure can cause some nasty lack-of-periodicity issues.

>"You are repeating that there is some conflict between periodicity and roughness. Newsflash! There isn't: for harmonic sounds JI intervals minimize roughness. "
It minimizes average roughness, not maximum roughness. The 1/1 to 15/14 minor second is my most obvious example of that (it's a fairly high maximum roughness dyad).
Newsflash...take the straight harmonic series of 7:8:9:10:11:12:13:14(octave). Hear the almost robotic degree of harmonic distortion? It may be periodic and incredibly based on JI intervals, but it's still roughness.
Sure JI works great for single tetrachords IE 2:3:4:5...but IMVHO if you want to get new chords that use new intervals in a 6+ tone scale (IE with enough notes to interest many musicians) you also have to think "at what point does roughness become intolerably high to most people...even between two sine tones with no harmonics". And I'm pretty sure it's below 15/14....

>"Feel free to start your own group where you can sensor any discussions that don't cater to your singular interests."
I have never tried to censor anyone or say "stop talking" in any form...how are you coming to the conclusion I am? Yes, I'm arguing, and I'm frustrated that I barely see anyone dealing with issues like roughness yet gobs of them discussing mean-tone and then see things like the Marcel's perfecting JI coming up over and over again with name-calling on all sides.
Yes, I did bring up the idea of splitting the group into two...but not with the idea of "those not into 'newer' tuning ideas don't deserve to be heard"...rather, I'm just sick of all the arguing and would like input from people who will say more than "just use existing micro-tonal scales & learn them...give up trying to improve any aspects of them". You may not agree with me and heck I may even bore you...but I haven't "you idiot"-ed anyone nor do I deserve credit for doing so.

-Michael

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Kalle>"They just don't fit your idiosyncratic need to have scales
> where any combination of tones produces a consonant chord."
>
> Doesn't have to be any combination of tones (though indeed
> that's one of the things I've been trying for).

OK.

> However I will beg the question that while we have temperaments
> that concentrate on pure thirds (magic), fifths (mean-tone), odd
> harmonics and tritaves (BP), etc.
> ....why do I see so little work going on with respect to things
> like purifying different types of seconds (or intervals between
> them)?

I don't understand this question. Seconds are already intervals, so
what are intervals between them?

> I will admit though I am somewhat obsessed with the idea of
> turning an interval in that area into something that can be used in
> chords within a scale.

Why can't seconds be used in chords? They are used all the time in
music. What's the problem?

> That and experimenting with timbre matching and getting fairly good
> periodicity even from scales with higher-limit fractions. I used
> to be more "obsessed" with PHI and Silver Ratio based scales. At
> one point in time, I was "obsessed" with scales derived from
> subsets of the x/16 harmonic series (as opposed to the diatonic JI
> scale, based on x/24). And before that, I was obsessed with
> Sethares' work. Man...isn't that a lot of obsessions for someone
> who's supposedly "single-minded"? In a few months who knows...it
> might be something else. And yes, they all have somewhat of a
> common thread of "minimizing roughness", but what's so hideous
> about that?

I didn't say it's hideous. I just said you're obviously obsessed. :D

> ***************************************************
> > "but keep in mind that almost no one else is so single-mindedly
> > interested in such scales.
> Well, would someone really be so bored if they found out they
> could play chords like c c# d# and still have them sound resolved
> enough to "rest" on...wouldn't it open a bunch of new compositional
> possibilities?

It seems to me that whether c c# d# can sound at least nice (if not
resolved) depends more on the musical context than tuning. Those kind
of sonorities are favoured by atonal composers and in that context
they don't demand resolution.

> > "And for a millionth time: for harmonic sounds these scales must
> > be harmonic series segments. "
> I wouldn't go that far...there can be a certain degree of
> temperament around those.

You must mean detuning because tempering harmonic series segments
makes no sense to me. Detuning and temperament are not the same
thing.

> Now for you...how many posts have I used with examples of chords
> like 2:3:4 and 6:7:9? You should know...that I well know what
> you're getting at here.

Sorry, I don't know what you are talking about here.

> > "As far as we know, there is no other way, so no need to complain
> > about "tonal color", what is that anyway?"
> One way I think of it is that a 2:3:4 chord can sound vastly
> different depending on a different root pitch or even just a little
> bit of "bending" of any tone in the chord.

That's a bit vague but maybe you just mean the chord's overall timbre?

> I don't believe in "a chord is perfectly pure or it's just a poor
> imitation of perfectly pure"...though I will agree too far from
> pure can cause some nasty lack-of-periodicity issues.

I don't know if anyone thinks that even a tiny deviation from pure
is a poor imitation.

> > "You are repeating that there is some conflict between
> > periodicity and roughness. Newsflash! There isn't: for harmonic
> > sounds JI intervals minimize roughness. "
> It minimizes average roughness, not maximum roughness. The 1/1
> to 15/14 minor second is my most obvious example of that (it's a
> fairly high maximum roughness dyad).

What is maximum roughness? If you mean the highest roughness between
frequency components then where's the evidence that it is perceived
in chords made of complex tones?

> Newsflash...take the straight harmonic series of
> 7:8:9:10:11:12:13:14(octave). Hear the almost robotic degree of
> harmonic distortion? It may be periodic and incredibly based on JI
> intervals, but it's still roughness.

Unless you have faulty speakers there is no harmonic distortion.
Harmonic distortion happens when poor quality electronic equipment
adds harmonics to sine waves. What you hear is something else, maybe
periodicity buzz.

> Sure JI works great for single tetrachords IE 2:3:4:5

That's not a tetrachord, tetrachords are bounded by fourths. Although
sometimes confusingly set theorists use this term for tetrads.

> ...but IMVHO if you want to get new chords that use new intervals
> in a 6+ tone scale (IE with enough notes to interest many
> musicians) you also have to think "at what point does roughness
> become intolerably high to most people...even between two sine
> tones with no harmonics". And I'm pretty sure it's below 15/14....

Even if two pure tones are at a maximally rough interval I don't
find it intolerable. You are talking as if it was some kind of
torture. BTW, what counts as new chords and new intervals?

> > "Feel free to start your own group where you can sensor any
> > discussions that don't cater to your singular interests."
> I have never tried to censor anyone or say "stop talking" in
> any form...how are you coming to the conclusion I am?

I am not coming to such a conclusion, you are putting words into my
mouth.

> Yes, I'm arguing, and I'm frustrated that I barely see anyone
> dealing with issues like roughness yet gobs of them discussing
> mean-tone and then see things like the Marcel's perfecting JI
> coming up over and over again with name-calling on all sides.
> Yes, I did bring up the idea of splitting the group into
> two...but not with the idea of "those not into 'newer' tuning ideas
> don't deserve to be heard"...rather, I'm just sick of all the
> arguing and would like input from people who will say more than
> "just use existing micro-tonal scales & learn them...give up trying
> to improve any aspects of them". You may not agree with me and
> heck I may even bore you...but I haven't "you idiot"-ed anyone nor
> do I deserve credit for doing so.

What makes you think that the interests could be divided in exactly
two groups? As how you answered to Petr you seem to think that even
such a xenharmonic scale as BP is "traditional". I wonder how many
people would be qualified for the "progressive" group.

Kalle Aho

A minor interjection... In the "Basic JI with 7-limit tritone" scale:

|
0: 1/1 C Dbb unison, perfect prime
1: 16/15 C# Db minor diatonic semitone
2: 9/8 D Ebb major whole tone
3: 6/5 minor third
4: 5/4 D## Ed major third
5: 4/3 F Gbb perfect fourth
6: 7/5 F< Gb+ septimal or Huygens' tritone,
BP fourth
7: 3/2 G Abb perfect fifth
8: 8/5 minor sixth
9: 5/3 G## Ad major sixth, BP sixth
10: 9/5 just minor seventh, BP seventh
11: 15/8 B Ax classic major seventh
12: 2/1 C Dbb octave

Intervals 16/15, 6/5, 4/3 and 8/5 are undertonal. They are related to
sub-partials, not overtones.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Feb 10, 2010, at 11:39 PM, hpiinstruments wrote:

> --- In tuning@yahoogroups.com, Michael
> <djtrancendance@...> wrote:
>>> "P.S. changing spectra to fit a tuning is an
>>> example of using a principle of harmonic
>>> correctness from JI."
>> How so? As I recall the equations Sethares
>> used were based on the minimum points in
>> roughness curves which cause overtones of
>> multiple tones in the scale to align the best
>> on average...nothing to do with JI-style periodicity.
>> Also, how can Sethares timbre-matching be
>> "harmonic correctness" if the timbre looks
>> nothing like the harmonic series so fundamental to JI?
>
>
> But that is making things much more complicated
> than necessary. Don't overlook the obvious:
>
> - JI intervals fit into a harmonic series
> - mapped spectral intervals fit into a warped spectrum
>
> The principle is exactly the same:
>
> - intervals : overtones
>
> You get your intervals from a system of overtones.
> In one case, the overtones are whole number multiples
> of a fundamental, in the other, they related to the
> fundamental by a mapping principle or formula
> applied to a scale.
>
>
>> Heck, even my own perspective that creating
>> an ideal scale involves minimizing root-tone
>> roughness via imitating 7TET and maximizing
>> "harmonic balance" by using ratios of 13/12
>> or lower to represent distances between
>> consecutive notes I don't think covers the
>> whole system.
>
>
> That's fine, but you seem to miss my point:
>
> - chain of pure fifths
> - JI intervals
> - ETs
>
> See how these relate to whatever you are doing,
> and you'll find the simple obviousness of whatever
> it is can be characterized as adaptations of the
> correctness or obviousness each of those things.
>
>
>> I'm convinced something that would cover the
>> entire gammut would explain
>> A) where consonance becomes dissonance
>> (roughness wise...for example with regard to
>> consecutive sine tones played in TET tunings)
>> B) where consonance becomes dissonance
>> (periodicity/"JI" wise)
>> C) If a chord meets A and B (is consonant
>> according to A and B) yet somehow sounds
>> dissonant, why does it?
>
>
> All valid questions that can inform the creation
> of musical systems, but there is no need to get
> bogged down in such gory details that will
> never have general solutions in order to
> validate the simple premises I've stated.
>
>
>> BTW, where is that 30-page explanation link you
>> supposedly sent? I never received it...
>
>
> It is at the end of my first post.
>
> Yours,
> AAH
> =====
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>

A quibble! Let's just say *Integer Ratios* and be
done with it. Non-zero ... 1 <= n/d
Anyway, I think my point was clear enough ; )
Cheers,
AAH
=====

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> A minor interjection... In the "Basic JI with 7-limit tritone" scale:
>
> |
> 0: 1/1 C Dbb unison, perfect prime
> 1: 16/15 C# Db minor diatonic semitone
> 2: 9/8 D Ebb major whole tone
> 3: 6/5 minor third
> 4: 5/4 D## Ed major third
> 5: 4/3 F Gbb perfect fourth
> 6: 7/5 F< Gb+ septimal or Huygens' tritone,
> BP fourth
> 7: 3/2 G Abb perfect fifth
> 8: 8/5 minor sixth
> 9: 5/3 G## Ad major sixth, BP sixth
> 10: 9/5 just minor seventh, BP seventh
> 11: 15/8 B Ax classic major seventh
> 12: 2/1 C Dbb octave
>
> Intervals 16/15, 6/5, 4/3 and 8/5 are undertonal. They are related to
> sub-partials, not overtones.
>
> Oz.
>
> ✩ ✩ ✩
> www.ozanyarman.com
>
> On Feb 10, 2010, at 11:39 PM, hpiinstruments wrote:
>
> > --- In tuning@yahoogroups.com, Michael
> > <djtrancendance@> wrote:
> >>> "P.S. changing spectra to fit a tuning is an
> >>> example of using a principle of harmonic
> >>> correctness from JI."
> >> How so? As I recall the equations Sethares
> >> used were based on the minimum points in
> >> roughness curves which cause overtones of
> >> multiple tones in the scale to align the best
> >> on average...nothing to do with JI-style periodicity.
> >> Also, how can Sethares timbre-matching be
> >> "harmonic correctness" if the timbre looks
> >> nothing like the harmonic series so fundamental to JI?
> >
> >
> > But that is making things much more complicated
> > than necessary. Don't overlook the obvious:
> >
> > - JI intervals fit into a harmonic series
> > - mapped spectral intervals fit into a warped spectrum
> >
> > The principle is exactly the same:
> >
> > - intervals : overtones
> >
> > You get your intervals from a system of overtones.
> > In one case, the overtones are whole number multiples
> > of a fundamental, in the other, they related to the
> > fundamental by a mapping principle or formula
> > applied to a scale.
> >
> >
> >> Heck, even my own perspective that creating
> >> an ideal scale involves minimizing root-tone
> >> roughness via imitating 7TET and maximizing
> >> "harmonic balance" by using ratios of 13/12
> >> or lower to represent distances between
> >> consecutive notes I don't think covers the
> >> whole system.
> >
> >
> > That's fine, but you seem to miss my point:
> >
> > - chain of pure fifths
> > - JI intervals
> > - ETs
> >
> > See how these relate to whatever you are doing,
> > and you'll find the simple obviousness of whatever
> > it is can be characterized as adaptations of the
> > correctness or obviousness each of those things.
> >
> >
> >> I'm convinced something that would cover the
> >> entire gammut would explain
> >> A) where consonance becomes dissonance
> >> (roughness wise...for example with regard to
> >> consecutive sine tones played in TET tunings)
> >> B) where consonance becomes dissonance
> >> (periodicity/"JI" wise)
> >> C) If a chord meets A and B (is consonant
> >> according to A and B) yet somehow sounds
> >> dissonant, why does it?
> >
> >
> > All valid questions that can inform the creation
> > of musical systems, but there is no need to get
> > bogged down in such gory details that will
> > never have general solutions in order to
> > validate the simple premises I've stated.
> >
> >
> >> BTW, where is that 30-page explanation link you
> >> supposedly sent? I never received it...
> >
> >
> > It is at the end of my first post.
> >
> > Yours,
> > AAH
> > =====
> >
> >
> >
> > ------------------------------------
> >
> > You can configure your subscription by sending an empty email to one
> > of these addresses (from the address at which you receive the list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> >
> >
> >
>

Thanks for listening Ozan to this 'Soft fire'. I enjoyed your 'Icicle Caverns'.

Most people who have commented say very relaxing and tranquil, which I find a bit surprising as there are a few 'dissonant intervals in the there too.

Please download from:
(right click on down arrow in the task bar of the play widget and listen on headphones as the piece is binaural)
 
http://soundcloud. com/our-common- ground/soft- fire
 
 

________________________________
From: Ozan Yarman <ozanyarman@ozanyarman.com>
To: tuning@yahoogroups.com
Sent: Thu, 11 February, 2010 4:27:32 AM
Subject: Re: [tuning] soft fire, to enjoy pleasure not quite to the limit

 
I like what I hear. Very ambient and tranquil.

Oz.

✩ ✩ ✩
www.ozanyarman. com

On Feb 10, 2010, at 4:11 AM, Steven Grainger wrote:

>
>
>Dear All,
>Would anyone like to submit a track to be added to this binaural peice I am creating?
> 
>Please download from:
>(right click on down arrow in the task bar of the play widget and listen on headphones as the piece is binaural)
> 
>http://soundcloud. com/our-common- ground/soft- fire
> 
>
>This peice 'soft fire' is a dozen or so sine waves which form a two chord progression.  Evolving polyrhythms are created by the binaural beating of similar and harmonically related intervals, one played in L channel and one played in the right channell.
> 
>
>The idea is that vast harmonic space can be created by resonating at the sweet spots in the stillness of the harmonic nodes. i am trying to create space rather than fill it with melody, though their is some travelling betweeen harmonic nodes via glissandos, some almost imperceptible.
> 
>
>The tonal centres of this peice are 128 hz, 320hz and 83.33 hz.
> 
>
>I want to weave many voices into the mix as mine is a bit boring and meaningless when not in community. I would appreciate some ebullient percussion that I could 'dub' into the far distance a la King Tubby. I would also appreciate some frugal but surprising higher pitched resonances (thinking of Vaughn Williams) to create that sense of vast height.
> 
>
>Thanks
>Steve

Thanks

On 9 February 2010 06:03, Mike Battaglia <battaglia01@...> wrote:

> So what's the name of the temperament eliminating the difference
> between 75/64 and 7/6? That would be the septimal comma, right? Isn't
> that pajara?

It's the septimal kleisma of 225/224. Pajara tempers it out, as do
meantone, miracle, magic, schismatic, and orwell. On its own it gives
you a planar temperament called marvel.

Graham

On 8 February 2010 09:55, Mike Battaglia <battaglia01@...> wrote:

> It's so frustrating. I've been a member of this list for like 3 years
> now and I still don't understand what's going on at all - and that's after
> reading tons of very insightful material generously referenced my way. I've learned
> a ton of math, a bunch about temperaments, tons about harmonic entropy
> and psychoacoustics, how to map things into a paradigm regularly, and
> so on and so forth -- but I have still yet to figure out how to just
> write expressive, emotional music with anything other than 12-tet that
> doesn't sound "weird."

Have you heard any music that sounds like that? If not, you can't
expect the theory to lead the practice. Some rules I follow though:

- Practice.

- Avoid small melodic steps. If you want to use them, start with a
framework of large steps and fill it in.

- Reuse notes in the melody, implying a scale.

- Progress with stepwise contrary motion. (Schulter)

- Introduce the 7-limit as a dissonance, and resolve it. It will
sound strange first time. Tell your listeners you know what you're
doing.

- New harmonies sound less weird the more you hear them. Be bold. If
your music is worth listening to multiple times, the weirdness will
fade. If it isn't that good, keep working until it is.

- The full 9-limit is less weird than the 7-odd limit. There are more
familiar intervals.

- Take 5-limit chords, add higher limit notes, and take the root away.
That shows the logic behind a strange chord. Reverse the process for
a strong resolution.

- A 4:5:6 can already sound wrong as the 5 is flatter than expected.
Sharp is better than flat.

My favorite 7-limit trick: resolve 6:7:8 to 4:5:6 with the middle
note held constant.

Graham

P.S. In my last message, "schismatic" assumes a circularly defined
septimal mapping of course. Also called "garibaldi".

Michael wrote:

> Of course 31EDO is a mean-tone temperament and (at least so far as I know)
> many of not most of all historical tunings (at least the non-ethnic ones) revolve around
> mean-tone....with only more recent research showing how mean-tone is really pushing for JI
> (even if those who created it didn't realize it since JI wasn't acknowledged back then).

If you allow, I would rephrase the first part of your sentence a bit. 31-EDO can do, among other things, meantone, which is just one of many 2D temperaments you can get there. This is what makes 31-EDO interesting both from the historical and from the "contemporary" point of view. Someone may have discovered the meantone-like possibilities of 31-EDO back in the 16th century, but, OTOH, only towards the end of the 20th century, it became apparent that it can also do temperaments like miracle, mothra, orwell, myna, or würschmidt.

> Couldn't someone have just as well learned, for example, that mean-tone is created
> by taking 1.5^x and then dividing by multiples of the octave and then learned JI to find the chords?

I'm not sure if I'm following you. You're swapping the order of events the other way round. We don't live in a 3-limit age anymore. If I only knew about Pythagorean tuning and nothing else in my life, maybe I wouldn't feel any need for tempering then, because I would treat C-E as a "ditone" (which has hte meaning of an unstable interval that should be resolved to something else) rather than a "major third" (which has the meaning of a stable interval because of its 5-limit origin). This is exactly what I was writing about in the document I uploaded yesterday.

> Let's start with BP since I haven't tried the other two temperaments yet. I know BP uses
> the octave * a fifth AKA the "tri-tave" as it's period, aims to foremost align the odd harmonics
> rather than the even ones, and uses the 3/5/7 chord (rather than the 6/5/4 chord (noting 6/4 = 3/2)
> as with meantone) to generate itself and thus produces very pure "thirds and fifths". To me it seems
> like just a variation on meantone with the triad shifted to odd harmonics: very connected to history,
> but not really showing anything new far as psychoacoustics, higher-limit intervals...at least
> on the surface. What is there that makes BP, Hanson...and other temperaments you say
> you learned well "only" because you learned meantone well first so special and new (at least
> so far...I'm unconvinced you're doing much more than connecting historical tuning
> to only-slightly-less historical tuning)?
I don't know what you want me to say. If I want to know why someone suggests 13 equal divisions of 3/1 (and not 12, for example), then I have to know answers for some questions regarding temperaments and what "tempering" means. If I want to know that, I have to find an example of tempering which is clear enough to me that I can say I've understood the point. Trying to explain why the so-called "BP diatonic scale" can be described using pentachords without first knowing why meantone diatonic can be destribed using tetrachords is a bit like trying to solve logarithms without understanding powers and roots. The same goes for hanson or tetracot or semisixths, although these use a 2/1 octave as meantone does. Why do I get only two one-step sizes in an 11-tone scale of hanson (4 large + 7 small) while I get two one-step sizes in a 7-tone scale of meantone (5l + 2s)? Why does the first and last chord of some harmonic progressions sound the same in tetracot while ther'yre not the same if I try to convert them to standard notation? Why can't I retune a piece from meantone to miracle just by tuning a 12-tone miracle scale on my keyboard and hearing what happens? Why is it impossible to retune a piece from meantone to miracle while it is possible to retune it from meantone to mavila? Why some harmonic progressions work well in porcupine while there's no equivalent for them in meantone? Well, it would be probably a few more words to read -- but if you really want, I can give you some example explanations how I found out about some temperaments (through understanding meantone) in the past.

> I never said they had nothing in common...just very little. Especially when it comes to how they go
> about making new scales or viewing why certain intervals "work" and psychoacoustics.
> From what I've heard from you in this e-mail, it sounds like you are focused mostly toward
> preserving the type of chords prominent in mean-tone (IE those with strong thirds and fifths)
> and slight variants of them such as those in BP.

#1. Where do you find slight variants of thirds and fifths in BP? Isn't eventually each of us meaning different things by BP? Yes, fifths and thirds are the aim in temperaments like hanson or tetracot, but not in BP.

#2. In many cases, my aim was not to approximate only fifths and thirds, but generally chords with "linearly equal" frequency differences (as they exploit an audible amount of periodicity), the simplest of which is something like 3:4:5:6 if we want to include higher primes than 3. That's the main reason why I'm so interested in the lots of 2D temperaments that have been discovered and classified less than 30 years ago. For the same reason, I was also interested to know more about BP because the "original target" of 3:5:7:9 not only exploits some periodicity but also offers a new "general feeling" of the chords because of the absence of even ratios. For the same reason, I'm planning to make a piece of music in my "Triharmonic scale" from 2006 which approximates 4:7:10:13:16 (see message #75311 for details). But then there are exceptions, although not many. One of them is, of course, the "Golden Spectrum" scale which you can find in my folder at Tuning Files -- I think you've actually heard my small improv in that scale when I recorded it a year ago.

> Part of it might be personallity too...to me BP is a historic scale
> and if it indeed has its roots in mean-tone that only seems to prove it moreso.

Depends on what you mean by "roots in meantone".

> To me Just Intonation is modern, but only when used to create scale that break traditional
> scale limits IE have more than 2 step sizes, differ more than 10 cents from traditional mean-tone
> intervals, etc. ...otherwise it seems to always end up becoming some sort of Pythagorean tuning.

#1. Are you saying that any scale that has two one-step sizes and a period of 2/1 becomes "some sort of Pythagorean tuning"?

#2. If you really do see two one-step sizes as a limitation, then what about the 3D temperaments I was mentioning in some of my earlier messages? In April last year, I recorded a short improv in a 3D temperament whose aim was to approximate chords like 8:10:11:13:16 and it only tempered out 2200/2197 and nothing else. And even though, I wouldn't say that this temperament has nothing to do with historical temperaments. First of all, I would never understand 3D temperaments without knowing about 2D temperaments (one of which is meantone). And then, one of the approximated intervals is 5/4 which was a highly appreciated interval in earlier times as well.

> One other observation...it seems those interested more in historical tunings obsess a bit about
> maintaining the purity of thirds and fifths (with Magic temperament, for example, concentrating
> on keeping the purity of thirds). What are your favorite counter-examples to this?

Again, I'm not sure if I'm following you. If you used pure thirds in magic, you would end up with pretty mistuned fifths (supposing we want pure octaves).

Petr

On 11.02.2010, at 13:10, Petr Parízek wrote:
> Someone may have discovered the meantone-like possibilities of 31-
> EDO back in the 16th century, but, OTOH, only towards the end of the
> 20th century, it became apparent that it can also do temperaments
> like miracle, mothra, orwell, myna, or würschmidt.

Please excuse my ignorance, but could you perhaps expand this remark a
bit?

Thanks!

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Aaron Hunt>
"7ET certainly is related to a chain of pure fifths;
a chain of pure fifths is at its heart - 3 tones its axis,
5 tones approximating pentatonic give a default scale
in 7ET."
If I have you right, you are saying 5 of the 7 tones approximate a chain of fifths. So part of it is related to a chain of pure fifths.
So I can understand why a 5 tone scale under 7TET would be chain of fifth based, but not the entire 7 tones (which is what I was aiming at: using all 7 tones as a scale and not just a subset as a tuning). If a 7 tone scale contained 5 of the 7 tones of diatonic JI would that alone necessarily make the whole scale a diatonic JI scale? Not at all... I think you are confusing the symptoms with the cause (IE 7TET used as a 7 note scale has symptoms/signs of a chain of 5ths but I'm pretty sure is not a chain of 5ths).
Let me put it this way: can a chain of fifths and nothing but a chain of fifths build 7TET within 14 cents or less accuracy (AKA as accurately as 12TET)?

This sounds to me like Pythagorus vs. Ptolemy: Pythagorus believe scales are exclusively related to chains of 5ths while Ptolemy said anything that can form tetrachords is fair game. So far I'm under the impression Ptolemy was the one seeing the forest and Pythagorus the trees: Magic temperament (chain of thirds) and Miracle (chain of seconds) being two obvious examples.
-----------------------------------------
>> The chain of
>> pure-fifths seems to be a common and IMVHO a bit
>> over-stated goal on this list...
>It's not a goal. It's a basic structure.

Not a goal...in that case, how come you seem to pointing at that all things must be related to the circle of 5ths when many scales simply are not? It seems clear to me the only reason why it would absolutely have to be a circle of 5ths would be that you choose it to be as such. I don't know the name for it (if anyone knows the name for it, I would be very interested to learn)...but I'm fairly sure someone must have based a scale on a chain of 7ths or even a chain of, say, 5th then 2nd then 5th....

>"Sure, that's a structure too, but a *less basic one* than the chain of fifths, unless you want to argue that 5 is less than 3?"
Interesting, so you'd argue a scale based on a chain of 7ths is more basic than the chain of fifths? I'll admit that 2/1 is easier to make consonant than a 3/2 which is easier than a 4/3 and so on...but then what happens to, say, the purity of 2nds or 6ths? I don't think it's a one way street...

>"Ask yourself the question: what is a tetrachord? Your answer points you back to the number 3."
Tetrachord = 4 note chord where the lowest and highest tones are 4/3 apart. So the fraction has a denominator of three...but what does that have to do with your list of
> > 1) - chain of pure fifths
> > 2) - JI intervals
> > 3) - ETs"
?
It seems to me that it points to JI and not at all the other two. I can chain tetrachords on top on each other, but I can also say, make a chain with the second tetrachord starting on the third note of the first one rather than the fourth. I'll gladly read your reference to Ptolemy...but even before that I'll note that, from what I've seen of his scales, many to a fair extent very much disobey the circle of 5ths and, at least to my ear, actually sound more balanced than meantone ones (especially with regards to his clever avoidance of the IMVHO very hard to use in chords "perfect" minor second).

>"You can't escape these things. They seem to be too simple for you..."
They are not "too simple" for me...it's just that reviewing a learning them mainly points me in the direction of making innovations that have already been made rather (or at best, slightly tweak them) than actually add much new.

So I respect those simplicities, but there's a huge difference between respecting something as a valid way to do things and thinking they must be the >only< way to do things. I never said anything like "scales designed from chains of 5ths fail to do what they are designed to do well". They do, and they are great for things like 5th (obviously), major 7ths, and triads.

However so far I've found if you want to do different things well, like make notes near (or between) minor seconds or major seconds starting with any root note in a scale sound resolved enough to work in chords...I've seen you have to abandon the security of those constructs. I've asked people "give me a meantone scale with the highest minimum purity" and have heard 1/4 comma meantone, JI diatonic, and even a straight set of harmonic series partials as a scale, suggested a bunch of times. I tried it, and the minor second still sounds rough enough to be unusable. I've tried Ptolemy Homalon scales and my own tempered variations on them to do the same thing and have had much better luck.

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

I guess that's my "problem". On one hand don't get me wrong: I understand how things like meantone work and see things like the circle of 5ths and 4ths and why they are valid for the kind of consonances composers normally see as thesible (IE fairly widely spaced ones). On the other hand I ask myself "why not try for something that compromises perfect periodicity for better/less roughness...rather than stay around the same range for both by following things like using exclusively JI ratios within exclusively mean-tone-like tunings or TET approximations of them"?

>"I don't understand this question. Seconds are already intervals, so
what are intervals between them? "

Well, say our minor second is 15:14 and our major is 9/8.
Now try 12/11. That's an in-between ratio used in Ptolemy's Homalon scales that I often experiment with tempering for my own scales. I ran into it myself upon experimentation, but Jacques reminded me that
A) It already was used by Ptolemy in some of his scales
B) Ptolemy's scales are among his favorites (and I can see why)

And, while it's obviously not so pure as 9/8...it (at least to my ears) strikes a much better balance of periodicity and roughness than 15/14 and just plain old sounds better in chords as a more-resolved substitute for a minor second.
This is the kind of thing I'm talking about when I say non-standard interval sizes.
--------------------------------------------------------------------
>"Why can't seconds be used in chords? They are used all the time in
music. What's the problem?"
Really the minor seconds and anything too close to them. Say the "chord" C C# G. I've found most people will jump at the C# as sounding too rough and most composers will jump as say "you can't use a minor second in a held/"rest" chord...it's a neighboring tone; hit it quickly and then quickly resolve it with a clearer chord...learn your music theory".
Meanwhile, sure, I've heard C D E G AKA C add2 used a lot...no problem with that. It's the "dark" area of the minor second that bugs me. Again (at least to me) something in-between the second and minor second is "close enough".
-------------------------------------------------------------
>"I didn't say it's hideous. I just said you're obviously obsessed. :D"
True enough. I tend to gravitate toward things I see hints could be done without too much trouble...but barely (if at all) see anyone working on.
I don't disrespect what others are working on, I just figure (at least for now) while everyone else is figuring out great ways to purify their 3rds, 5ths, 7ths....I might as well see what happens if I do something like try and purify something that can be used a bit like what it seems nearly everyone thinks is the nastiest interval, the minor second.
And, as a plus, try to do so without making the other intervals sound intolerably sour...that's kind of what I mean by the whole "chord-scale" obsession where virtually any combination of notes can make a fairly consonant chord. I also figure that trying to "knock through that wall" could (no guarantees but it would be nice) lead me to some sort of "loophole" in psycho-acoustic theory that allows all sorts of new chord combinations with more closely spaced notes. I think it has just become a dogmatic limitation among composers that close notes in chords must only mean atonal or "accidental".
---------------------------------------------------------------
>"It seems to me that whether c c# d# can sound at least nice (if not resolved) depends more on the musical context than tuning. Those kind
of sonorities are favoured by atonal composers and in that context they don't demand resolution. "
True, but I figured it would be nice to open chords a bit like that to a non-atonal audience. Sure, as stands, they have their values in uniqueness...but I think it would be fun to see what musicians would try to do if they found a way to use a chord with a similar feel as a point of resolution.
-------------------------------------------------------------
>"You must mean detuning because tempering harmonic series segments
makes no sense to me. Detuning and temperament are not the same
thing."
Please explain. http://en.wikipedia.org/wiki/Musical_temperament says "to intentionally choose an interval with beating as a substitute for a just interval is the act of tempering that interval." Does the proper term temperament have to exclusively deal with tempering out commas/schismas...in "chain of xths" generated scales to make octaves/tritaves/etc. match the chain or making a chain of multiple to approximate a scale (IE 12TET being tempered from meantone)? If it's anything like that...yes I mean "de-tuning" and not temperament.

Personally I "de-tune" simply as a means to balance between periodicity and roughness and reduce each to a tolerable amount. IE if two tones are too close, de-tune them to decrease roughness...if a tone is periodic with the tone next to it but not very much so with the tone two notes below it, de-tune it closer to a pure-JI ratio with the note two-tones below it a bit (but not so much it loses too much periodicity with regards to the note next to it.
--------------------------------------------------------------
>> One way I think of it is that a 2:3:4 chord can sound vastly
>> different depending on a different root pitch or even just a little
>> bit of "bending" of any tone in the chord.
>That's a bit vague but maybe you just mean the chord's overall timbre?
Yes, that's a fair way to say it. :-)
---------------------------------------------------------------
>> I don't believe in "a chord is perfectly pure or it's just a poor
>> imitation of perfectly pure"...though I will agree too far from
>> pure can cause some nasty lack-of-periodicity issues.
>I don't know if anyone thinks that even a tiny deviation from pure
>is a poor imitation.
Fair enough...I was going a bit on a ledge as it sounded like you were saying "chords have to be a >perfect< straight series AKA 4/4 5/4 6/4 (4:5:6), that's the only way to do make them" and I was quite eager to say "no, some deviation is legal".
------------------------------------------------------------
>"Unless you have faulty speakers there is no harmonic distortion.
Harmonic distortion happens when poor quality electronic equipment
adds harmonics to sine waves. What you hear is something else, maybe
periodicity buzz. "
I've heard the terms used interchangably but yes, you're right, I meant periodicity buzz and I'll exclusively use that term in the future.
-----------------------------------------------------
>> > "Feel free to start your own group where you can sensor any
>> > discussions that don't cater to your singular interests."
>> I have never tried to censor anyone or say "stop talking" in
>> any form...how are you coming to the conclusion I am?
>I am not coming to such a conclusion, you are putting words into my
>mouth.
Well you were at least hinting "Feel free to start your own group where you can sensor any discussions" as if I would somehow find that an attractive option. My somehow finding that an attractive option would imply I may well >enjoy< censoring others. So I think it's fair to say that comment you made was targetted as an indirect insult to me, which is why I jumped at it.
---------------------------------------------------------------------
>"What makes you think that the interests could be divided in exactly two groups? As how you answered to Petr you seem to think that even
such a xenharmonic scale as BP is "traditional" . I wonder how many people would be qualified for the "progressive" group."

I don't think it's about being 'qualified' so much as it is being tolerant. I usually get the same 5 or so answers for everything a bring up here (and often delivered in an almost angry fashion), including but not limited to
1) Use mean-tone (particularly 1/4 comma), diatonic JI, 53TET, or a straight set of partials harmonic series to get maximum average consonance...you're a bit crazy for thinking there might be another option for optimizing consonance.
2) Consonance is based only on periodicity and its close cousin tonallity, you won't get a serious answer on any other type of experimental optimization (IE roughness, difference tone patterns, timbre...)
3) All consonant chords must be based on only very low integer ratios...anything like 11-limit JI is a bit crazy...stick with 7-limit or less. It follows "forget about making scales with a ratio between a major and minor second/third/etc."...people give me weird responses when I say I'm going for something inbetween two widely accepted ratios.
4) There is no way any sort of irrational ratio can feel consonant...stop experimenting with 1+(1/sqrt(2))^x, 1 + (1/PHI)^x, 1 + (1/any other irrational)^x as generators.
5) If you want big chords and large scales, try octatonic scales of 22TET (for the record, I really like 22TET on the whole, just not for close-ratio chords).

Sethares (who pretty much sparked my interest in micro-tonallity) left this list. So did Rick Ballan over his GCD theories (which I still see promise in). Sevish (who I work with a lot) has not been on nearly as often and didn't seem too happy about the JI-or-nothing attitude floating around so far as I can tell. Charles Lucy and Marcel get constant heat...and is it really that much of an issue if they are right or not when they aren't telling people what to do and not to do by any means? Is it really worth all the ego battling for "academic correctness"?...and what if someone successfully finds something that improves on what was academically correct before: is it really that crazy?

Maybe (in fact, quite likely) there are only a few out of hundred people on here who give a ---- about what I'm trying to shoot for. And that's fine: I never said I expected any sort of fan club and I know what I've been doing musically is incredibly odd. But I would at least like to hear from those few who want to work with/on what I write as a possibility directly without a ton of people saying "you are just being ignorant, the solution has always been X why can't you accept that?!?!"
I'm just looking for some more clear reception and a place to build on ideas instead of have them torn down almost as if on impulse, that's all.

-Michael

--- Michael <djtrancendance@...>
> >Aaron Hunt:
> >"7ET certainly is related to a chain of pure fifths;
> >a chain of pure fifths is at its heart - 3 tones its axis,
> >5 tones approximating pentatonic give a default scale
> >in 7ET."
>
> If I have you right, you are saying 5 of the 7 tones
> approximate a chain of fifths. So part of it is related
> to a chain of pure fifths.
> So I can understand why a 5 tone scale under 7TET
> would be chain of fifth based, but not the entire 7
> tones (which is what I was aiming at: using all 7 tones
> as a scale and not just a subset as a tuning). If a 7
> tone scale contained 5 of the 7 tones of diatonic JI
> would that alone necessarily make the whole scale
> a diatonic JI scale? Not at all... I think you are
> confusing the symptoms with the cause (IE 7TET
> used as a 7 note scale has symptoms/signs of a
> chain of 5ths but I'm pretty sure is not a chain of
> 5ths).
> Let me put it this way: can a chain of fifths and
> nothing but a chain of fifths build 7TET within 14
> cents or less accuracy (AKA as accurately as 12TET)?

Michael, I have to be honest here; you are beginning
to waste my time. I just explained this to you, and
here it is on one of the webpages I referred you to
3 messages ago:
<http://www.h-pi.com/theory/superscales6.html#7&5ET>
I already said all of 7ET is related to a chain of fifths,
explaining how right after the sentence you quote
from me above.

> This sounds to me like Pythagorus vs. Ptolemy:
> Pythagorus believe scales are exclusively related
> to chains of 5ths while Ptolemy said anything that
> can form tetrachords is fair game. So far I'm under
> the impression Ptolemy was the one seeing the
> forest and Pythagorus the trees: Magic temperament
> (chain of thirds) and Miracle (chain of seconds)
> being two obvious examples.

Again, if you want to say something about Greek
music theory, then first learn something substantial
about it. BTW, no source texts exist for Pythagoras.

> -----------------------------------------
> >> The chain of
> >> pure-fifths seems to be a common and IMVHO a bit
> >> over-stated goal on this list...
> >It's not a goal. It's a basic structure.
>
> Not a goal...in that case, how come you seem to
> pointing at that all things must be related to the
> circle of 5ths when many scales simply are not?

If you want to ignore similarities to the most basic
musical patterns possible, you are of course free to
do so.

> It seems clear to me the only reason why it would
> absolutely have to be a circle of 5ths would be
> that you choose it to be as such. I don't know
> the name for it (if anyone knows the name for
> it, I would be very interested to learn)...but
> I'm fairly sure someone must have based a
> scale on a chain of 7ths or even a chain of,
> say, 5th then 2nd then 5th....

Anyone can base it on whatever they want. I'm afraid
you have completely missed the point ...

> > "Sure, that's a structure too, but a *less basic
> > one* than the chain of fifths, unless you want
> > to argue that 5 is less than 3?"
> Interesting, so you'd argue a scale based on
> a chain of 7ths is more basic than the chain of
> fifths?

... and, this shows how badly you've missed the
point. How on earth could anyone deduce from my
words that a chain of 7ths is more basic than a chain
of 5ths?

I assume the fault is mine. Let me try again...
An octave = harmonic number 2, whose powers do not
generate non-octave-duplicate pitches. A Fifth = harmonic
number 3, whose powers generate non-octave intervals.
Other numbers do this too, but 3 is less than all other
numbers that are greater than 3, for example 5 ? ...
therefore 3 is the most basic cycle of all; all other interval
cycles are *less basic*. Make sense?

> I'll admit that 2/1 is easier to make
> consonant than a 3/2 which is easier than a 4/3
> and so on...but then what happens to, say,
> the purity of 2nds or 6ths? I don't think it's
> a one way street...

OK, honestly, you are now officially wasting my time.
My original post stated as clear as the day that the cycle
of fifths starts sounding wrong harmonically.

> >"Ask yourself the question: what is a tetrachord?
> > Your answer points you back to the number 3."
> Tetrachord = 4 note chord where the lowest and
> highest tones are 4/3 apart. So the fraction has a
> denominator of three...but what does that have
> to do with your list of
> > > 1) - chain of pure fifths
> > > 2) - JI intervals
> > > 3) - ETs"
> ?

A tetrachord spans a fourth, so it is part of (1).

> >"You can't escape these things. They seem
> to be too simple for you..."
> They are not "too simple" for me...it's just
> that reviewing a learning them mainly points
> me in the direction of making innovations
> that have already been made rather (or at
> best, slightly tweak them) than actually add
> much new.
> So I respect those simplicities, but there's
> a huge difference between respecting something
> as a valid way to do things and thinking they
> must be the >only< way to do things.

I never said that. Now you are really annoying me.

> I never
> said anything like "scales designed from chains
> of 5ths fail to do what they are designed to do
> well". They do, and they are great for things
> like 5th (obviously), major 7ths, and triads.
>
> However so far I've found if you want to do
> different things well, like make notes near
> (or between) minor seconds or major seconds
> starting with any root note in a scale sound
> resolved enough to work in chords...I've seen
> you have to abandon the security of those
> constructs.

Yes, see what you get when you "abandon the security
of those constructs". The simplicities that emerge
from whatever you do will relate back to those very
things you think you are escaping. I *never said*
you have to use those constructs to build whatever
it is you want to build.

> I guess that's my "problem". On one hand
> don't get me wrong: I understand how things
> like meantone work and see things like the
> circle of 5ths and 4ths and why they are valid
> for the kind of consonances composers
> normally see as thesible (IE fairly widely spaced
> ones). On the other hand I ask myself "why
> not try for something that compromises perfect
> periodicity for better/less roughness...rather
> than stay around the same range for both by
> following things like using exclusively JI ratios
> within exclusively mean-tone-like tunings or
> TET approximations of them"?

By all means, go for it.

I'll not be discussing these things with you any
further, Michael. I hope you have understood the
point. If you haven't, then fault me for being a
bad teacher. If you do get it and just don't like it,
that's fine. I've presented the ideas here as clearly as I
can. They are not my ideas per se. Those things
have been said before by many, many people; I was
merely summarizing.

My contribution to this topic ends here.

Some words of advice: read what you respond to
more carefully, and when you paraphrase, be careful
not to change meanings, and avoid being emphatic.

I sincerely wish you good luck with your innovations.

Yours,
AAH
=====

>"We don’t live in a 3-limit age anymore. If I only knew about Pythagorean
tuning"
I was not talking about Pythagorean tuning, but about mean-tone...and I was talking about how a scale are generated, not how certain intervals in the scale are/were used composition-wise at the time the scale was derived. I think this is a common problem when I write something in the context of generating a tuning and someone follows up with a point about compositional practice throughout history.

>"Well, it would be
probably a few more words to read -- but if you really want, I can give you some
example explanations how I found out about some temperaments (through
understanding mean-tone) in the past."
I am interested in how you found out how to do miracle temperament via mean-tone, since miracle involves generation via chaining of seconds and, at first glance, you would think they have little in common (plus I am admittedly interested in the art of purifying seconds and minor-seconds since so many musicians consider them as a-tonal for use in chords).

>"#1.
Where do you find slight variants of thirds and fifths in BP? Isn’t eventually
each of us meaning different things by BP? Yes, fifths and thirds are the aim in
temperaments like hanson or tetracot, but not in BP."
I was wrong, I assumed thirds were strong since BP is built from the 3:5:7 chord that it optimized the third at 7/3. It is indeed a lot newer than I gave it credit for, in some sense. Counter question, what are some temperaments you know (other than Miracle) which focus on optimizing intervals other than 3rds, 4ths, and 5ths?

>"#2.
In many cases, my aim was not to approximate only fifths and thirds, but
generally chords with „linearly equal“ frequency differences (as they exploit an
audible amount of periodicity) , the simplest of which is something like 3:4:5:6
if we want to include higher primes than 3."
Isn't this basically scales that involves the chaining of four note chords (and not just tetra-chords)? If so, I'm all for you on that one...although I typically find myself messing with tetra-chords all the way up to about 8:9:10:11 on the series and ones with spaces in between steps up to more like 10:11:16:18. Oddly enough, Ptolemy did a lot with ratios like 12/11...but I don't hear many people talking about him.

>>
Part of it might be personality too...to me BP is a historic scale
>> and
if it indeed has its roots in mean-tone that only seems to prove it
moreso.
>Depends
on what you mean by „roots in meantone“.
Well let's start with this: how did you learn BP from meantone? So far I have the impression that the common thread is chaining chords together...which I think is a smart way to design scales, but doesn't seem to me to have its roots in music history.

>"#1.
Are you saying that any scale that has two one-step sizes and a period of 2/1
becomes „some sort of Pythagorean tuning“?"
No, the point of similarity to me has to do with using either a chain of 5ths or approximated 5ths to generate a scale.

>"the „Golden Spectrum“ scale"
Which is also based on a "chain of x" generator (chain of PHI^x/2^y, to be exact) as I understand it...kind of like my first PHI-based scales before I started using 1+(1/PHI)^x to split the notes into golden sections...isn't it?

Here a some for you...
1) What temperaments do you know which are not based on some sort of "chain of x interval" algorithm or a close approximation of one?
2) How does mean-tone theory apply to those?

>"#2.
If you really do see two one-step sizes as a limitation, then what about the 3D
temperaments I was mentioning in some of my earlier messages? In April last
year, I recorded a short improv in a 3D temperament whose aim was to approximate
chords like 8:10:11:13:16"
Now that does sound really interesting...my knowledge honestly probably wasn't up to stuff at the time you posted those. I'm a huge fan of scales that can manage step sizes down to about 11/10 (actually "all the way" up to closeness of about 12/11) and still sound fairly resolved. I'm also great believer in any sort of experiment that uses harmonics from the harmonic series up to 20 yet spaces them in a way that controls tonal roughness reasonably. I will admit, from what I've heard of 2-tone MOS that theory of scale generation seems a bit limited to me...going 3D (AKA hyper-MOS, right?) sounds quite interesting.

If you can put together some links to posts as to how you derived such 3D temperaments, I'd be happy to read about them. I think I've run into a few simply by stacking 4-note chords using some fairly high-limit ratios, but admittedly did so by experimentation rather than knowing the inner workings of how to "run a 3D temperament generator".

>> maintaining the purity of thirds and fifths (with
Magic temperament, for example, concentrating
>> on keeping the purity of
thirds). What are your favorite counter-examples to
this?
>Again,
I’m not sure if I’m following you. If you used pure thirds in magic, you would
end up with pretty mistuned fifths (supposing we want pure
octaves).
Well I said "with
Magic temperament, for example, concentrating on keeping the purity of
thirds"...I was trying to say Magic is fairly common and purifies thirds while other relatively common tunings (namely mean-tone) purify 5ths...I didn't say or mean "Magic purifies 3rds and fifths". It makes perfect sense to me that Magic purifies thirds at the expense of 5ths.

-Michael

>"Halfsteps and wholesteps of the diatonic naturals can be collapsed into a single step size,
resulting in 7 Tone Equal Temperament, 7ET."
Hmm...ok. As I understand it you assume the 7TET step size can be "heard" as a major or minor second and is in-between both tones...almost as if to say anything right in between two diatonic tones is "heard" as either one of those diatonic tones but not it's own entity...which I'm hard-pressed to believe. As I understand it, it sounds like a bit of a forced dogma.

> >5 tones approximating pentatonic give a default scale
> >in 7ET."
Yes and it seems clear from what you said that's 5 tones, not the entire 7 in 7TET. I'm assuming all 7 tones are used as the scale, not just 5...proving 5 are related does not prove 7 are; scale is not equal to tuning (and Lord knows how many threads there have been on this board about scale/tuning confusion).

>"Again, if you want to say something about Greek music theory, then first learn something substantial about it."
Did you ever think that just maybe I have composed with and learned about Ptolemy's scales? I have. The inconvenient truth is I haven't read anything about his Homalon or "smooth" scales having anything to do directly with meantone. Those scales are based on tetrachords of 9:10:11:12 and are very evenly spaced, much more so than anything I've heard under low-limit JI. What I don't know much about is specfics about Pythagorean music theory...to be honest, I'm not overly interested in the details of it because it is simply a chain of fifth's (with no tempering to make it match the octave, unlike mean-tone).

>"Some words of advice: read what you respond to more carefully, and when you paraphrase, be careful
not to change meanings, and avoid being emphatic."
I guess you could say it's time simply to hand this one over to the list and see what they thinl. I get a strong impression that even when I listen to you, you assume I am not listening mostly because I don't agree with you that it's the only way to do things...and that you were being at least as emphatic as myself if not more.

Perhaps I'm the opposite, if someone tells me there's only one way to do things I look for many types of proof before I agree. For the longest time I though music was limited by the periodicity of the harmonic series and 12TET was the ultimate compromise for that back in music school when they talked about basic frequency ratios. Then Sethares showed me it could be otherwise with his roughness/critical-band-based theories and brought me into being interested in microtonallity and bound it with my interest in psychoacoustics I already had from DSP programming. So if I'm really skeptical when someone seems to tell me everything is based on some construct that seems to be solely based on generating periodicity, don't take it personally.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> > "I don't understand this question. Seconds are already intervals,
> > so what are intervals between them?"
>
> Well, say our minor second is 15:14 and our major is 9/8.
> Now try 12/11.

OK, you mean intervals intermediate in size between minor and major
seconds. 11:12 is a neutral second.

> That's an in-between ratio used in Ptolemy's Homalon scales that I
> often experiment with tempering for my own scales. I ran into it
> myself upon experimentation, but Jacques reminded me that
> A) It already was used by Ptolemy in some of his scales
> B) Ptolemy's scales are among his favorites (and I can see why)
>
> And, while it's obviously not so pure as 9/8...it (at least to
> my ears) strikes a much better balance of periodicity and roughness
> than 15/14 and just plain old sounds better in chords as a
> more-resolved substitute for a minor second.

But play G B C E. This sweet-sounding chord contains a minor second
between B and C. Now substitute this with a neutral second. I don't
think it sounds more resolved, quite ugly in fact. So what you say is
not generally true.

> This is the kind of thing I'm talking about when I say
> non-standard interval sizes.

Non-standard how? Neutral seconds are already used in traditional
Arab music.

> --------------------------------------------------------------------
> > "Why can't seconds be used in chords? They are used all the time
> > in music. What's the problem?"
> Really the minor seconds and anything too close to them. Say
> the "chord" C C# G.

Well, that chord contains also a diminished fifth between C# and G
which is dissonant. Compare C C# G with C C# F G# (acoustically a
major seventh chord, spelled differently). Sounds much better?

> I've found most people will jump at the C# as sounding too rough
> and most composers will jump as say "you can't use a minor second
> in a held/"rest" chord...

Not true, play G B C E.

> it's a neighboring tone; hit it quickly and then quickly resolve it
> with a clearer chord...learn your music theory".

They (whoever they are) should learn music theory.

> -------------------------------------------------------------
> >"You must mean detuning because tempering harmonic series segments
> makes no sense to me. Detuning and temperament are not the same
> thing."
> Please explain. http://en.wikipedia.org
> /wiki/Musical_temperament says "to intentionally choose an interval
> with beating as a substitute for a just interval is the act of
> tempering that interval." Does the proper term temperament have to
> exclusively deal with tempering out commas/schismas...

Yes.

---------------------------------------------------------------------
> > "What makes you think that the interests could be divided in
> > exactly two groups? As how you answered to Petr you seem to think
> > that even such a xenharmonic scale as BP is "traditional". I
> > wonder how many people would be qualified for the "progressive"
> > group."
>
> I don't think it's about being 'qualified' so much as it is
> being tolerant. I usually get the same 5 or so answers for
> everything a bring up here (and often delivered in an almost angry
> fashion), including but not limited to
> 1) Use mean-tone (particularly 1/4 comma), diatonic JI, 53TET, or a
> straight set of partials harmonic series to get maximum average
> consonance...you're a bit crazy for thinking there might be another
> option for optimizing consonance.
> 2) Consonance is based only on periodicity and its close cousin
> tonallity, you won't get a serious answer on any other type of
> experimental optimization (IE roughness, difference tone patterns,
> timbre...)
> 3) All consonant chords must be based on only very low integer
> ratios...anything like 11-limit JI is a bit crazy...stick with
> 7-limit or less. It follows "forget about making scales with a
> ratio between a major and minor second/third/etc."...people give me
> weird responses when I say I'm going for something inbetween two
> widely accepted ratios.
> 4) There is no way any sort of irrational ratio can feel
> consonant...stop experimenting with 1+(1/sqrt(2))^x, 1 + (1/PHI)^x,
> 1 + (1/any other irrational)^x as generators.
> 5) If you want big chords and large scales, try octatonic scales
> of 22TET (for the record, I really like 22TET on the whole, just
> not for close-ratio chords).

11-limit is not generally considered crazy, there is healthy interest
in it. Those octatonic scales of 22-equal in fact approximate several
11-limit ratios.

> Sethares (who pretty much sparked my interest in micro-
> tonallity) left this list. So did Rick Ballan over his GCD
> theories (which I still see promise in). Sevish (who I work with a
> lot) has not been on nearly as often and didn't seem too happy
> about the JI-or-nothing attitude floating around so far as I can
> tell. Charles Lucy and Marcel get constant heat...and is it really
> that much of an issue if they are right or not when they aren't
> telling people what to do and not to do by any means? Is it really
> worth all the ego battling for "academic correctness"?...and what
> if someone successfully finds something that improves on what was
> academically correct before: is it really that crazy?

What you perceive as ego battling may actually be a serious offer of
help. Criticism is not intolerance. When did false beliefs help
anyone in their pursuits?

> Maybe (in fact, quite likely) there are only a few out of
> hundred people on here who give a ---- about what I'm trying to
> shoot for. And that's fine: I never said I expected any sort of
> fan club and I know what I've been doing musically is incredibly
> odd. But I would at least like to hear from those few who want to
> work with/on what I write as a possibility directly without a ton
> of people saying "you are just being ignorant, the solution has
> always been X why can't you accept that?!?!"
> I'm just looking for some more clear reception and a place to
> build on ideas instead of have them torn down almost as if on
> impulse, that's all.

I think the problem is that you are a moving target, so to speak.
Your approach is constantly changing as witnessed by my belief that
you are still searching for a chord-scale where any combination of
tones produces a consonant chord. Do you seriously expect anyone to
be able to follow your adventures with keen interest? Failure to do
so is not always intolerance.

Kalle Aho

> I think they sound perfectly natural because, contra Marcel, our
> brain doesn't analyze music in terms of JI. Our mind doesn't
> recognize a tempered scale or some extra harmonic relation not
> existing in its' JI version as some kind of unnatural perversion or
> illusion even if tempered intervals gain their resonance from their
> proximity to just intervals.

Then what do our brains analyze music in terms of? It can't all just
be arbitrary cultural conditioning.

-Mike

>     IMVHO a hole in this theory is the inability to, say, put half steps into a consonant chord.

I'm not sure why you keep saying that. I use half steps in my chords
all the time. There was actually a person here who said that chords
didn't sound GOOD if they didn't have a half step in them - that they
were either "crunchy" or "soggy", if I remember.

G E F B C G A - there's a great mixolydian voicing that uses half steps.
Gb D Eb A Bb F - another great one for Gb aug #9 that I just came up
with off the top of my head.
C E F A - a simple maj7 chord in an inversion.

Seriously man, I'm not sure what your vendetta against half steps is,
but they sound awesome when used in harmonies.

-Mike

> Have you heard any music that sounds like that? If not, you can't
> expect the theory to lead the practice. Some rules I follow though:

I have heard a lot of great music from a lot of great composers on
here, and a lot of it has given me a lot of ideas. But I have yet to
hear the masterpiece that fluidly ties it all together though. AKJ,
Neil Haverstick, GWS have all written at pieces in which I started to
see the very large picture at how 7-limit harmony could really work,
but I have yet to assimilate it myself.

5-limit harmony is so intuitive to me that I don't even have to think
about it. As an improvisational musician, that's pretty much my goal.
7-limit harmony I can safely say I'm useless with, except for just
throwing in a few cool chord ideas.

> - Practice.

And now we're at main problem #1, which is I have no instrument :)
Using eastwest with 6 detuned channels to get in 72tet is also pretty
inefficient.

>//snip
> - Progress with stepwise contrary motion. (Schulter)

BTW, are there any examples of Margo's work online? I've heard a lot
about her stuff, and the way she talks about this sounds like her work
is exactly what I need to hear.

> - Introduce the 7-limit as a dissonance, and resolve it. It will
> sound strange first time. Tell your listeners you know what you're
> doing.

I have heard a grand total of one piece in which the 7-limit sounded
completely natural the first time I heard it - AKJ's "melancholic." I
still don't know how he did it so effectively there - other pieces I
had to listen a few times before it started to sound natural.

Of course, now that I've said this, I'm going to remember some other
piece, but I can't right now. Don't be mad at me other composers, now
I'm on the spot!

> - Take 5-limit chords, add higher limit notes, and take the root away.
> That shows the logic behind a strange chord. Reverse the process for
> a strong resolution.

That might be why.

> - A 4:5:6 can already sound wrong as the 5 is flatter than expected.
> Sharp is better than flat.

This is something I've noticed as well, and I have no idea why. I
think it might have to do with how we tend to overestimate the size of
an octave with pure tones and such.

> My favorite 7-limit trick: resolve 6:7:8 to 4:5:6 with the middle
> note held constant.

Yes, tricks! Tricks are what I need.

A trick of my own: take the following chord structure: E- F C D G

and play it over a C. Sounds great. Now move it up a third - still
sounds good. Now move it another minor third up so it's over the fifth
- still sounds amazing. Now go 7/6 up from that and blast off.

So if you notice what I'm doing, I'm transposing it so that the "C" in
the middle of that chord structure moves to different otonal ratios.
First do it with C, then E- (G#-- A- E- F#- B) then with G, then with
Bb<, etc.

Long story short, once you get to 11:4, rumor has it that your brain
will actually melt right out of your ears. Flipping back and forth
between 11:4 and 13:4 is the most heavenly sound on planet earth. I
have a string quartet half composed on this chord progression from a
year ago.

Of course, I still don't have a clue why it sounds good, but I think
it has something to do with mixing otonal and utonal structures
together in a familiar way.

-Mike

>
> Graham
>
> P.S. In my last message, "schismatic" assumes a circularly defined
> septimal mapping of course. Also called "garibaldi".
>

> Hm, wikipedia... Written by a certain person named Anonymus, and full
> of errors and strange statements. Only trustful sources are some
> facts, but explanations and interpretations not always...
>
> I see it like this:
>
> - Polymodal chromaticism doesn't exist, both terms just describe two
> different approaches to music.

I don't really know anything about it. I just threw something in based
on what I'd heard and read. Clearly someone thinks it's real. Doesn't
bother me.

> - Of course if we superimpose, combine two or more modes or scales
> which have less tones then 12, we can get the chromatic scale in the
> result. But in such polymodal works composer doesn't use
> chromaticism, he works with modes. Chromaticism is more or less
> latent and can be avoided. Even dissonances and chromatic seconds can
> be avoided with careful composing method. I wouldn't talk in this
> case about chromaticism.

I'm not just superimposing two random modes. I took a sound I was
hearing and fleshed it out, and to my surprised it turned out to yield
every note of the chromatic scale functionally. This isn't that
unbelievable.

If you were to intonate this chromatic scale with JI, it would have a
different tuning than the usual 5-limit chromatic scale. There'd also
be a bunch of comma-shifted versions of the same note in there too.

> - Chromatic scale is a chromatic scale. Nothing else. To describe it
> as "12-tone polymode" just because it was a result from combining two
> or mode modes is really unnecessary.

Yes, but in the case of my scale - it's hardly "chromatic" in the
traditional sense, short of that it has 12 notes. Every note in that
scale can be used simultaneously. It's a sound I was hearing in my
head that I fleshed out; it really does stretch the meantone thing to
it's limit.

Viewed in a JI context, with the root as C, it goes two steps out into
the 5-axis (G#), and then a fifth over (so from C-D#). Then it goes
another fifth over to A#. The C# can be viewed as a fifth below 25/16,
or as a 135/128 over C, or as a 17/16 over C, and I will conceptually
use all of those and mix them together. The D# can also be a 19/16.
It's almost 7 AM and I'm way too tired to do the math now, but that
corresponds to some linear temperament, I am sure - a linear 19-limit
non-7 non-11 non-13 temperament.

-Mike

> Just my opinion.
>
> Daniel Forró
>
>

Everything you just said is exactly why I think the word "consonance"
should be considered a profanity around here. There are so many
meanings for the word that roughly 2/3 of conversations about it
degenerate into semantic disagreements within 10 or so posts.

There are many legitimate musical phenomena that go into the
perception of a chord:

- Its overall harmonicity and intonation
- The interaction between any and all of the multiplicity of harmonic
relationships perceived in the chord
- Critical band factors, roughness, beating
- Whether you've been writing a pleasant song in major the whole time
and then throw 4:5:6:7:9:11 in over the I chord out of nowhere
- Whether the high priest at your monestary thinks that the tritone is
the devil's interval
- Whether a certain chord reminds you of that one time your girlfriend
broke up with you while you were doing your taxes

I don't think a single qualitative dimension of "consonance" can
really describe whether random listener X will end up "liking" the
sound of a chord at the end of the day. That being said, the first
three things I mentioned are actual psychoacoustic principles that
have at least some reasonable tangible component to them, and I just
prefer to think of them as completely separate things that sometimes
overlap. The fourth likely has some kind of psychoacoustic basis
behind it as well, despite its usually being considered a cultural
thing, but I have no idea how to even start analyzing that.

We prioritize those things differently: For me #1 and #2 are about
equal, and #3 I don't even care about. Those around here who are
accustomed to tunings without the crystal clear pure fifths of
12-equal care in the order of #2, #1, and #3, I think. And Michael
Sheiman for some reason seems to care in the order of #3, #2, and #1.

In my view, just disregarding all that to pretend that a single
dimension of "consonance" can handle all of this really makes no
sense, although it can be kind of useful as a rough rule of thumb or
something.

-Mike

On Wed, Feb 10, 2010 at 5:07 PM, Cox Franklin <franklincox@yahoo.com> wrote:
>
>
>
> Responding to Michael:
>
> > I'm convinced something that would cover the
> > entire gammut would explain
> > A) where consonance becomes dissonance
> > (roughness wise...for example with regard to
> > consecutive sine tones played in TET tunings)
> > B) where consonance becomes dissonance
> > (periodicity/ "JI" wise)
> > C) If a chord meets A and B (is consonant
> > according to A and B) yet somehow sounds
> > dissonant, why does it?
>
> One of the problems I see in this is that it leaves harmonic/contrapuntal function and historical changes in perception of consonance/dissonance out of the equation. In common practice music one of Hindemith's most consonant chords, an 027 (say, [low to high] G C D) is is always a dissonance and must resolve, with the C always resolving downwards.  Any chord with tritones and half steps in Hindemiths system is automatically more dissonant that a chord lacking these intervals, yet a V m9 chord in minor, one of the most important chords in the harmonic syntax of late Romantic music. What is more, one can weave all sorts of non-chord tones that are more consonant with the bass than the m7 and m9, yet these will feel dissonant to this very dissonant chord.  This is owing to the harmonic syntax and to contrapuntal expectations (the m9 will eventually resolve down by half step, but if the m9 is clearly the chord tone,  a neighbor-tone M9 against the bass [i.e., a more consonant interval] will clearly be a non-chord tone).  Another interesting case involves borrowed chords--bVI in a clearly-established major key is more consonant than the diatonic vi or diatonic ii7, etc., but will always sound somewhat foreign and connote the minor tonality (owing to the b3 and the b6-5 tendency). The Neapolitan chord in a minor key gives a little island of major, but it clearly sounds foreign to the key, especially in the older tunings.  The  historical derivations for the Np6 chord are from the minor iv chord, with the 5th raised to a m6.  This was a standard tactic in figured bass practice, in which a triad (minor iv) was always considered more consonant than a sixth chord (Np6).  Ergo, the Np6 was more dissonant than the minor iv; in addition, it required chromatic voice leading (b2-1-l.t.).  So there are a lot more factors than harmonic sonority in play.
>
> Some of you probably know Tenney's little book, A History of Consonance' and 'Dissonance' .  It's a bit superficial, but it does show nicely how perceptions of consonance and dissonance have changed over the centuries.
>
> Franklin
>
>
>
>
>
> Dr. Franklin Cox
> 1107 Xenia Ave.
> Yellow Springs, OH 45387
> (937) 767-1165
> franklincox@yahoo.com
>
> --- On Wed, 2/10/10, hpiinstruments <aaronhunt@...> wrote:
>
> From: hpiinstruments <aaronhunt@...>
> Subject: [tuning] Re: The point of temperament
> To: tuning@yahoogroups.com
> Date: Wednesday, February 10, 2010, 9:39 PM
>
>
>
> --- In tuning@yahoogroups. com, Michael
> <djtrancendance@ ...> wrote:
> > >"P.S. changing spectra to fit a tuning is an
> > > example of using a principle of harmonic
> > > correctness from JI."
> > How so? As I recall the equations Sethares
> >used were based on the minimum points in
> >roughness curves which cause overtones of
> >multiple tones in the scale to align the best
> >on average...nothing to do with JI-style periodicity.
> >Also, how can Sethares timbre-matching be
> >"harmonic correctness" if the timbre looks
> >nothing like the harmonic series so fundamental to JI?
>
> But that is making things much more complicated
> than necessary. Don't overlook the obvious:
>
> - JI intervals fit into a harmonic series
> - mapped spectral intervals fit into a warped spectrum
>
> The principle is exactly the same:
>
> - intervals : overtones
>
> You get your intervals from a system of overtones.
> In one case, the overtones are whole number multiples
> of a fundamental, in the other, they related to the
> fundamental by a mapping principle or formula
> applied to a scale.
>
> > Heck, even my own perspective that creating
> > an ideal scale involves minimizing root-tone
> > roughness via imitating 7TET and maximizing
> > "harmonic balance" by using ratios of 13/12
> > or lower to represent distances between
> > consecutive notes I don't think covers the
> > whole system.
>
> That's fine, but you seem to miss my point:
>
> - chain of pure fifths
> - JI intervals
> - ETs
>
> See how these relate to whatever you are doing,
> and you'll find the simple obviousness of whatever
> it is can be characterized as adaptations of the
> correctness or obviousness each of those things.
>
> > I'm convinced something that would cover the
> > entire gammut would explain
> > A) where consonance becomes dissonance
> > (roughness wise...for example with regard to
> > consecutive sine tones played in TET tunings)
> > B) where consonance becomes dissonance
> > (periodicity/ "JI" wise)
> > C) If a chord meets A and B (is consonant
> > according to A and B) yet somehow sounds
> > dissonant, why does it?
>
> All valid questions that can inform the creation
> of musical systems, but there is no need to get
> bogged down in such gory details that will
> never have general solutions in order to
> validate the simple premises I've stated.
>
> > BTW, where is that 30-page explanation link you
> > supposedly sent? I never received it...
>
> It is at the end of my first post.
>
> Yours,
> AAH
> =====
>
>

> Eb is apart from E by 25/24, whereas E and E+ are apart
> by 81/80. As to why we heed one and ignore the other, it
> is cultural. Traditional Thai music is based on pentatonic
> scales in 7-ET, where 25/24 vanishes. And presumably one
> day the Bach of xenharmony will arrive, and we will get a
> genre where 81/80 (or some other comma that vanishes in 12)
> becomes commonly heard as chromatic.
>
> -Carl
>

This is what I feel as well. And it's very interesting when you consider
that you can hear the diatonic scale in 7-et. I tend to hear I, ii, iii, IV,
V, vi, vii, and so on, with them all slightly blurring together - but I do
still tend to hear "majorness" and "minorness" in distinct chords. At first
I thought that this was a product of cultural bias, and in some way it might
be -- but is it really any different than us hearing 7-limit ratios in the
works of Ravel? Perhaps not.

This all brings me back to a question I asked weeks ago, about whether the
brain can perceive an interval two ways - at the same time. So perhaps when
I'm banging away with modal harmonies over the blues, I'm hearing 16/9, 9/5,
and 7/4 all smashed into one simultaneously. I'm not sure I'd be able to
hear the difference between 16/9 and 9/5 over the root directly if I tried,
and it would certainly be something occurring on a more subconscious and
intuitive level if so.

-Mike

>
>

Torsten wrote:

> Please excuse my ignorance,
> but could you perhaps expand this remark a bit?

If you find the 7th root of 50/3, you get one possible generator for meantone (i.e. 4 fifths equal to a major third + 2 octaves). If you find the 19th root of 18/5, you get one possible generator for miracle (i.e. 6 minor sixths equal to 7 fifths if I keep using the conventional interval names). If you use the 17th root of 72/5, you get one possible generator for orwell (i.e. 7 minor sixths equal to 3 twelfths). If you use the 15th root of 144/5, you get a possible generator for würschmidt (i.e. 8 major thirds equal to a fifth + 2 octaves). If you use the 19th root of 30, you get one possible generator for myna (i.e. 10 minor thirds equal to a fifth + 2 octaves). And, lo and behold, 31-EDO serves for all of them.

Petr

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I think they sound perfectly natural because, contra Marcel, our
> > brain doesn't analyze music in terms of JI. Our mind doesn't
> > recognize a tempered scale or some extra harmonic relation not
> > existing in its' JI version as some kind of unnatural perversion or
> > illusion even if tempered intervals gain their resonance from their
> > proximity to just intervals.
>
> Then what do our brains analyze music in terms of? It can't all just
> be arbitrary cultural conditioning.

No, that's not what I had in mind. I actually think that the
importance of cultural conditioning has been somewhat overstated.

Let me start by saying in what sense it is correct to say that we
hear frequency ratios, both integer and irrational. We hear frequency
ratios between sounds by having auditory experiences of pitches
separated by intervals so that there is a regular causal connection
between a frequency ratio and the type of experience it produces in
us. That is, the same frequency ratio always produces the same type
of interval experience in us no matter what the pitches are (this
somewhat breaks down at very high registers) and this regular
connection gives us the ability to perceive frequency ratios.

It is true that low-numbered integer ratios are perceived as
special with exactly harmonic sounds and this is explained by
psychoacoustic theories of consonance. But it is also true that this
breaks down for even slightly inharmonic sounds like piano tones.
That is, the maximally consonant ratios are not exactly at low-
numbered integer ratios but somewhere close.

Another sense of "hearing frequency ratios" must be also examined.
That is the sense that some irrational ratios are purportedly
perceived as or as substitutes of low-numbered integer ratios as if
our brains categorized intervals into classes defined by low-numbered
integer ratios. Interpreting this claim very charitably it is correct
in the sense that pitches played simultaneously produce the experience
of a root when they form an approximate harmonic series. Both the
frequency ratio 2:3 and a ratio close to it produce the same type of
root experience (a virtual pitch at 1) even if the experience is
stronger with 2:3. Only in that rather contorted sense we can be said
to hear a ratio of 2:3 when we hear a 12-equal fifth for example.

But that's it. I claim that this is where it stops. The hearing of
ratios doesn't carry further into the cognition of musical structures
like scales and chord progressions. That is, multiples and ratios of
ratios are already not perceived as being composed of ratios.
When we have been ear-trained to recognize a fifth and a fourth we
are not thereby able to recognize a whole tone or an octave as being
made of a fifth and a fourth. That is why a tempered comma pump
progression doesn't sound like an illusion or a perversion. When the
tonic chord is reached and it doesn't sound a syntonic comma off
the brain doesn't go "WTF just happened! Four 2:3s should make a
16:81, not a 1:5. Initiate a sensation of vertigo!" It doesn't
calculate the relations of frequency ratios further than the basic
first-order level. Why would it do that? What evolutionary reason
would there be for the existence of such a faculty. How would it help
in hearing speech sounds for example?

Kalle Aho

Dear colleagues,

as some of you probably know, IMEB in France calls for help for the second time. Please consider your signing the petition.

Daniel Forro

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

SECOND APPEAL FOR SUPPORT FOR IMEB
Addressed to Colleagues, Artists, the Public and Friends of IMEB from All Countries

www.supportforimeb.org

At the end of 2009, 2513 of you from 63 countries showed your support for IMEB, in danger of being closed by the Ministry of Culture. We are extremely grateful to you all for your efforts! This wave of protest was taken up and broadcast by many personal and institutional websites all over the world, and the protest was so strong that both print and electronic media passed on the information. But despite your magnificent show of solidarity, the Ministry still stands by its decision.
We see only one possible response: start a new campaign of support louder and with even more participants than the first.
Therefore, we, the members of the Support Committee for the IMEB, call on you once more to join this second protest, even more vigorously than before, either by writing yourself to the addresses you will find at the site www.supportforimeb.org , or by signing the petition you will find there. If you sign the petition at the website, it will automatically be sent with your signature to all the parties concerned.
You will find a report of the current situation along with additional information at the sites www.supportforimeb.org and www.imeb.net (under Support Committee). We must, by our common efforts and our joined voices from more than 60 different countries, succeed in saving the IMEB!

For the Support Committee :

Judy Klein
Gerald Bennett
Gonzalo Biffarella
Jean-Claude Risset
Nicola Sani

I wrote:

> e=c/b, f=a/f, g=e/b, h=d/b, i=g/b, j=b/f, k=j/f

That was a typo, there should be "f=a/e", of course.

Petr

Michael wrote:

> I was not talking about Pythagorean tuning, but about mean-tone...and I was talking
> about how a scale are generated, not how certain intervals in the scale are/were used composition-wise
> at the time the scale was derived.

I know you weren’t talking about that and I’m not saying you were. I’m just explaining that I can’t imagine how I could ever understand meantone without first understanding JI. And I was giving an example that if someone told me to make a temperament with octaves as periods and fifths as generators, I would obviously go for Pythagorean and not bother with tempering at all because I wouldn’t treat C-E as a consonant interval (if I had never heard a larger part of the harmonic series) but rather as an unstable „ditone“ which should be resolved into a stable interval like a fourth or a fifth. Or otherwise, I just don’t know what you meant.

> I am interested in how you found out how to do miracle temperament via mean-tone,
> since miracle involves generation via chaining of seconds and, at first glance,
> you would think they have little in common (plus I am admittedly interested in the art
> of purifying seconds and minor-seconds since so many musicians consider them
> as a-tonal for use in chords).

Well, there are more possible methods of „discovering“ temperaments. Let’s start with the meantone example. Suppose I want to get a temperament approximating 3:4:5:6. Either I could find the factor of 81/80 and break it into two complementary prime exponent pairs with the target period of 2/1 (which tells me that the interval approximating 5/1 is 4 times larger than the one approximating 3/2), which eventually gives me a fifth as a generator (or a fourth if I prefer smaller intervals). Or I could take the three factors (a=4/3, b=5/4, c=6/5) and split them by each other as many times as I want (d=a/c, e=b/d, f=c/e, g=e/d), which gives me a scale of five 10/9s, two 16/15s, and three 81/80s. Then I‘ll temper out the smallest of the resulting intervals by widening the larger ones by a desired fraction of the small one, which gives me the meantone diatonic scale. Since I know how many of the three intervals I need to get a 4/3, 5/4, or 7/6, this allows me to find other intervals as well and thus possibly describe the meantone mapping. The important thing to note here is that both of these methods can reveal many different temperaments even if I leave the target primes at 2,3,5 (for the former method) or if I leave the target chord at 3:4:5:6 (for the latter).

Now to miracle. One method is to first temper out (let’s pick up something more obvious in miracle) 1029/1024 by breaking it into two complementary prime exponent pairs (which tells me that the interval approximating 3/2 is 3 times larger than the one approximating 8/7), then temper out 225/224 by breaking it into three prime exponent pairs (which tells me that the interval approximating 16/15 also approximates 15/14 and therefore stacking two of them approximates 8/7). Another method is to begin with a 7-limit chord like 5:7:8:12:14 (i.e. a=7/5, b=8/7, c=3/2, d=7/6) and split the intervals by each other as many times as I want while already thinking ahead of where I could get similar interval sizes (e=c/b, f=a/f, g=e/b, h=d/b, i=g/b, j=b/f, k=j/f), which gives me a scale spanning a total range of 14/5 where one octave contains ten 16/15s, one 49/48, one 1029/1024, and five 225/224s. Since both 1029/1024 and 225/224 are farily small, I can temper them out by widening the two larger intervals by a desired fraction of these, which gives me the 11-tone miracle scale. And again, since I know how many occurrences of the four original intervals I need to get a 7/5, 8/7, 3/2 or 7/6, this allows me to get other intervals as well, which eventually describes the possible mapping of miracle. Obviously, some intervals can’t be mapped with only 11 tones (for example, for a minor third, you need at least 13 generators to map 12/5, which requires at least 14 tones). However, this can easily be resolved by splitting the minor second into 49/48 and 256/245 (i.e. l=f/h), which gives me the 21-tone „blackjack“ and allows me to map a full part of the harmonic series from 1 to 10 and also such intervals like the chroma of 25/24.

> what are some temperaments you know (other than Miracle)
> which focus on optimizing intervals other than 3rds, 4ths, and 5ths?

#1. Personally the only tuning that I think would belong to this category is Bohlen-Pierce rather than miracle.

#2. Even though this tuning includes, among other things, major thirds, I think an interesting example may be a temperament I made in March 2008 which uses a period of 2/1 and a generator equal to the 13th root of 130 (or its octave inversion which is only about half of a cent away from 11/8). Its main target is to approximate chords like 8:10:11:13:16 but this is a 2D tuning which is not the 3D temperament I was talking about earlier. And then, there’s the „triharmonic scale“ whose description you can find in message #75311 and whose primary target approximation is 4:7:10:13:16. And then there’s an octave-reduced version of that where the primary approximation is 4:5:7:10:13 (I’ve made some music in this as well).

> Isn't this basically scales that involves the chaining of four note chords (and not just tetra-chords)?

You’re mixing up things from different contexts. What I meant was that if you temper out 81/80 within a target chord of 3:4:5:6 and you get a fifth as the resulting generator, you may better understand why you can easily split the meantone diatonic scale into two tetrachords like „C-D-E-F, G-A-B-C“. Similarly, if you temper out 245/243 within a target chord of 3:5:7:9 and you get ~440 cents as the resulting generator, you may better understand why you can easily split the „BP diatonic“ scale into two pentachords (where each pentachord will span a tempered 5/3 instead of 4/3).

> Well let's start with this: how did you learn BP from meantone?

Okay, I’ll give the 2D version of BP as an example. Again, let’s just apply the two methods I previously applied to meantone. The way I was doing it is to set a target chord of 3:5:7:9 instead of 3:4:5:6 (i.e. a=5/3, b=7/5, c=9/7) and splitting the intervals by each other as many times as I wish (d=a/c, e=b/d, f=d/c), which gives me a scale of four 9/7s, one 27/25, and two 245/243s. Then I simply temper out the smallest interval by widening the larger ones by a desired fraction of that. Another method is to take the factor of 245/243 and break it into two complementary prime exponent pairs with a target period of 3/1, which eventually gives me a tempered 9/7 as the resulting generator.

> So far I have the impression that the common thread is chaining chords together...which I think is
> a smart way to design scales, but doesn't seem to me to have its roots in music history.

Why do you think so?

> No, the point of similarity to me has to do with using either a chain of 5ths
> or approximated 5ths to generate a scale.

I’ve already said that even if you keep the period at 2/1 and even if you keep the approximants at 3/2 and 5/4, you can get many other generator sizes than fifths and therefore many possible mappings of the approximated intervals, which in turn offers you new harmonic progressions you might otherwise never think of.

> 1) What temperaments do you know which are not based on some sort of "chain of x
> interval" algorithm or a close approximation of one?

If we don’t want a „chain of something“, then why bother with tempering? Look at Partch’s tonality diamonds or my „epiworld“ and „epi2“ scales and you’ll know what I mean. And if we DO want to temper something, don’t forget tempering can also be linear, not only exponential. So you could, for example, take relative frequencies of 8:9:10:11:12:13:14 and change the differences to get 7.875:8.75:9.625:10.5:11.375:12.25:13.125:14, which changes the 7/4 into 16/9 and therefore „linearly“ tempers out 64/63. If I’m not mistaken, this is exactly what Mike Battaglia was doing when he shrunk a chord of 4:5:6:7:8:9:10:11 so much that the 11/4 turned into an 8/3.

> 2) How does mean-tone theory apply to those?

There’s tempering in both cases, although it’s exponential in one case and linear in the other.

> Now that does sound really interesting...my knowledge honestly probably wasn't up to stuff at the time
> you posted those. I'm a huge fan of scales that can manage step sizes down to about 11/10 (actually
> "all the way" up to closeness of about 12/11) and still sound fairly resolved. I'm also great believer in any
> sort of experiment that uses harmonics from the harmonic series up to 20 yet spaces them in a way
> that controls tonal roughness reasonably. I will admit, from what I've heard of 2-tone MOS that theory of
> scale generation seems a bit limited to me...going 3D (AKA hyper-MOS, right?) sounds quite interesting.

>

> If you can put together some links to posts as to how you derived such 3D temperaments, I'd be happy
> to read about them. I think I've run into a few simply by stacking 4-note chords using some fairly high-limit
> ratios, but admittedly did so by experimentation rather than knowing the inner workings
> of how to "run a 3D temperament generator".

In message #84266, you can find descriptions for three of the temperaments -- i.e. the octave-reduced variant of the „triharmonic“ tuning, then the 2D tuning from March 2008 (which i was privately calling „emka“ because of the prime mapping order), and then the 3D tuning from April last year. First, the target primes are listed. Then, the mapping is described in terms of period and generator counts, where the period is meant to be 2/1. And finally, the generator size in cents is given (or „sizes“ in the 3D case).

> Well I said "with Magic temperament, for example, concentrating on keeping the purity of thirds"...I was
> trying to say Magic is fairly common and purifies thirds while other relatively common tunings (namely
> mean-tone) purify 5ths...I didn't say or mean "Magic purifies 3rds and fifths". It makes perfect sense to me
> that Magic purifies thirds at the expense of 5ths.

#1. Do really both of us mean the same thing when saying „magic“?

#2. Why do you think that „magic is fairly common“?

Petr

>"Then what do our brains analyze music in terms of? It can't all just
be arbitrary cultural conditioning."

So far I've run into these things that challenge how our brain analyzes music
A) Lack of periodicity. Perhaps the most obvious one. I've found the period in a chord must be fairly short, but that shortness is in fact still much longer and more flexible than in ratios like 8:7. As the period gets shorter at higher octaves, the requirement for the critical band of hearing becomes more stringent and less periodic ratios and even noisey instruments like cymbals become more legal. I find that periodicity relates to the curve of the critical band no coincidence.

My ears tell me its not as strict a requirement as people think it is IE there's no need for strict JI and only the lowest limits...up to 11-limit really isn't that bad. For example, chords like 9:11:18 don't sound too bad so long as the closest intervals in the chord are far enough to avoid excessive...

B) Roughness. Even blind testing with pure sine waves lets me know at a certain point (I've found it's around 11/10) notes become so close the ears have trouble separating them and beating (or in formal terms "difference tones") become too prevalent to easily digest. Also a personal opinion: I do think there is such a thing as too much periodicity buzz where the brain starts to mind, against starting at around 11/10 and close intervals. Of course more roughness and lack of periodicity is introduced when you add

C) Non-matching timbres. Sethares has the solution to solving that one fairly well covered: ideally overtones must match or at least merge toward root tones. I've found a lot of times when people complain a "semi-periodic" scale (esp. 11-limit or 13-limit) sounds bad because of lack of periodicity, the complaint vanishes once matching timbres are applied.

I also have strong suspicions that, rather than simply focussing on "tonality" and finding a root harmonic series pitch for a chord, the brain focuses on periodicity (which may or may not point so obviously to a single root tone) and has problems when there is

D) Lack of obvious/"generated" patterns within the root tones of the scale. If I take a scale generated by 1+(1/sqrt(2)) ^x and start detuning notes even slightly from it the rhythm formed by the difference tones seems more chaotic.
Sure, this sort of alignment applies for things like TET scales as countless people have suspected. However, I'm pretty sure it has an effect on any scale formed by a "generator": the brain likes root tones to follow or at least merge near a single generator if some sort...just as it likes to follow a curve in visual art.

I get a lot of heat on this list, it seems, because I don't tie everything in music related to the sense of "resolve" down to simple A) and the concept of tonality. I'm a firm believer that the is much more to explore related to making music easier for the brain to digest yet more complex and flexible in its own right.

Those of you who also believe that it's about more than periodicity and tonality please show your hands. :-)

Petr, thanks for this. I will give this a read as soon as I get a spare
minute. You obviously have a very solid paradigm for microtonal music and
music in general, and I look forward to the read.

-Mike

On Wed, Feb 10, 2010 at 12:14 PM, Petr Parízek <p.parizek@...> wrote:

>
>
> Mike's question about microtonal music has inspired me to write a longer
> piece of text. At first, I intended to include it right in the body of the
> message. But then I thought it would be better to have the document stored
> separately.
> For people who are familiar with various 2D temperaments, maybe they find
> some statements too "introductory". But I'm not sure how to explain my view
> in an understandable way without touching on these things.
> Anyway, whether you find it useful to read or not, you can find it as an
> RTF document in this folder:
> /tuning/files/PetrParizek
>
> Petr
>
>
>
>

Mike B>"There was actually a person here who said that chords
didn't sound GOOD if they didn't have a half step in them - that they
were either "crunchy" or "soggy", if I remember."

To be honest, I like them for personal listening and think they open the door to all sorts of fresh new 5-tone chords, only I don't think I could ever get away with them for a full song. Lord knows I've tried...but every time I got a large number of the people saying "something is awfully out of tune" or even "dude, learn your music theory first". :-P

>"Seriously man, I'm not sure what your vendetta against half steps is, but they sound awesome when used in harmonies."
It's not my "vendetta" so to speak...I'm just looking at how much the average musician uses any intervals nearing the half-step and trying to think of ways to get them to use it more. Neil Haverstick once contacted me and said he thought a major problem with microtonallity is it needs to be displayed in a fashion that it's attractive to the average professional musician from a compositional standpoint. And I agree. If there were one quick way to get musicians away from the monotony of standard chords quickly, it would be to convince them to use such intervals. I've never seen any sort of musicians (including even my brother who's a professional jazz guitarist) who compose much with semi-tone chords, if at all.

I just figure if we micro-tonalists want anything like a minor-second to become commonplace for use among many of the non-avant-garde musicians we love to hear, it's probably worth it to try and think up a more resolved sounding alternative to the semitone.

>"G E F B C G A - there's a great mixolydian voicing that uses half steps.
Gb D Eb A Bb F - another great one for Gb aug #9 that I just came up
with off the top of my head.
C E F A - a simple maj7 chord in an inversion."

See my experiment on "tone clustering". I'm currently "messing around" trying to figure out just how many half-steps one can fit into a chord before they become so jumbled they come across as in-audible.
Out of your chords...

C E F A is actually a chord clear enough sounding for most "standard" musicians to actually just want to pick up and use. :-)
Do you have any more 4-note chords using the semitone with nearly as good or better consonance?

G E F B C G A is very cool but IMVHO a bit too dissonant and avant-garde sounding to get most musicians to accept and actually use. It's in chords like that where I'm tempted to use intervals like 11/10 or 12/11 in place of the "semi-tone" to give it that extra edge that would make so many more musicians open to using it.

Just wondering...could you make a list of, in your opinion, the best 5-tone-per-octave chords utilizing the half-step/semi-tone? I'd really appreciate it.
I'm also tempted to see if I can "adapt" those chords to fit an "extended semi-tone" scale.

_,_._,___

Daniel Forro wrote :

Dear colleagues,

as some of you probably know, IMEB in France calls for help for the
second time. Please consider your signing the petition.

Daniel Forro

----------------------------------------------------------
SECOND APPEAL FOR SUPPORT FOR IMEB
Addressed to Colleagues, Artists, the Public and Friends of IMEB from
All Countries

www.supportforimeb.org

Very good initiative, Daniel -
Sorry that I did not thought about relaying it myself to the TL.
But IMEB is (I hope I don't have to say was) one the last alternative and motivated international centers
we have in France for high-level electroacoustic music.
And under our actual president, the French Ministery of Culture is dissolving every place of unconventionnal musical creation.
Thanks to sign !
- - - - - - - - - - - -
Jacques

>"Everything you just said is exactly why I think the word "consonance"
should be considered a profanity around here. There are so many
meanings for the word that roughly 2/3 of conversations about it
degenerate into semantic disagreements within 10 or so posts."
Well, what term do you suggest? "Chordal resolve"?

>"- Critical band factors, roughness, beating"
Definitely, agreed. :-)

>"- Whether you've been writing a pleasant song in major the whole time
and then throw 4:5:6:7:9:11 in over the I chord out of nowhere"

Right, but that's compositional technique, not the art of making the scale itself more consonant.
The problem again, is I was discussing consonance with respect to tunings while Franklin was discussing it with respect to compositional technique.
Do we have to level it down between "compositional consonance" vs. "mathematical consonance"? Or what alternative term do you think would make it specific enough?

>"- Whether the high priest at your monestary thinks that the tritone is
the devil's interval"
>"- Whether a certain chord reminds you of that one time your girlfriend
broke up with you while you were doing your taxes"
Irrelevant, but still quite funny. :-D

>"I don't think a single qualitative dimension of "consonance" can
really describe whether random listener X will end up "liking" the
sound of a chord at the end of the day."

True, but look at the chord structures in, say, advanced jazz vs. pop and their popularity. Obviously, this is when jazz is actually the more technical and thorough art.

Point is...if we ever want lots of musicians to take micro-tonality seriously or most professional musicians to even give it a nod...we need to show them some scale with chords they could never do before and give them non-embarrassing levels of resolve (aka consonance) that they wouldn't be embarrassed to play live.
Then I figure we can worry about things like how the composition around those chords can evolve. Guaranteed virtually no professional composers are likely to care about switching to a scale where you maximize the purity of his third by a mere 10 cents...and they will definitely run if most chords in your scale sound like sour types of 13ths. And that's regardless of if they are composers who use context very well IE know not to throw a sudden chord with much more/less resolve suddenly into a piece without transition or warning.

Most people aren't going to recognize micro-tonality until micro-tonality takes their needs more seriously.

>"And Michael Sheiman for some reason seems to care in the order of #3, #2, and #1."

I did not insist on the order being in order of importance in the first place. I simply said those were some of the many things that can be used to improve "mathematical" consonance and "even" convince some professional musicians to take micro-tonality more seriously. Granted I put periodicity first...but only because I've heard so many people on the list talk about when they discuss "consonance".

>"In my view, just disregarding all that to pretend that a single
dimension of "consonance""

Single dimension? Shoot, I mentioned 5...and hinted that there well might be more.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I wrote:
> > That said, we couldn't get our stuff together enough to
> > craft a paper -- we tried, but it died amid constant
> > bickering over minutia. Perhaps that's to do with the
> > nature of mailing lists and long-distance collaboration.
> > Or perhaps we're all just jerks. So anyway, I'm very glad
> > these guys rose and did the exceptional job they did to
> > move these things closer to reality. And that includes
> > Jim, bless him.
>
> To be fair, several of us were sent drafts offlist, but we
> were asked to keep quiet, presumably because of a publishing
> embargo. And I suppose had the authors engaged on
> tuning-math, they would have risked getting dragged down
> into the bickering. So be it. -Carl
>

Hi all, just to clarify a few aspects about The Viking, TransFormSynth, and 2032, they are intended to be complementary - the first is an additive-subtractive synth, TFS is an analysis-resynthesis synth, the latter is a modal synth.

It is our intention to map MIDI note and channel number to generator in the manner shown at the bottom of this email (I think this has been done in TFS - I may be wrong), it has not yet been done in Viking, 2032 is still very much in alpha stage. There is absolutely no intention to limit this to just 12 different tones.

All of these software have been made available free, so I suppose development is a bit slow, but we are moving ahead (slowly).

Also, you may be interested in Hex - a microtonal MIDI sequencer designed to interface with the above synths. It's still in alpha stage, but briefly, any linear mapping from a 2-D tuning to a 2-D button lattice has an "isotone" axis (a series of parallel lines) that connects the centres of "buttons" with the same pitch. As the ratio of the two generators' tunings changes, the angle of the isotone rotates. This means that if a button lattice is rotated so as to keep the isotone horizontal, it can be used as a replacement for the standard piano roll interface, but can be used for any 2-D tuning. If you want more info, email me and I can send a draft paper that explains this properly.

Anyway, they can all be downloaded from www.dynamictonality.com.

Here's the MIDI mapping bumpf....

Both 2032 and Hex map MIDI channel 1 note numbers to in such a way as to give a standard meantone piano note-selection (i.e., C, C-sharp, D, E-flat, E, F, F-sharp, G, G-sharp, A, B-flat, B), whilst MIDI channel 2 note numbers are mapped to 12-TET enharmonic equivalents twelve fifths below (i.e., D-double flat, D-flat, E-double flat, F-double flat, F-flat, G-double flat, G-flat, A-double flat, A-flat, B-double flat, C-double flat, C-flat), and MIDI channel 3 to 12-TET enharmonic equivalents twelve fifths above (i.e., B-sharp, B-double sharp, C-double sharp, D-sharp, D-double sharp, E-sharp, E-double sharp, F-double sharp, F-triple sharp, G-double sharp, A-sharp, A-double sharp). This means that when playing in 12-TET, the channel number has no effect, but when playing in another relatively familiar tuning, such as meantone or Pythagorean, where enharmonically equivalent notes no longer have the same frequency, the user can choose between them simply by changing MIDI channel number. For example, D-sharp can be represented by MIDI note number 63, MIDI channel 1; whereas, E-flat can be represented by MIDI note number 63, MIDI channel 2.

In this way, 2032 maintains backwards compatibility with traditional hardware and software MIDI controllers and sequencers, whilst still enabling the new feature of being able to differentiate between the tunings of sharps and flats in certain tunings. The mapping also means that Hex can be used to control conventional 12-TET synthesizers.

For non-syntonic continua - the mapping between MIDI note number/channel and generators is the same...

Andy Milne

Chris,

Since the Silver scale seems to be doing so well (at least in your hands), you may want to try this new 5-tone version

1/1
13/12 (approximates 1.07106)
15/12 (approximates 1.24264)
17/12 (approximates 1.4142135...silver-Tave)
20/12 or 5/3 (approximates1.1715728*1.414)
2/1 (approximates 1.4142135^2...double Silver-Tave)

AKA

12:13:15:17:20:24

My latest ventures into periodicity seem to show the 18th harmonic partial is where periodicity fades into lack of resolve/"dissonance" and the ratio 12/11 is around where the mind start having serious trouble handling beating/roughness. So here's a new version of the Silver scale which de-tunes certain notes a bit so all the possible dyads meet those standards you may want to try.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
However..............

If you want more dissonance (or at least what I perceived as dissonance), you can always add 18/12 (approximates 1.4142135 * 1.1715728) and "grind" it against the nearby 17/12
OR
add 21/12 or 7/4 (approximates 1.4142135 * 1.24264)
OR
add 14/12 (approximates 1.4142135 * 1.07106) for some extra periodicity buzz.

Adding all of these would result in a "just-ified" yet fairly dissonance-capable 8-tone Silver Scale

12:13:14:15:17:18:20:21:24

I just figure hey....if you're going to make dissonance it might as well be somewhat periodic.

-Michael

> Another sense of "hearing frequency ratios" must be also examined.
> That is the sense that some irrational ratios are purportedly
> perceived as or as substitutes of low-numbered integer ratios as if
> our brains categorized intervals into classes defined by low-numbered
> integer ratios...
//snip
> But that's it. I claim that this is where it stops. The hearing of
> ratios doesn't carry further into the cognition of musical structures
> like scales and chord progressions.

Why not scales? If come up with a simple 3-note scale that's just 4:5:6, and
I play each note separately - C, E, G, E, C, E, G, E, C - does your brain
not still put it together as a major chord? Or, if I play an Eb chord, and
then go to just a C-G drone -- you will still hear some minor quality to it.

> That is, multiples and ratios of
> ratios are already not perceived as being composed of ratios.
> When we have been ear-trained to recognize a fifth and a fourth we
> are not thereby able to recognize a whole tone or an octave as being
> made of a fifth and a fourth.

As for what you said - that we don't hear an octave as a fifth + a fourth -
this is true, but I do think that to some extent we can hear a major 7th as
a 3rd + a fifth. And in the example I showed above:
C-E-F#-B-D#
If that C-D# were played in isolation, I think it'd probably sound like 6/5.
However - when the other notes are put in, the cracks are filled in, and the
brain gets an idea of how to travel from C to D#.

> That is why a tempered comma pump
> progression doesn't sound like an illusion or a perversion. When the
> tonic chord is reached and it doesn't sound a syntonic comma off
> the brain doesn't go "WTF just happened! Four 2:3s should make a
> 16:81, not a 1:5. Initiate a sensation of vertigo!"

Hahahaha! Well, it should. I think I'll start making my own artificial
vertigo so my brain can catch up.

Despite the examples I wrote above - what you said here is obviously right
as well. I'm not sure where to draw the line between how the brain can
"remember" intervals and how it can't.

Obviously the brain can remember previous intervals to some extent, or else
all chord progressions would sound the same, which is emotionless and dull.

> It doesn't
> calculate the relations of frequency ratios further than the basic
> first-order level. Why would it do that? What evolutionary reason
> would there be for the existence of such a faculty. How would it help
> in hearing speech sounds for example?

This is related to an experiment that I think you should try: Go to an
organ, and set the drawbars so that the only harmonics coming out are the
fundamental and 3/1. Turn the fundamental so it's down low, but still there.
Start playing happy birthday or something easy. Meanwhile, after playing it
through once or twice, start turning the fundamental down until it is
completely silent, and only 3/1 remains.

If you do it right, you can actually "trick" your brain into perceiving the
phantom 1/1, even though the only thing there is a 3/1 sinusoid. It helps to
keep imagining the original "happy birthday" song in the original key while
you do this. You'll find you can very easily "flip your brain" around to
just hear the 3/1 as a new 1/1, and once you do that, it's hard to go back.

This I think is related to the source separation and identification
processes going on in your brain. The concept of finding "different harmonic
spectra" for the wash of sound coming in is inherently tied in with notions
of source separation anyway. Once your brain has a harmonic spectrum picked
out, it holds onto it for a second.

-Mike

Hello Michael

Are there any mp3 links to music played in your scales?

I am especially interested in consonance.

Ta Steve
 

________________________________
From: Michael <djtrancendance@...>
To: tuning@yahoogroups.com
Sent: Sat, 13 February, 2010 8:06:07 AM
Subject: [tuning] Silver scale revisited...apparently enjoyed by a handful of people, if just that

 
Chris,

Since the Silver scale seems to be doing so well (at least in your hands), you may want to try this new 5-tone version

1/1
13/12 (approximates 1.07106)
15/12 (approximates 1.24264)
17/12                                                             (approximates 1.4142135... silver-Tave)
20/12 or 5/3 (approximates1. 1715728*1. 414)
2/1                                                                 (approximates 1.4142135^2. ..double Silver-Tave)

AKA

12:13:15:17: 20:24

      My latest ventures into periodicity seem to show the 18th harmonic partial is where periodicity fades into lack of resolve/"dissonance " and the ratio 12/11 is around where the mind start having serious trouble handling beating/roughness.  So here's a new version of the Silver scale which de-tunes certain notes a bit so all the possible dyads meet those standards you may want to try.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
  However..... .........

    If you want more dissonance (or at least what I perceived as dissonance), you can always add 18/12 (approximates 1.4142135 * 1.1715728)  and "grind" it against the nearby 17/12
OR
add 21/12 or 7/4 (approximates 1.4142135 * 1.24264)
OR
add 14/12 (approximates 1.4142135 * 1.07106) for some extra periodicity buzz. 

Adding all of these would result in a "just-ified" yet fairly dissonance-capable 8-tone Silver Scale

12:13:14:15: 17:18:20: 21:24

 I just figure hey....if you're going to make dissonance it might as well be somewhat periodic.

-Michael

Hello Michael

Just to clarify:
The TransFormSynth is NOT limited to 12 tones per octave. ONLY the Viking and 2032 are, and this is an artifact of the fact that they are designed in synthmaker. There are plans to change the layout to an isomorphic layout, I assume when time allows.

Until that happens, not only do I not recommend them, but I recommend *not* using them, because they use a piano layout which hides useful information about what is actually happening when changing the tuning.

Basically, in these two synths, only one of two enharmonic equivalents can be chosen to occupy a space on the keyboard and so when the tuning is changed you only have one or the other. This is not the case for the TFS, which has a different location for each enharmonic equivalent as shown in that above diagram.

If instead of The Viking or 2032 one tried the TFS, one would find that one would indeed have more than 12 tones per octave available, and they would be in this layout here:

http://en.wikipedia.org/wiki/Wicki-Hayden_note_layout

Notice the different locations of each enharmonic equivalent in 12-edo.

The interesting thing is that, as one progresses along the beta chain (or stacks of fifths), the pitches reached become less and less tonally relevant to a given tonic. As it turns out, only about 19 pitches are ever tonally relevant to a given tonic, these being the tonic itself and the first nine stacks of the generator (or fifth) above and below that tonic. So, in 31-equal divisions of the octave with a generator size of about 697 cents, only 19 of the generated 31 tones would be tonally useful at one given time, and those are the pitches that are mapped to the wicki/hayden isomorphic layout that the TFS uses.

The intent for the Thummer was to provide only these 19 pitches at once and then provide a function for modulation that would then transpose the instrument whenever a key change (a change in tonic) occurred. The instrument would then contain the 19 pitches relevant to the new tonic.

This is comparable to how in traditional notation, when playing with a tonic C, one never ever saw a D double sharp unless there was some serious modulation beforehand. The tonal function of a doubly augmented second is not useful in common practice tonal music.

So, no matter the tuning, only (about) the first nine generated pitches above and below your tonic and their octave equivalents are tonally useful to that given tonic. Sometimes, like with 5-,7-,12-, and 17-edo, there is overlapping of pitch within even these 19 harmonic functions, sometimes the overlapping occurs within a still relatively small number of stacks larger than 19 like with 31-, 43-, or 53-edo, and sometimes the overlapping does not occur for a very long time with the beta generators in between all of our generally recognized syntonic equal divisions of the octave.
I did a small analysis of tonal function across the syntonic temperament and blogged about it here:

http://xenharmonic.ning.com/profiles/blogs/harmonicdiatonic-function

If you want a little more depth on the matter, I have an unfinished powerpoint presentation that may be at least somewhat useful. You can find it here:
http://www.slideshare.net/JlMoriart/fundamentalsofmusic112909
The applicable information to this discussion starts on about slide 10.

Let me know if I'm speaking gibberish!

John M

I hate to be a pain...

is there an easy way to put this into scala?

12:13:14:15:17:18:20:21:24

Thanks,

Chris

On Fri, Feb 12, 2010 at 5:06 PM, Michael <djtrancendance@...> wrote:

>
>
> Chris,
>
> Since the Silver scale seems to be doing so well (at least in your hands),
> you may want to try this new 5-tone version
>
> 1/1
> 13/12 (approximates 1.07106)
> 15/12 (approximates 1.24264)
> 17/12
> (approximates 1.4142135...silver-Tave)
> 20/12 or 5/3 (approximates1.1715728*1.414)
> 2/1
> (approximates 1.4142135^2...double Silver-Tave)
>
> AKA
>
> 12:13:15:17:20:24
>
> My latest ventures into periodicity seem to show the 18th harmonic
> partial is where periodicity fades into lack of resolve/"dissonance" and the
> ratio 12/11 is around where the mind start having serious trouble handling
> beating/roughness. So here's a new version of the Silver scale which
> de-tunes certain notes a bit so all the possible dyads meet those standards
> you may want to try.
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> However..............
>
> If you want more dissonance (or at least what I perceived as
> dissonance), you can always add 18/12 (approximates 1.4142135 * 1.1715728)
> and "grind" it against the nearby 17/12
> OR
> add 21/12 or 7/4 (approximates 1.4142135 * 1.24264)
> OR
> add 14/12 (approximates 1.4142135 * 1.07106) for some extra periodicity
> buzz.
>
> Adding all of these would result in a "just-ified" yet fairly
> dissonance-capable 8-tone Silver Scale
>
> 12:13:14:15:17:18:20:21:24
>
> I just figure hey....if you're going to make dissonance it might as well
> be somewhat periodic.
>
> -Michael
>
>

Dear Petr,

On 10.02.2010, at 17:14, Petr Parízek wrote:
> you find it useful to read or not, you can find it as an RTF
> document in this folder:
> /tuning/files/PetrParizek

Thank you for this text.

Quote from text
> 12-EDO seems to do "the least harm" to the original Pythagorean
> tuning -- if I'm not mistaken, the next closest is 53-EDO.

Minor issue: 41-EDO closely approximates Pythagorean tuning. A 41-EDO
fifths is +0.48 cent too large.

> thirds determine what's called "tonal gender" in Czech (i.e.
> whether a triad is major or minor -- is there really no English
> translation for that?).

Chord quality or chord type?

Thanks again.

Best,
Torsten

Bon matin, Jacques,

if even France which was well known for good support of the art from the side of state, tries to narrow or cut money pipelines, it must be really crisis. Or bad politicians. Or both. We should do our best to save such institutions.

Daniel F

On 13 Feb 2010, at 4:20 AM, Jacques Dudon wrote:

>
>
> Daniel Forro wrote :
>
> Dear colleagues,
>
> as some of you probably know, IMEB in France calls for help for the
> second time. Please consider your signing the petition.
>
> Daniel Forro
>
> ----------------------------------------------------------
> SECOND APPEAL FOR SUPPORT FOR IMEB
> Addressed to Colleagues, Artists, the Public and Friends of IMEB from
> All Countries
>
> www.supportforimeb.org
>
>
> Very good initiative, Daniel -
> Sorry that I did not thought about relaying it myself to the TL.
> But IMEB is (I hope I don't have to say was) one the last > alternative and motivated international centers
> we have in France for high-level electroacoustic music.
> And under our actual president, the French Ministery of Culture is > dissolving every place of unconventionnal musical creation.
> Thanks to sign !
> - - - - - - - - - - - -
> Jacques

Petr,

That is a great explanation!! I learned a lot from it - though I'm still a
tuning novice.

Where can I hear

-- like those in my "Run Down The Whistle" or "Among Other Things" or
"Dinepome's Adventure".

Thanks,

Chris

On Fri, Feb 12, 2010 at 6:55 AM, Mike Battaglia <battaglia01@...>wrote:

>
>
> Petr, thanks for this. I will give this a read as soon as I get a spare
> minute. You obviously have a very solid paradigm for microtonal music and
> music in general, and I look forward to the read.
>
> -Mike
>
>
> On Wed, Feb 10, 2010 at 12:14 PM, Petr Parízek <p.parizek@...>wrote:
>
>>
>>
>> Mike's question about microtonal music has inspired me to write a longer
>> piece of text. At first, I intended to include it right in the body of the
>> message. But then I thought it would be better to have the document stored
>> separately.
>> For people who are familiar with various 2D temperaments, maybe they find
>> some statements too "introductory". But I'm not sure how to explain my view
>> in an understandable way without touching on these things.
>> Anyway, whether you find it useful to read or not, you can find it as an
>> RTF document in this folder:
>> /tuning/files/PetrParizek
>>
>> Petr
>>
>>
>>
>
>
>

Chris,
To put this ("JI Silver Scale") all into Scala simply input the following values into scala after selecting "new scale" type in
13/12,14/12,15/12,17/12,18/12, 20/12, 21/12
(with the commas to indicate the separation of the ratios).

Scala will automatically reduce the fractions for you.
Note how the 12:13:14:15: 17:18:20: 21:24 notation relates to the above fractions, only scala creates the 24/12 Silver double octave and 12/12 root tone for you.

________________________________
From: Chris Vaisvil <chrisvaisvil@...>
To: tuning@yahoogroups.com
Sent: Fri, February 12, 2010 6:00:27 PM
Subject: Re: [tuning] Silver scale revisited...apparently enjoyed by a handful of people, if just that

I hate to be a pain...

is there an easy way to put this into scala?

12:13:14:15: 17:18:20: 21:24

Thanks,

Chris

--- In tuning@yahoogroups.com, "jlmoriart" wrote:
>
> Just to clarify:
> The TransFormSynth is NOT limited to 12 tones per
> octave. ONLY the Viking and 2032 are, and this is an
> artifact of the fact that they are designed in synthmaker.
> There are plans to change the layout to an isomorphic
> layout, I assume when time allows.

Hi John.

Since in a previous post I went on about these programs
somehow limiting things to 12 tones per octave, I'm
answering your post so that I can stand corrected. But,
I'm not sure what you say about The Viking is correct, as
The Viking appears to be able to produce more than
12-tones per octave. I was able to get it to do 19ET;
it's just that the keyboard mapping is all screwed up.
No matter...

I'd like to point out a few things in what you say here
in your post which confirm some points I made before:

> If instead of The Viking or 2032 one tried the TFS,
> one would find that one would indeed have more
> than 12 tones per octave available, and they would
> be in this layout here:
>
> http://en.wikipedia.org/wiki/Wicki-Hayden_note_layout
>
> Notice the different locations of each enharmonic
> equivalent in 12-edo.
>
> The interesting thing is that, as one progresses
> along the beta chain (or stacks of fifths), the pitches
> reached become less and less tonally relevant to a
> given tonic.
>
> As it turns out, only about 19 pitches are
> ever tonally relevant to a given tonic, these being the
> tonic itself and the first nine stacks of the generator
> (or fifth) above and below that tonic.

This is an attitude, not a fact. "Tonally relevant"
according to whom, under what criteria? This is what I
was talking about earlier. To prove this premise suspect,
one need only to compose some music using those
pitches that are excluded, showing how relevant those
excluded pitches can be.

> So, in 31-equal divisions of the octave with a
> generator size of about 697 cents, only 19 of the
> generated 31 tones would be tonally useful at one
> given time, and those are the pitches that are
> mapped to the wicki/hayden isomorphic layout that
> the TFS uses.

This is the bias inherent within the approach
that's being taken with the Wicki/Hayden layout.
The approach begins with an assumption of privileged
subsets, based on a premise of tonal centricity. So
from scales having large numbers of pitches, the only
pitches anyone can use are those subsets that are
mapped to the keys for them.

> The intent for the Thummer was to provide only
> these 19 pitches at once and then provide a function
> for modulation that would then transpose the
> instrument whenever a key change (a change in
> tonic) occurred. The instrument would then contain
> the 19 pitches relevant to the new tonic.

Again, the exclusion rules of tonal centricity, forcing
choices to only some pitches and not others.

> This is comparable to how in traditional notation,
> when playing with a tonic C, one never ever saw
> a D double sharp unless there was some serious
> modulation beforehand. The tonal function of a
> doubly augmented second is not useful in common
> practice tonal music.

Which shows again the bias here towards thinking
only in terms of diatonicism.

> So, no matter the tuning, only (about) the first
> nine generated pitches above and below your
> tonic and their octave equivalents are tonally
> useful to that given tonic.

Same assertion, deciding for me what is and is
not tonally useful.

> Sometimes, like with
> 5-,7-,12-, and 17-edo, there is overlapping
> of pitch within even these 19 harmonic functions,
> sometimes the overlapping occurs within a still
> relatively small number of stacks larger than
> 19 like with 31-, 43-, or 53-edo, and sometimes
> the overlapping does not occur for a very long
> time with the beta generators in between all of
> our generally recognized syntonic equal divisions
> of the octave.
> I did a small analysis of tonal function across the
> syntonic temperament and blogged about it here:
>
> http://xenharmonic.ning.com/profiles/blogs/harmonicdiatonic-function
>
> If you want a little more depth on the matter, I
> have an unfinished powerpoint presentation that
> may be at least somewhat useful. You can find it here:
> http://www.slideshare.net/JlMoriart/fundamentalsofmusic112909
> The applicable information to this discussion
> starts on about slide 10.
>
> Let me know if I'm speaking gibberish!
>
> John M
>

Not at all. It makes sense, it's just extremely
biased towards one way of thinking about
making music. Like I said before, it's all really
cool, but it's way too limiting.

To me, microtonal music means freedom of choice.
I want the freedom to choose any pitches of any
combination. These programs are not allowing that.

Dynamic Tonality is an automatic system. So, it
is what it is. So why am I railing against it? It is only
exactly what it is claiming to be...

I'm railing against it because I find this whole question of
pitch selection to be a profoundly significant fundamental
issue having immense implications for musical
creativity, and I do not take these assertions lightly,
that only these or those pitches are "tonally relevant".

And I say this as someone who taught University music
theory at all levels, who knows traditional music theory
cold, inside and out.

Yours,
AAH
=====

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

> > So, in 31-equal divisions of the octave with a
> > generator size of about 697 cents, only 19 of the
> > generated 31 tones would be tonally useful at one
> > given time, and those are the pitches that are
> > mapped to the wicki/hayden isomorphic layout that
> > the TFS uses.
>
> This is the bias inherent within the approach
> that's being taken with the Wicki/Hayden layout.
> The approach begins with an assumption of privileged
> subsets, based on a premise of tonal centricity. So
> from scales having large numbers of pitches, the only
> pitches anyone can use are those subsets that are
> mapped to the keys for them.

I'm not sure what you mean here, Aaron. Wicki/Hayden
is just another isomorphic layout, isn't it? Then it's
just a question of specifying the x & y step sizes, and
the angle between them. We can argue over that choice
(3/2 @ 60 and 2/1 @ 90) all we want, but it seems like
a matter of degrees, not fundamentals (yuk yuk).

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@> wrote:
>
> > > So, in 31-equal divisions of the octave with a
> > > generator size of about 697 cents, only 19 of the
> > > generated 31 tones would be tonally useful at one
> > > given time, and those are the pitches that are
> > > mapped to the wicki/hayden isomorphic layout that
> > > the TFS uses.
> >
> > This is the bias inherent within the approach
> > that's being taken with the Wicki/Hayden layout.
> > The approach begins with an assumption of privileged
> > subsets, based on a premise of tonal centricity. So
> > from scales having large numbers of pitches, the only
> > pitches anyone can use are those subsets that are
> > mapped to the keys for them.
>
> I'm not sure what you mean here, Aaron. Wicki/Hayden
> is just another isomorphic layout, isn't it? Then it's
> just a question of specifying the x & y step sizes, and
> the angle between them. We can argue over that choice
> (3/2 @ 60 and 2/1 @ 90) all we want, but it seems like
> a matter of degrees, not fundamentals (yuk yuk).
>
> -Carl

Yes, but not the way the program appears to be using it.
It's the rhetoric about selecting 19 pitches that is
bothersome...

The programs have appeared to be catering
to the Wicki/Hayden layout with 19 pitches chosen
dynamically, presumably because this was the maximum
number of pitches the Thummer was supposed to support.

I asked around, and never got a straight answer as to
whether or not Jim Plamondon was footing the bill for
this work, but all indicators point to yes: his ideas favored,
his name listed as co-author of an academic article, his
name listed as co-inventor on related patents, etc. Full
disclosure on that point would be welcome.

Thanks,
AAH
=====

Thank you, Andy, for this additional information,
and I stand corrected concerning limitations to 12
tones for these programs; my apologies! And my
compliments on the high quality of the software
and the open manner in which it is being presented.

I didn't see an obvious bias towards the Wicki/Hayden
in the channel/note mapping paradigm you outlined,
which pleasantly surprised me. According to your
outline, an arrangement of 3 stacked keyboards, each
sending on a different MIDI channel, like an organ
console, comes to mind, ergo Bosanquet's harmonium,
ergo the hex adaptations of that design by Erv Wilson,
as implemented on the Starr Labs microzone. Is that
the direction your mappings are taking?

Cheers,
AAH
=====

--- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > I wrote:
> > > That said, we couldn't get our stuff together enough to
> > > craft a paper -- we tried, but it died amid constant
> > > bickering over minutia. Perhaps that's to do with the
> > > nature of mailing lists and long-distance collaboration.
> > > Or perhaps we're all just jerks. So anyway, I'm very glad
> > > these guys rose and did the exceptional job they did to
> > > move these things closer to reality. And that includes
> > > Jim, bless him.
> >
> > To be fair, several of us were sent drafts offlist, but we
> > were asked to keep quiet, presumably because of a publishing
> > embargo. And I suppose had the authors engaged on
> > tuning-math, they would have risked getting dragged down
> > into the bickering. So be it. -Carl
> >
>
> Hi all, just to clarify a few aspects about The Viking, TransFormSynth, and 2032, they are intended to be complementary - the first is an additive-subtractive synth, TFS is an analysis-resynthesis synth, the latter is a modal synth.
>
> It is our intention to map MIDI note and channel number to generator in the manner shown at the bottom of this email (I think this has been done in TFS - I may be wrong), it has not yet been done in Viking, 2032 is still very much in alpha stage. There is absolutely no intention to limit this to just 12 different tones.
>
> All of these software have been made available free, so I suppose development is a bit slow, but we are moving ahead (slowly).
>
> Also, you may be interested in Hex - a microtonal MIDI sequencer designed to interface with the above synths. It's still in alpha stage, but briefly, any linear mapping from a 2-D tuning to a 2-D button lattice has an "isotone" axis (a series of parallel lines) that connects the centres of "buttons" with the same pitch. As the ratio of the two generators' tunings changes, the angle of the isotone rotates. This means that if a button lattice is rotated so as to keep the isotone horizontal, it can be used as a replacement for the standard piano roll interface, but can be used for any 2-D tuning. If you want more info, email me and I can send a draft paper that explains this properly.
>
> Anyway, they can all be downloaded from www.dynamictonality.com.
>
> Here's the MIDI mapping bumpf....
>
> Both 2032 and Hex map MIDI channel 1 note numbers to in such a way as to give a standard meantone piano note-selection (i.e., C, C-sharp, D, E-flat, E, F, F-sharp, G, G-sharp, A, B-flat, B), whilst MIDI channel 2 note numbers are mapped to 12-TET enharmonic equivalents twelve fifths below (i.e., D-double flat, D-flat, E-double flat, F-double flat, F-flat, G-double flat, G-flat, A-double flat, A-flat, B-double flat, C-double flat, C-flat), and MIDI channel 3 to 12-TET enharmonic equivalents twelve fifths above (i.e., B-sharp, B-double sharp, C-double sharp, D-sharp, D-double sharp, E-sharp, E-double sharp, F-double sharp, F-triple sharp, G-double sharp, A-sharp, A-double sharp). This means that when playing in 12-TET, the channel number has no effect, but when playing in another relatively familiar tuning, such as meantone or Pythagorean, where enharmonically equivalent notes no longer have the same frequency, the user can choose between them simply by changing MIDI channel number. For example, D-sharp can be represented by MIDI note number 63, MIDI channel 1; whereas, E-flat can be represented by MIDI note number 63, MIDI channel 2.
>
> In this way, 2032 maintains backwards compatibility with traditional hardware and software MIDI controllers and sequencers, whilst still enabling the new feature of being able to differentiate between the tunings of sharps and flats in certain tunings. The mapping also means that Hex can be used to control conventional 12-TET synthesizers.
>
> For non-syntonic continua - the mapping between MIDI note number/channel and generators is the same...
>
> Andy Milne
>

Hi Aaron

Any misunderstandings are mostly our fault because we've done very little to actually document what we're doing...

With regard to the mapping chosen: No single mapping from MIDI note number (and channel) to the number of periods and generators that define a tone in a 2-D tuning system can suit all its tunings (because the pitch order of the tones changes as the size ratio of the generator and period changes).

So we decided to choose a mapping that made standard MIDI controllers compatible when using conventional (diatonic) tunings - when any of the synths are set to "syntonic", they can be played with a standard MIDI keyboard or sequencer. When set to any other continuum, the pitches produced by a standard MIDI controller will have no obvious logic. Of course, a user can remap the MIDI produced by their controller so as to produce a mapping that suits them - or use three stacked keyboards, if that suits.

But, these synths are ideally controlled by a 2-D button lattice. The purpose of the sequencer Hex is to make a software 2-D "button"-lattice sequencer freely available.

Another thing to note about the DT synths is that although they are based on 2-D tunings, using the tone-diamond interface, it is possible to move smoothly to two different 5-limit (3-D) JI scales that are related to the 2-D chain (they are JI notes that are mapped to the 2-D notes by the mapping matrix - i.e. the temperament class - with comma-variants selected so the chain contains the highest density if 4:5:6 triads). In other words, the JI-notes form a band running across a JI-tonnetz.

Also, I'm a bit out-of-touch with exactly what's been coded (in terms of MIDI mappings) with each of the synths - I'm not doing the hands-on programming myself. But hopefully these posts will provide the impetus to move things forward some more.

Andy

--- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@...> wrote:
>
> Thank you, Andy, for this additional information,
> and I stand corrected concerning limitations to 12
> tones for these programs; my apologies! And my
> compliments on the high quality of the software
> and the open manner in which it is being presented.
>
> I didn't see an obvious bias towards the Wicki/Hayden
> in the channel/note mapping paradigm you outlined,
> which pleasantly surprised me. According to your
> outline, an arrangement of 3 stacked keyboards, each
> sending on a different MIDI channel, like an organ
> console, comes to mind, ergo Bosanquet's harmonium,
> ergo the hex adaptations of that design by Erv Wilson,
> as implemented on the Starr Labs microzone. Is that
> the direction your mappings are taking?
>
> Cheers,
> AAH
> =====
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > I wrote:
> > > > That said, we couldn't get our stuff together enough to
> > > > craft a paper -- we tried, but it died amid constant
> > > > bickering over minutia. Perhaps that's to do with the
> > > > nature of mailing lists and long-distance collaboration.
> > > > Or perhaps we're all just jerks. So anyway, I'm very glad
> > > > these guys rose and did the exceptional job they did to
> > > > move these things closer to reality. And that includes
> > > > Jim, bless him.
> > >
> > > To be fair, several of us were sent drafts offlist, but we
> > > were asked to keep quiet, presumably because of a publishing
> > > embargo. And I suppose had the authors engaged on
> > > tuning-math, they would have risked getting dragged down
> > > into the bickering. So be it. -Carl
> > >
> >
> > Hi all, just to clarify a few aspects about The Viking, TransFormSynth, and 2032, they are intended to be complementary - the first is an additive-subtractive synth, TFS is an analysis-resynthesis synth, the latter is a modal synth.
> >
> > It is our intention to map MIDI note and channel number to generator in the manner shown at the bottom of this email (I think this has been done in TFS - I may be wrong), it has not yet been done in Viking, 2032 is still very much in alpha stage. There is absolutely no intention to limit this to just 12 different tones.
> >
> > All of these software have been made available free, so I suppose development is a bit slow, but we are moving ahead (slowly).
> >
> > Also, you may be interested in Hex - a microtonal MIDI sequencer designed to interface with the above synths. It's still in alpha stage, but briefly, any linear mapping from a 2-D tuning to a 2-D button lattice has an "isotone" axis (a series of parallel lines) that connects the centres of "buttons" with the same pitch. As the ratio of the two generators' tunings changes, the angle of the isotone rotates. This means that if a button lattice is rotated so as to keep the isotone horizontal, it can be used as a replacement for the standard piano roll interface, but can be used for any 2-D tuning. If you want more info, email me and I can send a draft paper that explains this properly.
> >
> > Anyway, they can all be downloaded from www.dynamictonality.com.
> >
> > Here's the MIDI mapping bumpf....
> >
> > Both 2032 and Hex map MIDI channel 1 note numbers to in such a way as to give a standard meantone piano note-selection (i.e., C, C-sharp, D, E-flat, E, F, F-sharp, G, G-sharp, A, B-flat, B), whilst MIDI channel 2 note numbers are mapped to 12-TET enharmonic equivalents twelve fifths below (i.e., D-double flat, D-flat, E-double flat, F-double flat, F-flat, G-double flat, G-flat, A-double flat, A-flat, B-double flat, C-double flat, C-flat), and MIDI channel 3 to 12-TET enharmonic equivalents twelve fifths above (i.e., B-sharp, B-double sharp, C-double sharp, D-sharp, D-double sharp, E-sharp, E-double sharp, F-double sharp, F-triple sharp, G-double sharp, A-sharp, A-double sharp). This means that when playing in 12-TET, the channel number has no effect, but when playing in another relatively familiar tuning, such as meantone or Pythagorean, where enharmonically equivalent notes no longer have the same frequency, the user can choose between them simply by changing MIDI channel number. For example, D-sharp can be represented by MIDI note number 63, MIDI channel 1; whereas, E-flat can be represented by MIDI note number 63, MIDI channel 2.
> >
> > In this way, 2032 maintains backwards compatibility with traditional hardware and software MIDI controllers and sequencers, whilst still enabling the new feature of being able to differentiate between the tunings of sharps and flats in certain tunings. The mapping also means that Hex can be used to control conventional 12-TET synthesizers.
> >
> > For non-syntonic continua - the mapping between MIDI note number/channel and generators is the same...
> >
> > Andy Milne
> >
>

On 12.02.2010, at 23:54, jlmoriart wrote:
> The interesting thing is that, as one progresses along the beta > chain (or stacks of fifths), the pitches reached become less and > less tonally relevant to a given tonic. As it turns out, only about > 19 pitches are ever tonally relevant to a given tonic, these being > the tonic itself and the first nine stacks of the generator (or > fifth) above and below that tonic. So, in 31-equal divisions of the > octave with a generator size of about 697 cents, only 19 of the > generated 31 tones would be tonally useful at one given time, and > those are the pitches that are mapped to the wicki/hayden isomorphic > layout that the TFS uses.

What do you mean by "tonally useful"? You mean a chain of more than 19 fifths is incomprehensible? That might be so, but is there some research to back your claim?

However, what about the other dimensions (5, 7, ...)? One can easily end up with far more pitches than 19 that are interesting (e.g., when using 31-TET).

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Hi Chris,

two of them are temporarily available here:
www.sendspace.com/file/ruijqt
www.sendspace.com/file/revhcd

Regarding Dinepome, you can find it at: www.untwelve.org/competition.html

Petr

I had forgot about these excellent pieces! - sounds like Medieval music from
a truly foreign land.

How do you compose these then verses doing the composition 12 EDO?

I am asking about your thought process.

Chris

On Sat, Feb 13, 2010 at 6:32 AM, Petr Parízek <p.parizek@...> wrote:

>
>
> Hi Chris,
>
> two of them are temporarily available here:
> www.sendspace.com/file/ruijqt
> www.sendspace.com/file/revhcd
>
> Regarding Dinepome, you can find it at: www.untwelve.org/competition.html
>
> Petr
>
>
>
>

Torsten wrote:

> Minor issue: 41-EDO closely approximates Pythagorean tuning.
> A 41-EDOfifths is +0.48 cent too large.

Oops, how could I have missed that ... Now I'll have to update the essay! :-( :-D

Petr

I'm ready to take the plunge, this time.

Apologies to Carl and others who gave me a list last time--I can't find it.

This time, I'll make multiple backups of any responses.

I'm defining my goals, gear, and background for people--not to preen or complain, but so that you folks can give me appropriate advice.

Basically, I'm looking for what microtonal soft-synths to get, or soft samplers, etc.

Goal: To make 'tape' pieces--that is, recorded microtonal pieces, done here in my home studio. Mainly for my own pleasure, possibly for scoring, down the road.

Microtonal angle: To learn about the scales and techs you are talking about on the list. Must be accurate to better than 1 cent. Must do up to 72 notes per octave.
Can be Halberstadt (if I'm correct in thinking this means conventional) and, the mapping from keys to sound should be simple. The software shouldn't make any assumptions about what I'm trying to do. (Software that makes assumptions often makes things harder.)

I want to do extended Just, 31-per 2/1, etc.

Current Gear: Mac OS X, with a range of conventional keyboards as input. Logic Pro. These are adequate, as far as I'm concerned.

I can't write code.

Something that works right away, but has a minimum of consumerist bells and whistles would be nice.

Something that works as a package and/or somehow works with Logic Pro would be nice.

As a sideline, I'd be interested in something that retunes existing sound, like Melodyne.

My budget is probably adequate to purchase 1 or 2 softsynths, Melodyne, and some other stuff.

It would be great if I had some software tools to help me understand some of the sophisticated tunings you people are talking about, but that would be third priority.

The main thing is to get a soft synth that I can be playing quickly, which will let me hear these tunings.

My interest is, generally, avant-classical, with a little jazz background.

I think like Mike Battaglia (on a good day); would like to write pieces like some by Daniel Forro; would like to know how the heck Petr Parizek comes up with his scales;
would like to be as open to everything as Ozan Yarman is.

There, I hope I've insulted everyone, now.

Let's assume softsynths rather than old hardware--let's not renew that debate.

Caleb

Dear John,

On 12.02.2010, at 23:54, jlmoriart wrote:
> If you want a little more depth on the matter, I have an unfinished > powerpoint presentation that may be at least somewhat useful. You > can find it here:
> http://www.slideshare.net/JlMoriart/fundamentalsofmusic112909
> The applicable information to this discussion starts on about slide > 10.

This presentation confirms Aarons comments concerning a focus on diatonic music and 5-limit.

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Hi Caleb,

Pianoteq is excellent - it has the best micro support of any VSTi I've used
that imitates a real instrument - and pianoteq imitates a piano to an
excellent degree - downside is that it is very expensive.
http://www.pianoteq.com/

Z3ta+ has been good - I think cakewalk sells that separately

http://www.cakewalk.com/Products/Z3TA/default.asp

I also use Garritan Personal Orchestra 4.0 - ok microsupport

There are others that I use besides but these are my essential ones.

Chris

On Sat, Feb 13, 2010 at 9:49 AM, c

On 13.02.2010, at 07:08, Carl Lumma wrote:
> I'm not sure what you mean here, Aaron. Wicki/Hayden
> is just another isomorphic layout, isn't it? Then it's
> just a question of specifying the x & y step sizes, and
> the angle between them. We can argue over that choice
> (3/2 @ 60 and 2/1 @ 90) all we want, but it seems like
> a matter of degrees, not fundamentals (yuk yuk).

Just to clarify: these pieces of software implement dynamic temperaments that are always two dimensional and where the generator is always 3/2 and the period is 2/1?

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Torsten wrote:

> Just to clarify: these pieces of software implement dynamic
> temperaments that are always two dimensional and where the generator
> is always 3/2 and the period is 2/1?

If you keep the generator at 3/2, you get Pythagorean. This thing can certainly do a lot more than that. :-)

Petr

Chris wrote:

> How do you compose these then verses doing the composition 12 EDO?

Hah, this may be a tough question to answer. First of all, if you want to understand the qualities of those unfamiliar temperaments, it’s necessary to get rid of the prejudices trying to compare everything to classical harmony. The systém of relating chords and keys by fifths and ommitting the syntonic comma differences comes undeniably from the properties of meantone (the same for standard notation); and it’s important to note that the syntonic comma is the one and ONLY interval which is tempered out in 5-limit meantone while other intervals (including smaller ones) are not. In 5-limit hanson, for example, the only interval which is tempered out is the kleisma (15625/15552) while other intervals (including the syntonic comma) are not. For this reason, a piece originally intended for meantone can’t be retuned to something like hanson (preserving the same chords) or vice versa.

But even so, you still have other possibilities. One of them is to také a 12-tone chain of the desired generators and apply that (or try to apply that) to the conventional 12-tone keyboard, although many temperaments don’t make a MOS with 12 tone scales and therefore, unlike meantone, their 12-tone versions have more than two intervals per interval class (for example, hanson makes a MOS with a scale of 11 tones, 15, or 19, among others). If you use Scala, you may get a possible version of 5-limit hanson by first doing „equal 11 15/2“ and then „normalize“ (i.e. first make a chain of 11 slightly wider minor thirds and then reduce this into a single octave range). Because we already know that hanson uses minor thirds as generators and that it tempers out 15625/15552, this can also tell us that 6 generators approximate 3/1 and that 5 generators approximate 5/2 -- i.e. something which doesn’t have an equivalent in meantone or in standard notation because 6 minor thirds don’t make a twelfth (like E#, G#, B, D, F, Ab, Cb -- and not B#). This is more or less all you need to know to be able to understand how hanson works. When you eventually get the scale on your keyboard, I would suggest to first verify that you can find all the desired tones of the chain to make sure that none of them is missing or „mistuned“ and that there are no „bugs“ in your scale -- i.e. if your 12-tone chain of minor thirds goes from C upwards, the last tone of the chain should be B (obviously, in cases like this, the keyboard mapping can’t always match the intervals you hear because stacking 6 minor thirds in 12-EDO doesn’t make a twelfth). Now the only thing that remains is to improvize in it for 10 minutes or so, and you’ll probably get it.

Another possibility is to begin with a chord progression that actually works as a triadic comma pump for the particular temperament and make some music based on that. There are a couple of ways how these chord progressions can be calculated by breaking the ratio for the „comma“ into a complementary pair of exponents of some other factors, and I’m currently updating an unfinished article explaining this in detail. Basically, first you find out how many generators approximate each of the three basic intervals (3/1, 5/1, and 5/3 for the 5-limit temperaments) and the highest of these generator counts then equals to the number of chords required for one repetition of the progression (i.e. 4 for meantone or mavila, 5 for magic or porcupine, 6 for hanson, 7 for negri, 9 for tetracot or semisixths).

Petr

Dear Caleb,

Just to clarify: you are asking for "gear to create sound" (e.g., softsynths) that you can use in Logic via MIDI? I.e., not alternative controllers (like generalised keyboards) or alternative techniques to organise your music (non-MIDI) or ways to compose?
> Current Gear: Mac OS X, with a range of conventional keyboards as
> input. Logic Pro. These are adequate, as far as I'm concerned.
>
Are you aware that you can freely tune the softsynths that come with Logic via Scala files? Even (5-limit) adaptive JI is supported. However, you are always limited to at max 12 pitches per octave, but its not too bad for a start :)

If you want to stay in MIDI land (for understandable reasons :) but want more that 12 pitches per octave then you may consider the "classical method": write for individual voices and each voice associated with its own MIDI channel. You can then freely detune each voice with pitch bend messages.

Finally, if you want more than 12 pitches per octave and also more than one note per MIDI channel tuned freely, then there is relatively little software available for doing that. I wrote some script for the sampler Kontakt that allows to detune individual pitch classes with MIDI CC messages. I also did a module for the Tassman softsynth that does the same (there seems to be some principle Tassman limitation though that detuning some already sounding pitch classes suddently always results in some annoying portamento, so one has to take that into account).

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

On 13.02.2010, at 14:49, caleb morgan wrote:

> I'm ready to take the plunge, this time.
>
> Apologies to Carl and others who gave me a list last time--I can't
> find it.
>
> This time, I'll make multiple backups of any responses.
>
> I'm defining my goals, gear, and background for people--not to preen
> or complain, but so that you folks can give me appropriate advice.
>
> Basically, I'm looking for what microtonal soft-synths to get, or soft
> samplers, etc.
>
> Goal: To make 'tape' pieces--that is, recorded microtonal pieces,
> done here in my home studio. Mainly for my own pleasure, possibly for
> scoring, down the road.
>
> Microtonal angle: To learn about the scales and techs you are talking
> about on the list. Must be accurate to better than 1 cent. Must do
> up to 72 notes per octave.
> Can be Halberstadt (if I'm correct in thinking this means
> conventional) and, the mapping from keys to sound should be simple.
> The software shouldn't make any assumptions about what I'm trying to
> do. (Software that makes assumptions often makes things harder.)
>
> I want to do extended Just, 31-per 2/1, etc.
>
> Current Gear: Mac OS X, with a range of conventional keyboards as
> input. Logic Pro. These are adequate, as far as I'm concerned.
>
> I can't write code.
>
> Something that works right away, but has a minimum of consumerist
> bells and whistles would be nice.
>
> Something that works as a package and/or somehow works with Logic Pro
> would be nice.
>
> As a sideline, I'd be interested in something that retunes existing
> sound, like Melodyne.
>
> My budget is probably adequate to purchase 1 or 2 softsynths,
> Melodyne, and some other stuff.
>
> It would be great if I had some software tools to help me understand
> some of the sophisticated tunings you people are talking about, but
> that would be third priority.
>
> The main thing is to get a soft synth that I can be playing quickly,
> which will let me hear these tunings.
>
> My interest is, generally, avant-classical, with a little jazz
> background.
>
> I think like Mike Battaglia (on a good day); would like to write
> pieces like some by Daniel Forro; would like to know how the heck Petr
> Parizek comes up with his scales;
> would like to be as open to everything as Ozan Yarman is.
>
> There, I hope I've insulted everyone, now.
>
> Let's assume softsynths rather than old hardware--let's not renew that
> debate.
>
> Caleb
>

On 13.02.2010, at 16:28, Petr Parízek wrote:
> > Just to clarify: these pieces of software implement dynamic
> > temperaments that are always two dimensional and where the generator
> > is always 3/2 and the period is 2/1?
>
> If you keep the generator at 3/2, you get Pythagorean. This thing
> can certainly do a lot more than that. :-)

Sorry for causing this misunderstanding. What I mean is: the generator
is restricted to an approximation of 3/2 (namely 686-720 cent) and the
period to an approximation of 2/1?

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

>
> Petr
>
>
>
>

Torsten wrote:

> Sorry for causing this misunderstanding. What I mean is: the generator
> is restricted to an approximation of 3/2 (namely 686-720 cent) and the
> period to an approximation of 2/1?

I don't think so -- at least regarding the generator. Not sure about the period though.

Petr

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
> I'm ready to take the plunge, this time.
> Apologies to Carl and others who gave me a list last time--
> I can't find it.

That's ok, I just did one for another Mac user:
/makemicromusic/topicId_21655.html#21656

> Can be Halberstadt (if I'm correct in thinking this means
> conventional)

Correct. If you can afford it, I recommend an AXiS
http://www.c-thru-music.com

or if you can afford a little more, an Opal
http://www.theshapeofmusic.com

> The software shouldn't make any assumptions about what I'm
> trying to do.

Don't worry, it won't!

> Current Gear: Mac OS X, with a range of conventional keyboards
> as input. Logic Pro. These are adequate, as far as I'm
> concerned.

Logic is the only DAW I know of with a built-in microtuning
function. I've never used it, but from what I understand, it's
limited to 12/oct. I'm told it can do Hermode adaptive tuning,
which is fun to tool around with. But Logic will host the
softsynths I mention, so it's as good as any other DAW beyond
it's built-in microtuning features.

> As a sideline, I'd be interested in something that retunes
> existing sound, like Melodyne.

Melodyne is stellar for things like adaptive tuning, though
this still must be done by hand, meticulously.

> It would be great if I had some software tools to help me
> understand some of the sophisticated tunings you people are
> talking about, but that would be third priority.

With the exception of LMSO and the H-Pi stuff, none of the
apps I mention are micro-specific. But they will support
arbitrary tunings, with the limit of 128 pitches per
MIDI channel.

In the way of micro-specific stuff, everything I know about
is pretty beta. But several are very promising.
Rationale for instance:
http://www.badmuthahubbard.com/cgi-bin/rationaleinfo.py

And the DT apps we were just discussing:
http://www.dynamictonality.com

> would like to know how the heck Petr Parizek comes up with
> his scales;

He's a regular mapper (we should make t-shirts). Did you
see the RTF document he just put in the Files section?

It looks like Mike is just diving into regular mapping.
Maybe you can collab with him a bit.

Or search the archives for "regular mapping" or
"regular temperament" and read anything you find by Graham,
myself, Herman, Petr, etc.

> Let's assume softsynths rather than old hardware--let's not
> renew that debate.

Glad you've finally seen the light!

-Carl

Hi Torsten,

> > I'm not sure what you mean here, Aaron. Wicki/Hayden
> > is just another isomorphic layout, isn't it? Then it's
> > just a question of specifying the x & y step sizes, and
> > the angle between them. We can argue over that choice
> > (3/2 @ 60 and 2/1 @ 90) all we want, but it seems like
> > a matter of degrees, not fundamentals (yuk yuk).
>
> Just to clarify: these pieces of software implement dynamic
> temperaments that are always two dimensional and where the
> generator is always 3/2 and the period is 2/1?

The Viking supports three systems: syntonic (3/2 & 2/1),
Hanson (6/5 & 2/1) and Magic (5/4 & 2/1).

-Carl

On 13.02.2010, at 16:42, Petr Parízek wrote:
> Torsten wrote:
>> Sorry for causing this misunderstanding. What I mean is: the
>> generator
>> is restricted to an approximation of 3/2 (namely 686-720 cent) and
>> the
>> period to an approximation of 2/1?
>
> I don't think so -- at least regarding the generator. Not sure about
> the
> period though.

It is stated in this talk by John:

http://www.slideshare.net/JlMoriart/fundamentalsofmusic112909

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

On 13.02.2010, at 16:51, Carl Lumma wrote:
> > Can be Halberstadt (if I'm correct in thinking this means
> > conventional)
>
> Correct. If you can afford it, I recommend an AXiS
> http://www.c-thru-music.com
>
> or if you can afford a little more, an Opal
> http://www.theshapeofmusic.com

Anyone considered an Eigenharp already. Its keys can be freely tuned, and it would be very nice for going beyond just "pressing buttons" :) Not exactly cheap though, but it looks worth its price.

http://www.eigenlabs.com/

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

On 13.02.2010, at 16:59, Carl Lumma wrote:
> > > I'm not sure what you mean here, Aaron. Wicki/Hayden
> > > is just another isomorphic layout, isn't it? Then it's
> > > just a question of specifying the x & y step sizes, and
> > > the angle between them. We can argue over that choice
> > > (3/2 @ 60 and 2/1 @ 90) all we want, but it seems like
> > > a matter of degrees, not fundamentals (yuk yuk).
> >
> > Just to clarify: these pieces of software implement dynamic
> > temperaments that are always two dimensional and where the
> > generator is always 3/2 and the period is 2/1?
>
> The Viking supports three systems: syntonic (3/2 & 2/1),
> Hanson (6/5 & 2/1) and Magic (5/4 & 2/1).=
>
Ah, thank you!

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Petr>"In 5-limit hanson, for example, the only
interval which is tempered out is the kleisma (15625/15552) while other
intervals (including the syntonic comma) are not. For this reason, a piece
originally intended for meantone can’t be retuned to something like hanson
(preserving the same chords) or vice versa."

Ok, trying to understand. Before I understood temperament as the used of one note in place of two meant to substitute for either of those two notes. Yet here it sounds as if "tempering out" only effects a certain notes and, I'd guess, scales with melodies that >depend< on changes between those two notes simply fail to be re-tuned correctly.

In detailed terms with examples of ratios involved, how does "tempering out" prevent conversion between different scales?

Thank you Andy, for this explanation and added info.
The diamond interface is really fascinating! I do hope
that things will move forward, and I'm sure there are
many here who will be happy to act as a sounding
board.

Cheers,
Aaron
=====

--- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
> Hi Aaron
>
> Any misunderstandings are mostly our fault because we've done very little to actually document what we're doing...
>
> With regard to the mapping chosen: No single mapping from MIDI note number (and channel) to the number of periods and generators that define a tone in a 2-D tuning system can suit all its tunings (because the pitch order of the tones changes as the size ratio of the generator and period changes).
>
> So we decided to choose a mapping that made standard MIDI controllers compatible when using conventional (diatonic) tunings - when any of the synths are set to "syntonic", they can be played with a standard MIDI keyboard or sequencer. When set to any other continuum, the pitches produced by a standard MIDI controller will have no obvious logic. Of course, a user can remap the MIDI produced by their controller so as to produce a mapping that suits them - or use three stacked keyboards, if that suits.
>
> But, these synths are ideally controlled by a 2-D button lattice. The purpose of the sequencer Hex is to make a software 2-D "button"-lattice sequencer freely available.
>
> Another thing to note about the DT synths is that although they are based on 2-D tunings, using the tone-diamond interface, it is possible to move smoothly to two different 5-limit (3-D) JI scales that are related to the 2-D chain (they are JI notes that are mapped to the 2-D notes by the mapping matrix - i.e. the temperament class - with comma-variants selected so the chain contains the highest density if 4:5:6 triads). In other words, the JI-notes form a band running across a JI-tonnetz.
>
> Also, I'm a bit out-of-touch with exactly what's been coded (in terms of MIDI mappings) with each of the synths - I'm not doing the hands-on programming myself. But hopefully these posts will provide the impetus to move things forward some more.
>
> Andy
>
>
> --- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@> wrote:
> >
> > Thank you, Andy, for this additional information,
> > and I stand corrected concerning limitations to 12
> > tones for these programs; my apologies! And my
> > compliments on the high quality of the software
> > and the open manner in which it is being presented.
> >
> > I didn't see an obvious bias towards the Wicki/Hayden
> > in the channel/note mapping paradigm you outlined,
> > which pleasantly surprised me. According to your
> > outline, an arrangement of 3 stacked keyboards, each
> > sending on a different MIDI channel, like an organ
> > console, comes to mind, ergo Bosanquet's harmonium,
> > ergo the hex adaptations of that design by Erv Wilson,
> > as implemented on the Starr Labs microzone. Is that
> > the direction your mappings are taking?
> >
> > Cheers,
> > AAH
> > =====
> >
> > --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > > >
> > > > I wrote:
> > > > > That said, we couldn't get our stuff together enough to
> > > > > craft a paper -- we tried, but it died amid constant
> > > > > bickering over minutia. Perhaps that's to do with the
> > > > > nature of mailing lists and long-distance collaboration.
> > > > > Or perhaps we're all just jerks. So anyway, I'm very glad
> > > > > these guys rose and did the exceptional job they did to
> > > > > move these things closer to reality. And that includes
> > > > > Jim, bless him.
> > > >
> > > > To be fair, several of us were sent drafts offlist, but we
> > > > were asked to keep quiet, presumably because of a publishing
> > > > embargo. And I suppose had the authors engaged on
> > > > tuning-math, they would have risked getting dragged down
> > > > into the bickering. So be it. -Carl
> > > >
> > >
> > > Hi all, just to clarify a few aspects about The Viking, TransFormSynth, and 2032, they are intended to be complementary - the first is an additive-subtractive synth, TFS is an analysis-resynthesis synth, the latter is a modal synth.
> > >
> > > It is our intention to map MIDI note and channel number to generator in the manner shown at the bottom of this email (I think this has been done in TFS - I may be wrong), it has not yet been done in Viking, 2032 is still very much in alpha stage. There is absolutely no intention to limit this to just 12 different tones.
> > >
> > > All of these software have been made available free, so I suppose development is a bit slow, but we are moving ahead (slowly).
> > >
> > > Also, you may be interested in Hex - a microtonal MIDI sequencer designed to interface with the above synths. It's still in alpha stage, but briefly, any linear mapping from a 2-D tuning to a 2-D button lattice has an "isotone" axis (a series of parallel lines) that connects the centres of "buttons" with the same pitch. As the ratio of the two generators' tunings changes, the angle of the isotone rotates. This means that if a button lattice is rotated so as to keep the isotone horizontal, it can be used as a replacement for the standard piano roll interface, but can be used for any 2-D tuning. If you want more info, email me and I can send a draft paper that explains this properly.
> > >
> > > Anyway, they can all be downloaded from www.dynamictonality.com.
> > >
> > > Here's the MIDI mapping bumpf....
> > >
> > > Both 2032 and Hex map MIDI channel 1 note numbers to in such a way as to give a standard meantone piano note-selection (i.e., C, C-sharp, D, E-flat, E, F, F-sharp, G, G-sharp, A, B-flat, B), whilst MIDI channel 2 note numbers are mapped to 12-TET enharmonic equivalents twelve fifths below (i.e., D-double flat, D-flat, E-double flat, F-double flat, F-flat, G-double flat, G-flat, A-double flat, A-flat, B-double flat, C-double flat, C-flat), and MIDI channel 3 to 12-TET enharmonic equivalents twelve fifths above (i.e., B-sharp, B-double sharp, C-double sharp, D-sharp, D-double sharp, E-sharp, E-double sharp, F-double sharp, F-triple sharp, G-double sharp, A-sharp, A-double sharp). This means that when playing in 12-TET, the channel number has no effect, but when playing in another relatively familiar tuning, such as meantone or Pythagorean, where enharmonically equivalent notes no longer have the same frequency, the user can choose between them simply by changing MIDI channel number. For example, D-sharp can be represented by MIDI note number 63, MIDI channel 1; whereas, E-flat can be represented by MIDI note number 63, MIDI channel 2.
> > >
> > > In this way, 2032 maintains backwards compatibility with traditional hardware and software MIDI controllers and sequencers, whilst still enabling the new feature of being able to differentiate between the tunings of sharps and flats in certain tunings. The mapping also means that Hex can be used to control conventional 12-TET synthesizers.
> > >
> > > For non-syntonic continua - the mapping between MIDI note number/channel and generators is the same...
> > >
> > > Andy Milne
> > >
> >
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Another sense of "hearing frequency ratios" must be also examined.
> > That is the sense that some irrational ratios are purportedly
> > perceived as or as substitutes of low-numbered integer ratios as
> > if our brains categorized intervals into classes defined by
> >low-numbered integer ratios...
> //snip
> > But that's it. I claim that this is where it stops. The hearing of
> > ratios doesn't carry further into the cognition of musical
> > structures like scales and chord progressions.
>
> Why not scales? If come up with a simple 3-note scale that's just
> 4:5:6, and I play each note separately - C, E, G, E, C, E, G, E, C
> - does your brain not still put it together as a major chord? Or,
> if I play an Eb chord, and then go to just a C-G drone -- you will
> still hear some minor quality to it.

Yes. My wording was a bit misleading. All I meant was that the
perception of ratios stays at the first-order level and I
elaborated on that here:

> > That is, multiples and ratios of ratios are already not perceived
> > as being composed of ratios. When we have been ear-trained to
> > recognize a fifth and a fourth we are not thereby able to
> > recognize a whole tone or an octave as being made of a fifth and
> > a fourth.
>
> As for what you said - that we don't hear an octave as a fifth + a
> fourth - this is true, but I do think that to some extent we can
> hear a major 7th as a 3rd + a fifth.

Yes but I think that whatever explains this is not some faculty that
literally mathematically calculates interval composites as multiples
of rational numbers. A more likely explanation is our familiarity
with major 7th chords. This kind of explanation is cognitive: hearing
major 7ths as 3rd + 5th is based on a mental schema of diatonic
structure. Of course such mental schemata don't have to conform to
the logic of rational numbers.

> And in the example I showed above: C-E-F#-B-D#
> If that C-D# were played in isolation, I think it'd probably sound
> like 6/5. However - when the other notes are put in, the cracks are
> filled in, and the brain gets an idea of how to travel from C to D#.

Yes but I really doubt that the interval from C to D# is thereby
literally represented in the brain as the ratio 32:75 even if it is
tuned so. I'm not even sure if I hear that chord in the way that
spelling suggests when it is played alone without any tonal context.

> > It doesn't calculate the relations of frequency ratios further
> > than the basic first-order level. Why would it do that? What
> > evolutionary reason would there be for the existence of such a
> > faculty. How would it help in hearing speech sounds for example?
>
> This is related to an experiment that I think you should try: Go to
> an organ, and set the drawbars so that the only harmonics coming
> out are the fundamental and 3/1. Turn the fundamental so it's down
> low, but still there. Start playing happy birthday or something
> easy. Meanwhile, after playing it through once or twice, start
> turning the fundamental down until it is completely silent, and
> only 3/1 remains.
>
> If you do it right, you can actually "trick" your brain into
> perceiving the phantom 1/1, even though the only thing there is a
> 3/1 sinusoid. It helps to keep imagining the original "happy
> birthday" song in the original key while you do this. You'll find
> you can very easily "flip your brain" around to just hear the 3/1
> as a new 1/1, and once you do that, it's hard to go back.
>
> This I think is related to the source separation and identification
> processes going on in your brain. The concept of finding "different
> harmonic spectra" for the wash of sound coming in is inherently
> tied in with notions of source separation anyway. Once your brain
> has a harmonic spectrum picked out, it holds onto it for a second.

I tried this and what a kick-ass experiment it is, really
interesting! But I fail to see its' relevance to what I said.

Kalle Aho

> Yes but I think that whatever explains this is not some faculty that
> literally mathematically calculates interval composites as multiples
> of rational numbers. A more likely explanation is our familiarity
> with major 7th chords. This kind of explanation is cognitive: hearing
> major 7ths as 3rd + 5th is based on a mental schema of diatonic
> structure. Of course such mental schemata don't have to conform to
> the logic of rational numbers.

I agree with that, but if you listen closely enough, you notice that
often it does. That is, the tritone C-F# can function in a thousand
possible ways. Play that tritone, then imagine it as part of a D7
chord. Then imagine it as part of an Ab7 chord. Then imagine it as
part of a C7#11 chord, and then a Cmaj7#11 chord. Voila, same thing.
You're "imagining" different bridges from C to F#.

The only thing is that you treat this purely in psychological terms -
in terms of mental schemata and such - but I think that it isn't quite
so isolated. You have a bit of influence in how you hear a chord, and
the schema that pops up when you hear it is a part of it. Play a 350
cent third and then "imagine" that it's a really flat 6/5, and then
"imagine" it as a really flat 5/4. Voila again. The same thing is
happening here as above. I think what's happening here is that when
you imagine other notes in addition to a chord, your brain basically
analyzes the notes you hear + the ones you imagine all together. It
just gives the imagined notes less "weight," the same as if they
existed in real life but at a lower volume.

> Yes but I really doubt that the interval from C to D# is thereby
> literally represented in the brain as the ratio 32:75 even if it is
> tuned so. I'm not even sure if I hear that chord in the way that
> spelling suggests when it is played alone without any tonal context.

You hear the C-E, the E-B, and the B-D#. If you can't hear this as a
coherent chord but rather some dissonant stack of noise, I would
expect your brain would hear it more as "bitonal" or "polytonal" -
consisting of multiple harmonic structures - and not have the 32:75.
However, if you can hear the whole thing as a single harmonic
structure, I think that would imply the 32:75 has been recognized.

> I tried this and what a kick-ass experiment it is, really
> interesting! But I fail to see its' relevance to what I said.

It's relevant to what you said here:

> > > It doesn't calculate the relations of frequency ratios further
> > > than the basic first-order level. Why would it do that? What
> > > evolutionary reason would there be for the existence of such a
> > > faculty. How would it help in hearing speech sounds for example?

When you said this, you mentioned that the brain doesn't "remember"
previous frequency ratios and that's why comma pumps don't cause you
to become psychotic. Then you said, why would it do that, what
evolutionary reason would there be?

Well, I'm saying that it DOES remember previous frequency ratios, and
the above experiment is proof of that. The evolutionary reason is that
this capability would have assisted in source identification. I think
this is also responsible for why chord progressions "work."

Perhaps, in this context, comma pumps "work" because they're just
perceived as a slight "background inharmonicity" in the chord
progression, similar to Sethares' detuning of timbres being perceived
as a slight inharmonicity. It might just be so slight that we don't
notice it or can't hear it.

Just my theory anyway, but I do think there's something to
second-order periodicity coming into play. That's why minor chords can
be perceived as having multiple fundamentals, and they also don't
sound like completely chaotic polytonal mush.

-Mike

> Kalle Aho
>
>

> Another sense of "hearing frequency ratios" must be also examined.
> That is the sense that some irrational ratios are purportedly
> perceived as or as substitutes of low-numbered integer ratios as if
> our brains categorized intervals into classes defined by low-numbered
> integer ratios...
Agreed...
The question to me then becomes...how high limit do ratios does a chord have to be before the brain starts trying to "round it to low-numbered ratios...and how low must those ratios be not to be interpretted as "noise"?
For example, take the relatively "irrational" 21:29:35 chord and a 3:4:5 chord...do they sound more or less the same to you...does the brain effectively interpret one chord as the other (at least for the most part)?

Now what if you play (with sine waves) a 3:4:5 chord a 4:5:6 chord with the 3 in the first chord and the 4 in the second starting on the same note. IE the first chord could be 300hz,400hz,500hz while the second would be 300hz, (300*5/4=)375hz,(300*6/4=450hz).

Do you sense the brain seems to successfully hear the chords seperately to simplify hearing them OR does it sound to you more like the brain simply shoves them both into one "higher limit" chord?

>"Obviously the brain can remember previous intervals to some extent, or else all chord progressions would sound the same, which is emotionless and dull."
Again, agreed.
On the side...I wonder if this has anything to do with the "temporal masking" IE the technique in mp3s used to eliminate having to store tones in a new time frame that had been sounded very recently before. The brain indeed seems to have a certain "ghosting" effect of holding a mood from a previous chord right after a chord has ended.

> >"Obviously the brain can remember previous intervals to some extent, or else all chord progressions would sound the same, which is emotionless and dull."
>    Again, agreed.
>    On the side...I wonder if this has anything to do with the "temporal masking" IE the technique in mp3s used to eliminate having to store tones in a new time frame that had been sounded very recently before.  The brain indeed seems to have a certain "ghosting" effect of holding a mood from a previous chord right after a chord has ended.

It might have to do with temporal masking, but I think it's a bit
different than that. It might be the same underlying mechanism though,
I'm really not sure.

-Mike
>

Sorry about the powerpoint presentation, it's unfinished and not well worded. I'm not sure what it sounded like I said, but what I mean is this:

In the <b>Syntonic temperament</b>, the generators are the fifth and octave. The Syntonic Temperament defines each tonal/harmonic/diatonic function as a located in the stack of fifths's reduced into every octave. In order for the described functions to be retained, the fifth can not be above 720 cents or below 686. Above or below these value, fourths overlap with fifths, thirds overlap with fourths, etc. These values are called the Sytonic Temperament's "Valid Tuning Range".

This subject is described here:
http://www.mitpressjournals.org/doi/pdf/10.1162/comj.2007.31.4.15

Other 2D temperaments can have any two generators, but generally they tend to be a tempered variations of just intonation intervals, one of which is almost always the octave, or 2/1. The Syntonic Temperament tempers the 3/2 major fifth, the Magic Temperament tempers the 5/4 major third, and the Hanson Temperament tempers the 6/5 minor third, and so on.

2D temperaments do not merely define mappings of notes to pitches, but also of partials to pitches, as is described in this paper declaring "The Matrix" as a new parsimonious paradigm for music:
http://www.igetitmusic.com/papers/Matrix.pdf

Each Temperament defines certain locations within the matrix (or locations in the stack of generators reduced by the period)as the pitches for a partial of a timbre, this allowing for both maximized sensory consonance in the tuning as well as for appropriate harmonic function.

Consequently there are temperaments other than the Syntonic that also use the functions of the octave and fifth as generators, but map the acquired pitches to different partials. One such temperament is the Schismatic Temperament which, instead of using the major third (or, more specifically, up 4 fifths, down 2 octaves) for triadic harmony, uses the diminished fourth (or down 8 fifths and up 5 octaves). It places the tempered timbres partials differently than the Syntonic Temperament does making each tuning it creates functionally different. It also has a different valid tuning range.

Is this more clear? I'm not an expert on these subjects, but this has been my understanding.

John Moriarty

Mike B>"Just my theory anyway, but I do think there's something to second-order periodicity coming into play. That's why minor chords can be perceived as having multiple fundamentals, and they also don't
sound like completely chaotic polytonal mush."

Ok, back to my theory of "multiple implied fundamentals" being somewhat OK despite so many people thinking consonant chords must sum into one and only one straight harmonic series. Indeed the minor chord is an ideal example, pointing to two distinct harmonic series.
How do you think the brain puts limits one how much it can handle of hearing multiple distinct harmonic series in a chord? Also, do you think it has anything to do with if the "virtual pitch root tones" at the bottom of the harmonic series that those ratios point to are periodic in comparison to each other?

It would just, at least IMVHO, be very useful to have a way to, for example, gauge the resolved-ness of things like minor chords beside saying things like "it's just how the human ear is trained for evolutionary purposes". That would also take us back to the question of why does a major triad sound better than a minor one (and if there are certain minor chords very similar to major chords that sound much more similar in terms of resolved-ness/consonance than those two triads, why)?

Mike wrote:
> Well, I'm saying that it DOES remember previous frequency ratios,
> and the above experiment is proof of that. The evolutionary reason
> is that this capability would have assisted in source
> identification. I think this is also responsible for why chord
> progressions "work."

It's a fallacy that every trait is adaptive. What's the
evolutionary purpose of our tendency to become addicted to
coffee beans?

-Carl

> Ok, back to my theory of "multiple implied fundamentals" being somewhat OK despite so many people thinking consonant chords must sum into one and only one straight harmonic series. Indeed the minor chord is an ideal example, pointing to two distinct harmonic series.
> How do you think the brain puts limits one how much it can handle of hearing multiple distinct harmonic series in a chord? Also, do you think it has anything to do with if the "virtual pitch root tones" at the bottom of the harmonic series that those ratios point to are periodic in comparison to each other?

Well, first off, the idea that the brain perceives multiple harmonic
structures in the same chord is far from new... Folks have been
throwing that idea around for a while.

I'm actually coming up with a model for this now. I think that the
idea is, the chord will have an entire "harmonic profile" that pops up
when it's heard, which consists of all of the possible periodicities
heard in that chord.

This seems pretty intuitive when you consider the simple case of the
major chord:

For a C major chord, for example, there will be 5 total periodic
structures heard: the C itself as a fundamental, the E itself as a
fundamental, the G itself as a fundamental, the C-G dyad as a 2:3, and
the C-E, the E-G, and the C-E-G which all refer to a root 2 octaves
below the C.

This manifests itself in a very predictable way: you simultaneously
hear the C-E-G as notes themselves, the C-G as a solid dyad with a
root an octave below, the C-E and E-G as solid dyads with roots 2
octaves below, and C-E-G as a solid triad with a rood two octaves
below.

It seems like a very elegant and intuitive solution to me, and
accurately represents the way I hear a major chord. The whole set of
periodicities I've been calling the chord's "harmonic profile," the
set minus the periodicities of the notes themselves I've been calling
the "subharmonic profile," and the periodicities of the notes
themselves I've been calling the "apparent profile." Subharmonic
profile + apparent profile = harmonic profile.

The "apparent profile" of a chord, in short, represents the notes
themselves, without any regard to how they interact. The "subharmonic
profile" refers to everything else. The entire perceptual experience
that we have of a "chord," I think, is related to the interaction
between the two of these, and with the subharmonic profile with
itself.

I'll make a more formal post about this once I can get the math worked
out, but that's what I've been thinking, anyway.

> It would just, at least IMVHO, be very useful to have a way to, for example, gauge the resolved-ness of things like minor chords beside saying things like "it's just how the human ear is trained for evolutionary purposes". That would also take us back to the question of why does a major triad sound better than a minor one (and if there are certain minor chords very similar to major chords that sound much more similar in terms of resolved-ness/consonance than those two triads, why)?

A major triad doesn't sound "better" than a minor one. It's just different.

-Mike

>

> It's a fallacy that every trait is adaptive. What's the
> evolutionary purpose of our tendency to become addicted to
> coffee beans?

Yes, technically, but what does that have to do with any of this?

-Mike

>

On 14 Feb 2010, at 1:30 AM, Torsten Anders wrote:
> Finally, if you want more than 12 pitches per octave and also more
> than one note per MIDI channel tuned freely, then there is relatively
> little software available for doing that. I wrote some script for the
> sampler Kontakt that allows to detune individual pitch classes with
> MIDI CC messages. I also did a module for the Tassman softsynth that
> does the same (there seems to be some principle Tassman limitation
> though that detuning some already sounding pitch classes suddently
> always results in some annoying portamento, so one has to take that
> into account).
>
> Best wishes,
> Torsten
>

Another method I use often is to combine more MIDI channels for one sound and tune notes differently on them, so by combining those channels I get all notes I need. For example for 17ET for my "Study Nr. 4" (from "Seven Microtonal Studies") I tuned this:

(step 70.6 Cents, approximated as 10 x 71, 7 x 70 Cents)

MIDI Channel 1
Key: C Db Eb E F# G Ab Bb B
Cents: 0 142 284 426 568 710 850 990 1130
Cent Deviation from 12ET: 0 +42 -16 +26 -32 +10 +50 -10 +30

(keys D, F, A are not used on this channel)

MIDI Channel 2
Key: C Db D Eb F F# Ab A Bb
Cents: 0 71 213 355 497 639 780 920 1060
Cent Devistion from 12ET: 0 -29 +13 +55 -3 +39 -20 +20 +60

(keys E, G, B are not used on this channel)

Key C can be used on both channels.

Daniel Forro

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > It's a fallacy that every trait is adaptive. What's the
> > evolutionary purpose of our tendency to become addicted to
> > coffee beans?
>
> Yes, technically, but what does that have to do with any of this?

It applies to what you wrote, that I quoted but you snipped
here. Speaking of snipping, can you please leave attributions
in tact? It's harder to follow threads without them.

-Carl

> > > > Well, I'm saying that it DOES remember previous frequency ratios,
> > > > and the above experiment is proof of that. The evolutionary reason
> > > > is that this capability would have assisted in source
> > > > identification. I think this is also responsible for why chord
> > > > progressions "work."
> > > >
> > > It's a fallacy that every trait is adaptive. What's the
> > > evolutionary purpose of our tendency to become addicted to
> > > coffee beans?
> >
> > Yes, technically, but what does that have to do with any of this?
>
> It applies to what you wrote, that I quoted but you snipped
> here. Speaking of snipping, can you please leave attributions
> in tact? It's harder to follow threads without them.

OK, I put the quote back.

That experiment basically demonstrates that even a single sinusoid can
be viewed as 2/1, or 3/1, rather than just as 1/1, depending on prior
input. It also demonstrates that even an isolated overtone from that
series can still be perceived as referring to the fundamental. Without
this, an effect like a flanger, which is basically a sweeping
feedforward comb filter would sound completely different.

It isn't that much of a stretch to imagine a scenario in nature in
which this would be useful - if you're running in a forest, and
there's rapidly changing comb filtering going on all around you, it
would be very handy to still be able to keep track of what sources are
what.

-Mike

> That experiment basically demonstrates that even a single sinusoid can
> be viewed as 2/1, or 3/1, rather than just as 1/1, depending on prior
> input. It also demonstrates that even an isolated overtone from that
> series can still be perceived as referring to the fundamental. Without
> this, an effect like a flanger, which is basically a sweeping
> feedforward comb filter would sound completely different.

Sorry, that should have said a feedBACK comb filter, of course.

- Mike

Michael wrote:

> Ok, trying to understand. Before I understood temperament as the used of one note
> in place of two meant to substitute for either of those two notes. Yet here it sounds as if
> "tempering out" only effects a certain notes and, I'd guess, scales with melodies that
> >depend< on changes between those two notes simply fail to be re-tuned correctly.

There’s no reason why one statement should exclude the other, both can be true.

> In detailed terms with examples of ratios involved, how does
> "tempering out" prevent conversion between different scales?

I think the primary answer why it’s impossible to convert music from one temperament to another lies rather in the fact that something <isn‘t tempered out> than that something <is tempered out>. For example, in meantone, 3/2 is approximated by the interval 4 times smaller than the one approximating 5/1, which means that if you do „C, A, D, G, C“ in 5-limit JI, you finish a syntonic comma lower than where you started (i.e. the bass tones being 5/6, 4/3, 2/3, 4/3), while in meantone you end up with the same C with which you started (this is also true for standard notation which is essentially a written representation of meantone). In hanson, the interval approximating 6/5 is 6 times smaller than the one approximating 3/1, which means that if you rise by 6 minor thirds and then fall by a „twelfth“ (although these names actually shouldn’t be used outside the meantone context), you finish where you started. This is impossible to represent in standard notation because the kleisma (15625/15552) isn’t tempered out in meantone -- i.e. 6 minor thirds minus a twelfth come out as B#, D#, F#, A, C, Eb, Gb, Cb -- and not B#. Similarly, if you convert the original JI sequence of „5/6, 4/3, 2/3, 4/3“ to hanson, you don’t arrive at the pitch you started with because the syntonic comma isn’t tempered out there.

Not sure if you’ve read my replies to your questions in messages #86312 and #86311 but I think this should give you a lot of answers you were looking for.

Petr

Dear John,

Thanks for this clarification. (I understood that you indented your slides for a different audience and did not want to make things overcomplicated..)

Best wishes,
Torsten

On 14.02.2010, at 05:47, jlmoriart wrote:
> Sorry about the powerpoint presentation, it's unfinished and not > well worded. I'm not sure what it sounded like I said, but what I > mean is this:
>
> In the <b>Syntonic temperament</b>, the generators are the fifth and > octave. The Syntonic Temperament defines each tonal/harmonic/> diatonic function as a located in the stack of fifths's reduced into > every octave. In order for the described functions to be retained, > the fifth can not be above 720 cents or below 686. Above or below > these value, fourths overlap with fifths, thirds overlap with > fourths, etc. These values are called the Sytonic Temperament's > "Valid Tuning Range".
>
> This subject is described here:
> http://www.mitpressjournals.org/doi/pdf/10.1162/comj.2007.31.4.15
>
> Other 2D temperaments can have any two generators, but generally > they tend to be a tempered variations of just intonation intervals, > one of which is almost always the octave, or 2/1. The Syntonic > Temperament tempers the 3/2 major fifth, the Magic Temperament > tempers the 5/4 major third, and the Hanson Temperament tempers the > 6/5 minor third, and so on.
>
> 2D temperaments do not merely define mappings of notes to pitches, > but also of partials to pitches, as is described in this paper > declaring "The Matrix" as a new parsimonious paradigm for music:
> http://www.igetitmusic.com/papers/Matrix.pdf
>
> Each Temperament defines certain locations within the matrix (or > locations in the stack of generators reduced by the period)as the > pitches for a partial of a timbre, this allowing for both maximized > sensory consonance in the tuning as well as for appropriate harmonic > function.
>
> Consequently there are temperaments other than the Syntonic that > also use the functions of the octave and fifth as generators, but > map the acquired pitches to different partials. One such temperament > is the Schismatic Temperament which, instead of using the major > third (or, more specifically, up 4 fifths, down 2 octaves) for > triadic harmony, uses the diminished fourth (or down 8 fifths and up > 5 octaves). It places the tempered timbres partials differently than > the Syntonic Temperament does making each tuning it creates > functionally different. It also has a different valid tuning range.
>
> Is this more clear? I'm not an expert on these subjects, but this > has been my understanding.
>
> John Moriarty
>

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Hi, everybody,

I've gotten replies from Torsten, Chris, Daniel, and Carl, which I've saved to a text file.

Also from Aaron. It's absolutely ok if you want to join any discussion about this.

Everyone, keep in mind that, although I had a lot of hands-on in the 90's with my own idiosyncratic extended-Just tuning--that I played on 3 stacked Midi controllers--I know almost nothing about the current state of the art.

I mean both in terms of technology and thinking about the scales.

Give me a little while to digest, and I'll get back on this.

Thanks,

Caleb

>"Well, first off, the idea that the brain perceives multiple harmonic
structures in the same chord is far from new... Folks have been
throwing that idea around for a while."
Bizarre thing is...I posted the first message in this thread about a week ago and only now am I getting this answer and/or even a single person mentioning there is evidence for such a theory already being studied.

I am not surprised at all that there is, but I have been surprised how many people on this list seem stuck on the idea that the is only one virtual root tone for a "valid" consonant chord (and anyone who thinks otherwise must simply be uneducated). Finally, it sounds like you may have opened the door on this one. :-)
******************************************************
>"I'm actually coming up with a model for this now. I think that the idea is, the chord will have an entire "harmonic profile" that pops up when it's heard, which consists of all of the possible periodicities
heard in that chord."
>"the C-G dyad as a 2:3, and the C-E, the E-G, and the C-E-G which all refer to a root 2 octaves
below the C."
Ok, here's the odd thing (at least as I calculated it), they don't all seem to point to just one virtual root.
The C-G indeed seems to point to 2:3 with the virtual pitch being 1/2 or an octave below it IE the 2:4 in (2 virtual pitch):4:5:6. Meanwhile the C-E dyad seems to imply a harmonic series of 1:2:3:4 leading up to the 4 in 4:5:6...thus representing a 1/4 IE double octave below the root. The 5:6 also seems to point to the same harmonic series. So even then, according to my calculations, we have both an octave and a double octave below the 4 in 4:5:6 as virtual root tones. The only way to get a single virtual root tone then appears to be a 1:2:3 chord, which makes sense since it's literally is a triad at the root of the harmonic series.

>"This manifests itself in a very predictable way: you simultaneously hear the C-E-G as notes themselves, the C-G as a solid dyad with a root an octave below, the C-E and E-G as solid dyads with roots 2
octaves below, and C-E-G as a solid triad with a rood two octaves below."
Actually there, man I jumped the gun and wrote the above before I read this. It seems you clarified it yourself it seems...it doesn't simply point to the one virtual pitch two octaves below, but two tones (one and two octaves below).
********************************************************************************************************
>"Subharmonic profile + apparent profile = harmonic profile."
Exactly...and now IMVHO its time to make some good postings about what makes subharmonic tones clash more vs. sound better, how many the brain seems to be able to handle at ones confidently, how "low" a virtual tone can be before the brain loses track of it (esp. if you get very high in the harmonic series far as ratios)...now that we seem to agree how they are derived. :-)
********************************************************************************************************
>"A major triad doesn't sound "better" than a minor one. It's just different."
True, it's not "better" but perhaps "tenser" is a better word. I certainly don't avoid using minor chords as much or more than major ones in practice, heck I throw in things like chords with semitones at times in personal compositions.

> He's a regular mapper (we should make t-shirts). Did you
> see the RTF document he just put in the Files section?

Haha! BRB, designing "I map regularly" t-shirts. And then maybe the
serious regular mappers could get "I regularly map regularly" shirts.

> It looks like Mike is just diving into regular mapping.
> Maybe you can collab with him a bit.
>
> Or search the archives for "regular mapping" or
> "regular temperament" and read anything you find by Graham,
> myself, Herman, Petr, etc.

Yeah, to Caleb I recommend Graham's "Regular Mapping Paradigm"
walkthrough - makes it very clear.

I've also been trying to figure out for some time now how to design a
cheap DIY microtonal controller. It would be trivial to design the
MIDI architecture with an Arduino microcontroller or something like
that. The only problem - where am I going to find a huge regularly
mapped button array to use? Computer keyboards are hardly adequate.

-Mike

Look into Korg's nano series

They have 3 types of devices in the $50 range with pressure sensitive pads,
keys, etc.

http://www.korg.com/nanoseries

It might be worth hacking.

On Sun, Feb 14, 2010 at 1:50 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> > He's a regular mapper (we should make t-shirts). Did you
> > see the RTF document he just put in the Files section?
>
> Haha! BRB, designing "I map regularly" t-shirts. And then maybe the
> serious regular mappers could get "I regularly map regularly" shirts.
>
> > It looks like Mike is just diving into regular mapping.
> > Maybe you can collab with him a bit.
> >
> > Or search the archives for "regular mapping" or
> > "regular temperament" and read anything you find by Graham,
> > myself, Herman, Petr, etc.
>
> Yeah, to Caleb I recommend Graham's "Regular Mapping Paradigm"
> walkthrough - makes it very clear.
>
> I've also been trying to figure out for some time now how to design a
> cheap DIY microtonal controller. It would be trivial to design the
> MIDI architecture with an Arduino microcontroller or something like
> that. The only problem - where am I going to find a huge regularly
> mapped button array to use? Computer keyboards are hardly adequate.
>
> -Mike
>
>

--- In tuning@yahoogroups.com, "jlmoriart" wrote:
> http://www.igetitmusic.com/papers/Matrix.pdf

Hyperbolic language using academic references to
prop up an obvious agenda is not scholarship; it is
propaganda. That, along with the URL, gives away
the author of this paper, though his name is not
stated.

The theory is fine. DT is fine. The substantive ideas
are all fine, but the author of this paper has no
substantive ideas of his own, only an agenda.
Pseudo-scholarship and bandwagon marketing
propaganda are not fine.

I get it, for sure. The revolution will not be televised.

I mean no offense to John Moriaty, whose posts have
been clear and well reasoned and obviously not the
same as this paper. I responded to an earlier post in
this thread, expressing concerns about the language
used to describe DT theory, and I believe that
improving the language will help the theory, which
can stand on its own merits and doesn't need propping
up.

Yours,
AAH
=====

Eh, what I really need is something more like this:

http://img.alibaba.com/photo/253336348/POS_Programmable_Keyboard.jpg

Except I don't need a magnetic card reader and security lock and all of
that. I also don't even really need it to be programmable. A cannibalized
button panel would do fine.

-Mike

On Sun, Feb 14, 2010 at 2:22 PM, Chris Vaisvil <chrisvaisvil@...m>wrote:

>
>
> Look into Korg's nano series
>
> They have 3 types of devices in the $50 range with pressure sensitive pads,
> keys, etc.
>
> http://www.korg.com/nanoseries
>
> It might be worth hacking.
>
>
> On Sun, Feb 14, 2010 at 1:50 PM, Mike Battaglia <battaglia01@...>wrote:
>
>>
>>
>> > He's a regular mapper (we should make t-shirts). Did you
>> > see the RTF document he just put in the Files section?
>>
>> Haha! BRB, designing "I map regularly" t-shirts. And then maybe the
>> serious regular mappers could get "I regularly map regularly" shirts.
>>
>> > It looks like Mike is just diving into regular mapping.
>> > Maybe you can collab with him a bit.
>> >
>> > Or search the archives for "regular mapping" or
>> > "regular temperament" and read anything you find by Graham,
>> > myself, Herman, Petr, etc.
>>
>> Yeah, to Caleb I recommend Graham's "Regular Mapping Paradigm"
>> walkthrough - makes it very clear.
>>
>> I've also been trying to figure out for some time now how to design a
>> cheap DIY microtonal controller. It would be trivial to design the
>> MIDI architecture with an Arduino microcontroller or something like
>> that. The only problem - where am I going to find a huge regularly
>> mapped button array to use? Computer keyboards are hardly adequate.
>>
>> -Mike
>>
>
>
>

On 14.02.2010, at 07:41, Daniel Forró wrote:
> Another method I use often is to combine more MIDI channels for one
> sound and tune notes differently on them, so by combining those
> channels I get all notes I need.

Sure.

Caleb mention that he is using Logic, and Logic only allows for a
single global tuning for the softsynths it ships. So, for your
approach you need some gear where the pitches can be tuned
individually (e.g., with a Scala file, not by pitch bend) and where
you can tune multiple channels individually.

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Yes but I think that whatever explains this is not some faculty
> > that literally mathematically calculates interval composites as
> > multiples of rational numbers. A more likely explanation is our
> > familiarity with major 7th chords. This kind of explanation is
> > cognitive: hearing major 7ths as 3rd + 5th is based on a mental
> > schema of diatonic structure. Of course such mental schemata
> > don't have to conform to the logic of rational numbers.
>
> I agree with that, but if you listen closely enough, you notice that
> often it does. That is, the tritone C-F# can function in a thousand
> possible ways. Play that tritone, then imagine it as part of a D7
> chord. Then imagine it as part of an Ab7 chord. Then imagine it as
> part of a C7#11 chord, and then a Cmaj7#11 chord. Voila, same thing.
> You're "imagining" different bridges from C to F#.
>
> The only thing is that you treat this purely in psychological terms
> - in terms of mental schemata and such - but I think that it isn't
> quite so isolated. You have a bit of influence in how you hear a
> chord, and the schema that pops up when you hear it is a part of
> it. Play a 350 cent third and then "imagine" that it's a really
> flat 6/5, and then "imagine" it as a really flat 5/4. Voila again.
> The same thing is happening here as above. I think what's happening
> here is that when you imagine other notes in addition to a chord,
> your brain basically analyzes the notes you hear + the ones you
> imagine all together. It just gives the imagined notes less
> "weight," the same as if they existed in real life but at a lower
> volume.

If you mean that the higher cognitive level can feed back and have
a "downward" influence on the lower sensory and perceptual levels, I
agree.

> > Yes but I really doubt that the interval from C to D# is thereby
> > literally represented in the brain as the ratio 32:75 even if it
> > is tuned so. I'm not even sure if I hear that chord in the way
> > that spelling suggests when it is played alone without any tonal
> > context.
>
> You hear the C-E, the E-B, and the B-D#. If you can't hear this as a
> coherent chord but rather some dissonant stack of noise, I would
> expect your brain would hear it more as "bitonal" or "polytonal" -
> consisting of multiple harmonic structures - and not have the 32:75.
> However, if you can hear the whole thing as a single harmonic
> structure, I think that would imply the 32:75 has been recognized.

The hearing of that particular harmonic structure is indeed
"modelled" quite well with rational number math. But although integer
ratios have an important role in the explanation of psychoacoustic
consonance and root perception I suspect that the brain doesn't
literally use rational number math in the perception and cognition of
music. Not only is this a bit hard to believe but JI doesn't even
generally work as a theory of music perception because there are many
commonly used chords that cannot be analyzed in terms of JI. Play the
chord A:C:D:G in some meantone tuning, for example 12-equal. A:C is
heard as a minor 3rd, A:D and D:G are heard as 4ths and C:G is heard
as a 5th. The chord sounds perfectly natural and commonplace but it
nevertheless cannot be tuned in JI so that all those intervals
are pure! Ergo, diatonic hearing and structure cannot be modelled
with JI math and this makes the claim that the brain analyzes music
in terms of JI dubious.

> > I tried this and what a kick-ass experiment it is, really
> > interesting! But I fail to see its' relevance to what I said.
>
> It's relevant to what you said here:
>
> > > > It doesn't calculate the relations of frequency ratios further
> > > > than the basic first-order level. Why would it do that? What
> > > > evolutionary reason would there be for the existence of such a
> > > > faculty. How would it help in hearing speech sounds for
> > > > example?
>
> When you said this, you mentioned that the brain doesn't "remember"
> previous frequency ratios and that's why comma pumps don't cause you
> to become psychotic.

No, I didn't say that. Of course the brain remembers previous
intervals to an extent. Tempered comma pump progressions sound fine
because we hear them diatonically. There is even a diatonic math that
models this but it cannot be based on JI. It is actually the JI comma
pumps that sound weird and "unnatural" to intonationally naive
western listeners! How can that be if the brain represents music
in terms of JI?

Kalle Aho

> > You hear the C-E, the E-B, and the B-D#. If you can't hear this as a
> > coherent chord but rather some dissonant stack of noise, I would
> > expect your brain would hear it more as "bitonal" or "polytonal" -
> > consisting of multiple harmonic structures - and not have the 32:75.
> > However, if you can hear the whole thing as a single harmonic
> > structure, I think that would imply the 32:75 has been recognized.
>
> The hearing of that particular harmonic structure is indeed
> "modelled" quite well with rational number math. But although integer
> ratios have an important role in the explanation of psychoacoustic
> consonance and root perception I suspect that the brain doesn't
> literally use rational number math in the perception and cognition of
> music. Not only is this a bit hard to believe but JI doesn't even
> generally work as a theory of music perception because there are many
> commonly used chords that cannot be analyzed in terms of JI. Play the
> chord A:C:D:G in some meantone tuning, for example 12-equal. A:C is
> heard as a minor 3rd, A:D and D:G are heard as 4ths and C:G is heard
> as a 5th. The chord sounds perfectly natural and commonplace but it
> nevertheless cannot be tuned in JI so that all those intervals
> are pure! Ergo, diatonic hearing and structure cannot be modelled
> with JI math and this makes the claim that the brain analyzes music
> in terms of JI dubious.

That's a great example. I figuring out why that chord works is the
same as why my chord progression works.

Yeah, A:C:D:G (and some other even worse chords I've sound) screw it
up. But what I think is happening is the same thing that's happening
with C-Ev-G: the Ev will tend to "flip" back and forth between Eb and
E, and in this case, the C, D, and G will "flip" back and forth
between C:D:G and C+:D+:G+. However, not only is C:D:G/C+:D+:G+ a much
more subtle change than Eb/E - I don't think many listeners could
recognize such a perceptual change if they hear it.

Since it's easy for us to put a label on the way we're perceiving the
C-Ev-G example - as the first dyad being "major" (5/4) vs "minor" -
that example is relatively easy to figure out. However - we're not
used to a system of tuning in which 32/27 and 6/5 are different
intervals, nor in which 4/3 and 27/20 are different intervals, nor in
which 16/9 and 9/5 are different intervals. So my theory is that our
modes of perception for these intervals are constantly shifting
without us really being aware of this. Alternatively, or perhaps it's
more that our 12-tet experience of a minor seventh just is 16/9 and
9/5 all smushed together.

So I guess in the end I really am saying what you're saying, but in a
slightly different way. We do perceive music in terms of more
"diatonic" pitch sets and intervals - at least for now, since that's
what we're used to - but these diatonic pitch sets can then be
analyzed in terms of JI. Each equal tempered interval can map back to
more than one JI pitch, but mentally, schematically, we just lump all
of these possible JI functions into the same schema for the chord.

> > When you said this, you mentioned that the brain doesn't "remember"
> > previous frequency ratios and that's why comma pumps don't cause you
> > to become psychotic.
>
> No, I didn't say that. Of course the brain remembers previous
> intervals to an extent. Tempered comma pump progressions sound fine
> because we hear them diatonically. There is even a diatonic math that
> models this but it cannot be based on JI. It is actually the JI comma
> pumps that sound weird and "unnatural" to intonationally naive
> western listeners! How can that be if the brain represents music
> in terms of JI?

Well, one thing's for sure - you're absolutely right about that. But
how does the diatonic math work? It can't just be arbitrary, JI has to
be involved -somewhere- down the line.

-Mike

--- In tuning@yahoogroups.com, "Kalle" wrote:
> Play the chord A:C:D:G in some meantone tuning,
> for example 12-equal. A:C is heard as a minor 3rd,
> A:D and D:G are heard as 4ths and C:G is heard
> as a 5th. The chord sounds perfectly natural and
> commonplace but it nevertheless cannot be tuned in JI
> so that all those intervals are pure!

How's that? I immediately see at least two easy ways to
tune the chord A:C:D:G in JI.

(1) 15:18:20:27

A to +C is 5:6
A to D is 3:4
A to +G is 5:9

(2) 12:14:16:21

A to ~C is 6:7
A to D is 3:4
A to ~G is 4:7

> Ergo, diatonic hearing and structure cannot be modelled
> with JI math and this makes the claim that the brain
> analyzes music in terms of JI dubious.

I'm not making any claims, just saying, that chord certainly
can be tuned so that all intervals are pure, and in more than
one way. Maybe I missed something in the discussion.

Yours,
AAH
=====

--- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@...> wrote:
>
> --- In tuning@yahoogroups.com, "Kalle" wrote:
> > Play the chord A:C:D:G in some meantone tuning,
> > for example 12-equal. A:C is heard as a minor 3rd,
> > A:D and D:G are heard as 4ths and C:G is heard
> > as a 5th. The chord sounds perfectly natural and
> > commonplace but it nevertheless cannot be tuned in JI
> > so that all those intervals are pure!
>
> How's that? I immediately see at least two easy ways to
> tune the chord A:C:D:G in JI.
>
> (1) 15:18:20:27
>
> A to +C is 5:6
> A to D is 3:4
> A to +G is 5:9
>
> (2) 12:14:16:21
>
> A to ~C is 6:7
> A to D is 3:4
> A to ~G is 4:7

We have to consider all the dyads in the chord.
In tuning 1, D to G is 20:27, and in tuning 2 this
interval is 16:21. Both of these are wolf fourths.
Meantone makes the wolf go away in tuning 1, and
pajara (think 22-ET) makes it go away in tuning 2.

In the past there has been lengthy discussion about
these so-called "magic" chords (also called "super
saturated suspensions" by analogy to chemistry).
Other examples include the dim7 and augmented triad.
I've synthesized many versions of these, and usually
there is a JI version that sounds at least as good
as the tempered version -- but not in all inversions.
That is, comparing all inversions, the tempered tuning
sounds better. In the case of C F Bb Eb for instance,
9:12:16:21 sounds best to my ear. But if the 16:21 is
in any other position than on top, the 22-ET version
sounds better. YMMV.

-Carl

Carl,

Has there been any research done on the perception of these chords
that have small commas tempered out of them? I think my understanding
of it is pretty good, but it would be nice to see some kind of hard
data on the subject.

-Mike

> We have to consider all the dyads in the chord.
> In tuning 1, D to G is 20:27, and in tuning 2 this
> interval is 16:21. Both of these are wolf fourths.
> Meantone makes the wolf go away in tuning 1, and
> pajara (think 22-ET) makes it go away in tuning 2.
>
> In the past there has been lengthy discussion about
> these so-called "magic" chords (also called "super
> saturated suspensions" by analogy to chemistry).
> Other examples include the dim7 and augmented triad.
> I've synthesized many versions of these, and usually
> there is a JI version that sounds at least as good
> as the tempered version -- but not in all inversions.
> That is, comparing all inversions, the tempered tuning
> sounds better. In the case of C F Bb Eb for instance,
> 9:12:16:21 sounds best to my ear. But if the 16:21 is
> in any other position than on top, the 22-ET version
> sounds better. YMMV.
>
> -Carl
>
>

You mean like, peer-reviewed research? No.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Carl,
>
> Has there been any research done on the perception of these
> chords that have small commas tempered out of them? I think
> my understanding of it is pretty good, but it would be nice
> to see some kind of hard data on the subject.
>
> -Mike
>
> > We have to consider all the dyads in the chord.
> > In tuning 1, D to G is 20:27, and in tuning 2 this
> > interval is 16:21. Both of these are wolf fourths.
> > Meantone makes the wolf go away in tuning 1, and
> > pajara (think 22-ET) makes it go away in tuning 2.
> >
> > In the past there has been lengthy discussion about
> > these so-called "magic" chords (also called "super
> > saturated suspensions" by analogy to chemistry).
> > Other examples include the dim7 and augmented triad.
> > I've synthesized many versions of these, and usually
> > there is a JI version that sounds at least as good
> > as the tempered version -- but not in all inversions.
> > That is, comparing all inversions, the tempered tuning
> > sounds better. In the case of C F Bb Eb for instance,
> > 9:12:16:21 sounds best to my ear. But if the 16:21 is
> > in any other position than on top, the 22-ET version
> > sounds better. YMMV.
> >
> > -Carl
> >
> >
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "hpiinstruments" <aaronhunt@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Kalle" wrote:
> > > Play the chord A:C:D:G in some meantone tuning,
> > > for example 12-equal. A:C is heard as a minor 3rd,
> > > A:D and D:G are heard as 4ths and C:G is heard
> > > as a 5th. The chord sounds perfectly natural and
> > > commonplace but it nevertheless cannot be tuned in JI
> > > so that all those intervals are pure!
> >
> > How's that? I immediately see at least two easy ways to
> > tune the chord A:C:D:G in JI.
> >
> > (1) 15:18:20:27
> >
> > A to +C is 5:6
> > A to D is 3:4
> > A to +G is 5:9
> >
> > (2) 12:14:16:21
> >
> > A to ~C is 6:7
> > A to D is 3:4
> > A to ~G is 4:7
>
> We have to consider all the dyads in the chord.

OK, I assumed there had to be some reason these
dead simple answers I gave would not give
satisfaction ...

But, I also beg to differ with this "having to" consider all
the dyads. Overkill IMO. It's a chord. When you have a
chord, who cares about dyads? Tune something as it
needs to be tuned. When you have a dyad, tune it to
its best tuning. When you have a chord, tune that to
its best tuning. You don't hear the wolf intervals when
they are part of the chord ... now I'm not trying to start
anything here; I'm fully aware of the problems that
arise melodically.

Oh well, I wasn't paying much attention. Sorry about
that.

Carry on, gentlemen.
AAH
=====

> In tuning 1, D to G is 20:27, and in tuning 2 this
> interval is 16:21. Both of these are wolf fourths.
> Meantone makes the wolf go away in tuning 1, and
> pajara (think 22-ET) makes it go away in tuning 2.
>
> In the past there has been lengthy discussion about
> these so-called "magic" chords (also called "super
> saturated suspensions" by analogy to chemistry).
> Other examples include the dim7 and augmented triad.
> I've synthesized many versions of these, and usually
> there is a JI version that sounds at least as good
> as the tempered version -- but not in all inversions.
> That is, comparing all inversions, the tempered tuning
> sounds better. In the case of C F Bb Eb for instance,
> 9:12:16:21 sounds best to my ear. But if the 16:21 is
> in any other position than on top, the 22-ET version
> sounds better. YMMV.
>
> -Carl