Manuel: Thanks for the counter-example to CS equalling strict propriety.

I stand corrected

As for harmonic and inharmonic vocal timbres. I was apparently mistaken.

What confused me was the fact that outside of the European culture area,

vocal timbres are usually nasal and/or strident and their use may be

correlated with non-JI (or close approximations) tunings and intervals.

For example, how harmonic is the spectrum of the Indonesian singing

voice or that of American Indians? For that matter, how harmonically

related are the formants of speech in many languages (Khoisan, North

Caucasian, etc.). It seemed to me that to produce the clear harmonic

tone of European singing (primarily Church and Italianate styles) takes

a lot of training. Untrained voices often sound less harmonic to me, but

I could be wrong.

How in tune are the harmonics and are the usual pitches of the vowel

formants for most speakers actually close to harmonics? I don't know. Is

this information in the literature (Sundberg, perhaps?)?

--John

> From: tuning-math@yahoogroups.com

> Reply-To: tuning-math@yahoogroups.com

> Date: 29 Mar 2002 16:15:12 -0000

> To: tuning-math@yahoogroups.com

> Subject: [tuning-math] Digest Number 331

>

> that's the pentachordal decatonic scale -- hopefully you're also

> aware of the symmetrical decatonic i proposed. each of the two

> decatonics can be seen as a pair of interlaced 3/2-generated

> pentatonics -- in the symmetrical case the separation is 600 cents

> instead of 109 cents.

Hence my diagram

>

> (note that there is no 'equal' in the title of my paper).

Seems that I have a duff titled copy then. Apologies : I will correct it

asap.

>

> it seems you are choosing a mode without a 4/3 over the tonic --

> nothing inherently wrong with this choice, but i wonder what is

> motivating it. most likely we have different views about which

> properties of the diatonic scale are appropriate to keep in the

> process of generalization -- it would be fun to flesh this out.

I am off for the next few days, but I will get back to you on this. I will

say that I considered the 5 pentatonic

as 9 0 2 4 7 9 0 2 4 7

3 2 2 3 2 3 2 2 3 etc

22 Tone:

11 13 16 18 20 0 2 4 7 9 11 13 16

2 3 2 2 2 2 2 3 2 2 2 3

The decatonic, like the pentatonic, has two groups of 2s. Taking the smaller

group and putting 3s around it we get:

4 7 9 11 13 16

3 2 2 2 3

Then choosing the top tone : 16, in the same way as the pentatonic:

4 7 9 0 Choosing 0.

3 2 3

That was my choice, based purely on shape and symmetry. No maths at all.

The other 'tonic' is the inverse of this: 4 for the pentatonic, and 4 again

for the decatonic in my web 'sheet'.

As for the choice of cyclic intervals for the 'generators', or the grid

intervals, these came about by the simple method of searching manually until

the pentatonics arose. I then simply overlaid the necessary transposed

pentatonic. The tonic derivation I give above. I will look at your other

decatonics in due course. If this is all very unmathematical, then I am not

ashamed to say that the 'maths' is not of concern to me, only the 'shapes'.

Mark

Mark

--- In tuning-math@y..., John Chalmers <JHCHALMERS@U...> wrote:

> Manuel: Thanks for the counter-example to CS equalling strict

propriety.

> I stand corrected

>

> As for harmonic and inharmonic vocal timbres. I was apparently

mistaken.

> What confused me was the fact that outside of the European culture

area,

> vocal timbres are usually nasal and/or strident and their use may be

> correlated with non-JI (or close approximations) tunings and

intervals.

> For example, how harmonic is the spectrum of the Indonesian singing

> voice or that of American Indians?

perfectly harmonic, with a certain amount of noise, as always.

> For that matter, how harmonically

> related are the formants of speech in many languages (Khoisan, North

> Caucasian, etc.).

i don't know what you mean by 'harmonically related formants'.

formants are recognized by their absolute frequency, and of course

they operate by amplifying harmonics near that frequency. but . . . ?

> It seemed to me that to produce the clear harmonic

> tone of European singing (primarily Church and Italianate styles)

takes

> a lot of training. Untrained voices often sound less harmonic to

me, but

> I could be wrong.

they may contain more noise, but do an fft (or anything like that)

and you won't find a systematic significant deviation of the partials

from a harmonic series, in one direction or the other.

> How in tune are the harmonics and are the usual pitches of the vowel

> formants for most speakers actually close to harmonics?

again, not sure what you mean by this.

--- In tuning-math@y..., Mark Gould <mark.gould@a...> wrote:

>

>

> > From: tuning-math@y...

> > Reply-To: tuning-math@y...

> > Date: 29 Mar 2002 16:15:12 -0000

> > To: tuning-math@y...

> > Subject: [tuning-math] Digest Number 331

> >

> > that's the pentachordal decatonic scale -- hopefully you're also

> > aware of the symmetrical decatonic i proposed. each of the two

> > decatonics can be seen as a pair of interlaced 3/2-generated

> > pentatonics -- in the symmetrical case the separation is 600 cents

> > instead of 109 cents.

> Hence my diagram

> >

>

> > (note that there is no 'equal' in the title of my paper).

> Seems that I have a duff titled copy then. Apologies : I will

correct it

> asap.

> >

> > it seems you are choosing a mode without a 4/3 over the tonic --

> > nothing inherently wrong with this choice, but i wonder what is

> > motivating it. most likely we have different views about which

> > properties of the diatonic scale are appropriate to keep in the

> > process of generalization -- it would be fun to flesh this out.

>

> I am off for the next few days, but I will get back to you on this.

I will

> say that I considered the 5 pentatonic

>

> as 9 0 2 4 7 9 0 2 4 7

> 3 2 2 3 2 3 2 2 3 etc

>

> 22 Tone:

>

> 11 13 16 18 20 0 2 4 7 9 11 13 16

> 2 3 2 2 2 2 2 3 2 2 2 3

>

> The decatonic, like the pentatonic, has two groups of 2s. Taking

the smaller

> group and putting 3s around it we get:

>

> 4 7 9 11 13 16

> 3 2 2 2 3

>

> Then choosing the top tone : 16, in the same way as the pentatonic:

>

> 4 7 9 0 Choosing 0.

> 3 2 3

>

> That was my choice, based purely on shape and symmetry. No maths at

all.

so analogy based on outward appearance.

i use just as little math in my paper. but i feel i base my choices

on less arbitrary and more acoustically plausible criteria. i show

that the 'statically tonal' modes of the pentatonic scale are the

familiar major and minor pentatonic modes, correctly identify the

most tonal modes of the diatonic scale, and go on to present choices

for the decatonic scale which seem to hold up remarkably well in

continued musical exploration on 22-tone instruments.

> As for the choice of cyclic intervals for the 'generators', or the

grid

> intervals, these came about by the simple method of searching

manually until

> the pentatonics arose.

if you draw an actual harmonic lattice of 22-equal, where the 'rungs'

are the 7-limit consonant intervals, you'll see these pentatonics

immediately (each living within a single 3-7 plane). no searching

necessary.

> I then simply overlaid the necessary transposed

> pentatonic. The tonic derivation I give above. I will look at your

other

> decatonics in due course. If this is all very unmathematical, then

I am not

> ashamed to say that the 'maths' is not of concern to me, only

the 'shapes'.

likewise. i think one can peer a little deeper into the shapes, and

i'm excited at the opportunity to share what i (and others like gene)

have discovered with you. hope you'll be patient with my exuberance!

>they may contain more noise, but do an fft (or anything like that)

>and you won't find a systematic significant deviation of the partials

>from a harmonic series, in one direction or the other.

Do you know of any web site where they did this? Would there be any

point in having the boys over on the main list run some stuff through

their latest?

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> Would there be any

> point in having the boys over on the main list run some stuff

through

> their latest?

>

> -Carl

sure -- or we could ask francois, as he's apparantly done plenty of

analyses on human voices. i'm quite confident we won't find human

voices with statistically significantly stretched or contracted

partials relative to the harmonic series -- the vocal folds simply

have no way of vibrating in such a manner.

>sure -- or we could ask francois, as he's apparantly done plenty of

>analyses on human voices. i'm quite confident we won't find human

>voices with statistically significantly stretched or contracted

>partials relative to the harmonic series -- the vocal folds simply

>have no way of vibrating in such a manner.

Why does it have to be stretched or contracted? What about random

differences on each partial, say of over 10 cents? Is such a thing

possible?

-Ca.

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> >sure -- or we could ask francois, as he's apparantly done plenty

of

> >analyses on human voices. i'm quite confident we won't find human

> >voices with statistically significantly stretched or contracted

> >partials relative to the harmonic series -- the vocal folds simply

> >have no way of vibrating in such a manner.

>

> Why does it have to be stretched or contracted? What about random

> differences on each partial, say of over 10 cents?

sure. you can add that to my statement, if you wish.