Re: [tuning-math] Digest Number 331

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.