Researchers rediscover just intonation by analyzing speech formants

Most of the results are obvious to us microtonalists, but nevertheless I found it interesting to read.

http://www.pnas.org/cgi/gca?allch=&SEARCHID=1&FULLTEXT=vowel&FIRSTINDEX=0&hits=10&RESULTFORMAT=&gca=pnas%3B0703140104v1&allchb=

It shows among other things which JI intervals are most common between formants in speech, and shows the ranges of formants in males and females in terms of what harmonics they can emphasize.

Perhaps this post would be better on the tuning or tuning-math list but I am not subscribed there anymore so I apologize. Feel free to move it there.

/ Magnus

> I'd love to see their evidence that "throughout history and
> across cultures" people use 12 tones/octave.

Yup. They always seem to just take is as postulated. A bit annoying, eh.

> There are so many of these neuroscience/music papers now
> that get the basics wrong I've given up caring.

Maybe time for someone to take a crack at debunking such papers? Or at
least debunking the assumptions. Why not a letter to the editor of PNAS?

Rick

Greetings,

Perhaps an article for the Skeptical Enquirer? Actually a letter would be very good.

All best wishes,

Gordon Rumson

On 26-May-07, at 12:50 PM, Rick McGowan wrote:

>> I'd love to see their evidence that "throughout history and
>> across cultures" people use 12 tones/octave.
>
> Yup. They always seem to just take is as postulated. A bit > annoying, eh.
>
>> There are so many of these neuroscience/music papers now
>> that get the basics wrong I've given up caring.
>
> Maybe time for someone to take a crack at debunking such papers? Or at
> least debunking the assumptions. Why not a letter to the editor of > PNAS?

At 11:50 AM 5/26/2007, you wrote:
>> I'd love to see their evidence that "throughout history and
>> across cultures" people use 12 tones/octave.
>
>Yup. They always seem to just take is as postulated. A bit annoying, eh.
>
>> There are so many of these neuroscience/music papers now
>> that get the basics wrong I've given up caring.
>
>Maybe time for someone to take a crack at debunking such papers? Or at
>least debunking the assumptions. Why not a letter to the editor of PNAS?
>
> Rick

I might just. I'm reading the new paper now...

The abstract is apparently a bit of salesmanship. They don't
go into the '12 tones is universal' claim in the text. Instead
they say that 'pentatonic and diatonic subsets of the chromatic
scale' are universal. There's some truth to this, but the text
still seems to state it much too strongly.

Another part of the text is worth quoting at length:

""
...the present results are pertinent to the longstanding argument
in music about which of several tuning systems is "natural". In
so far as the observations here inform this argument, the observed
ratios in speech spectra accord most closely with a just intonation
tuning system. Ten of the 12 intervals generated by the analysis of
either English or Mandarin vowel spectra are those used in just
intonation tuning, whereas 4 of the 12 match the Pythagorean tuning
and only 1 of the 12 intervals matches those used in equal
temperament. The two anomalies in our data with respect to just
intonation concern the minor second and the tritone. The interval
ratio of the minor second defined by F2/F1 in speech is 1.0625
whereas, in just intonation (which is based on maintaining perfect
fifths and major thirds in each octave), this interval is 1.0667.
This difference occurs because 1.0667 is the ratio of 16:15, which
does not occur in speech because the range of maximum intensity in
the first formant peak extends only up to the 10th harmonic. Our
value of 1.0625 for the minor second arises from formant ratios
of 17:8, 17:4, and 17:2 (see Fig. 3 and Methods). Similarly, our
value for the tritone is 1.400 whereas the just intonation value
is 1.406. This difference arises because 1.406 is the ratio of
45:32, which again does not occur in speech, in this case because
the range of maximum intensity in the second formant peak extends
only up to the 26th harmonic. The values 1.400 in speech arise
from the F2/F1 ratios in the database of 7:5, 14:5, 21:5, 14:10,
and 21:10 (see again Fig. 3 and Methods). In summary, just
intonation tuning closely fits the chromatic scale defined by
speech data. The fact that instruments in just intonation tuning
are widely agreed to sound "brighter" than in the equal temperament
tuning used for the last three centuries (a compromise that allows
multiple instruments to play pieces that include notes in more than
one key) is in keeping with our conclusion that the chromatic scale
arises from formant ratios in speech.""

So they actually do reach the right conclusions, but they frame
it in a language that makes it sounds wrong. They find that JI
is a better fit than ET, even though they aren't giving themselves
credit for 7:5 and 17:16! And they say that ET has been used for
300 years, which is wrong.

-Carl

> ....the present results are pertinent to the longstanding argument
> in music about which of several tuning systems is "natural". [etc]

Ah, yes, I liked that part too.

> So they actually do reach the right conclusions, but they frame
> it in a language that makes it sounds wrong.

Some of the right conclusions, but stated too strongly in terms of
chromaticism, rather than in terms of just ratios.

Rick

--- In MakeMicroMusic@yahoogroups.com, Rick McGowan <rick@...> wrote:
>
> > I'd love to see their evidence that "throughout history and
> > across cultures" people use 12 tones/octave.
>
> Yup. They always seem to just take is as postulated. A bit annoying, eh.
>
> > There are so many of these neuroscience/music papers now
> > that get the basics wrong I've given up caring.

It's not only the neuroscience/music people who get the basics wrong. Many on the tuning
associated lists have the same problem.

>
> Maybe time for someone to take a crack at debunking such papers? Or at
> least debunking the assumptions. Why not a letter to the editor of PNAS?
>
> Rick
>
Go for it.

Rick

I have even more problems with this paper that Carl does.

The author(s) seem to have managed to think beyond 12edo.
They have acknowledged that something interesting is happening at integer frequency
ratios.
Yet like Carl and many of the other "JI-blinded" (or should it be "JI-deafened") experts,
they have failed to think past this paradoxical anomaly to the next stage.

Most people will agree that integer frequency ratios produce intervals which can be heard
as having zero-beating when compared to very close intervals, and that as a string
or other vibrating source is progressively tuned towards an integer frequency ratio, the
perceived beat rate reduces.

At this stage, Carl, and many other naive or lazy thinkers jump (or should that I say
"stumble") to the conclusion that these points must also be the intervals at which the
musical "harmonics" occur.

Hence many people still fallaciously believe that Just Intonation must be the only possible
reference grid from which "harmonious" music can be mapped.

> At this stage, Carl, and many other naive or lazy thinkers jump (or should that I say
> "stumble") to the conclusion that these points must also be the intervals at which the
> musical "harmonics" occur.
>
> Hence many people still fallaciously believe that Just Intonation must be the only possible
> reference grid from which "harmonious" music can be mapped.

I really agree with your point, and really disagree with your tone.

Creating "harmonious music" is only one reason to use integer ratios,
and it's pretty naive to assume that it's the result of lazy thinking.

To spell out my agreement though, right now I'm experimenting with
synthesizing inharmonic timbres with spectra that mesh with the scales
I'm using. Still JI for the most part, but not with
whole-number-multiple overtones. It seems to be working pretty well
at creating a less-familiar "harmonious-ness."

-Chris Bryan

--
"The future of faith does not lie in the declaration of certainties,
but in the living out of uncertainty." -Barry Taylor

possibly the paper implies that our hearing is bias toward what we hear in speech, just as the hearing of birds go toward bird songs.
go with it or against it. or like some, ignore the ears altogether. Regardless there are always artist who will exceed beyond what can and can be substantiated by science.
I am still waiting for the paper that supports the bias toward ETs, which is supported only by the convention of a small percentage of human practice.

Charles Lucy wrote:
>
> --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>, Rick McGowan <rick@...> wrote:
> >
> > > I'd love to see their evidence that "throughout history and
> > > across cultures" people use 12 tones/octave.
> >
> > Yup. They always seem to just take is as postulated. A bit annoying, eh.
> >
> > > There are so many of these neuroscience/music papers now
> > > that get the basics wrong I've given up caring.
>
> It's not only the neuroscience/music people who get the basics wrong. > Many on the tuning
> associated lists have the same problem.
>
> >
> > Maybe time for someone to take a crack at debunking such papers? Or at
> > least debunking the assumptions. Why not a letter to the editor of PNAS?
> >
> > Rick
> >
> Go for it.
>
> Rick
>
> I have even more problems with this paper that Carl does.
>
> The author(s) seem to have managed to think beyond 12edo.
> They have acknowledged that something interesting is happening at > integer frequency
> ratios.
> Yet like Carl and many of the other "JI-blinded" (or should it be > "JI-deafened") experts,
> they have failed to think past this paradoxical anomaly to the next stage.
>
> Most people will agree that integer frequency ratios produce intervals > which can be heard
> as having zero-beating when compared to very close intervals, and that > as a string
> or other vibrating source is progressively tuned towards an integer > frequency ratio, the
> perceived beat rate reduces.
>
> At this stage, Carl, and many other naive or lazy thinkers jump (or > should that I say
> "stumble") to the conclusion that these points must also be the > intervals at which the
> musical "harmonics" occur.
>
> Hence many people still fallaciously believe that Just Intonation must > be the only possible
> reference grid from which "harmonious" music can be mapped.
>
> -- Kraig Grady
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