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Re: Pitch learning

Two books come to mind on this:
"How Equal Temperament Ruined Harmony (and why you should care)" by Ross W. Duffin, 2006: Norton
"Temperament: How Music Became a Battleground for the Great Minds of Western Civilization" by Stuart Isacoff, 2003: Vintage


On Mar 1, 2007, at 4:38 PM, Edward Large wrote:

Hi Susan and Linda,

I agree that there is a large degree of variability
in performance intonation. (By saying variability,
I don't mean random
variation ... for masters it is of course expressive).
But huge variations are
also present for Western music played on non-fixed
tuning instruments, such as violin, or in
vocal performance. Every study of which I am aware
confirms this basic point. This, as it sounds like you
would agree, makes the very measurement of
mean frequency suspect. However, it doesn't
mean there is no tuning system.

Is there more variability in Indian or Chinese music?
I don't know. I have never seen a comparative study.

And, by the way, these are empirical issues, not political


On Mar 1, 2007, at 5:00 PM, Susan Allen wrote:

Thank you, Linda, for this clarification.

Susan Allen

On Mar 1, 2007, at 5:53 AM, Linda Seltzer wrote:

The descriptions of non-Western tuning systems given below are incorrect.
Concerning Indian music: I studied North Indian classical singing with
Ustad Vilayat Khan. He sometimes demonstrated different versions of each
note to me. It is really a slur and maligning of the vast creativity of
improvisation in Asian musical culture to say that Asian music has systems
and fixed intervals. It is part of the fa;se stereotype of Asians as
memorizing and not being creative. Each raga is different. Each
performance of a raga is different. The performances of the same raga in
different gharanas are different. A master can elaborate different
subtle intonations of the pitch and color of a note among different ragas,
within a raga, or within a performance. That is part of the subtlety of a
master. When real master is performing you never know what brilliant
musical idea he or she is going to follow. The intervals of a fifth and a
fourth exist, but I have even heard Vilayat Khan demonstrate singing Sa
(the base note) slightly off pitch as an expressive device. Improvisation
in Indian music is not a mindless outpouring of whatever junk comes into
the mind. It is an instantaneous, well-thought-out, imaginative
development of a musical idea.

As for Chinese music, how can be there "a system" when there are 400
different kinds of Chinese opera alone? The tuning of the strings of the
ch'in and the zheng by master performers can be analyzed, but then they
will go all over the place in expressive intonations and pitch curves in a
performance. But if you want to know about Chinese music, Bell Yung at
Pittsburgh is the expert, not me. I had an introduction to Chinese music
in the Chinese literature classes of Prof. Yu-Kung Kao at Princeton and I
took some lessons on the zheng. I couldn't take the regimented Shanghai
conservatory method of teaching the zheng that I was being subjected to.

The best assumption in really professional Asian music is that any pitch
or intonation is available as an expressive device by a master performer.
You can study the relationships among pitches in one performance but that
is about all.

The three largest non-Western tuning systems are Indian, Chinese and
Each of these has inclusive 12-tone scales whose frequency
relationships are
similar to the Western chromatic scales. Two of these systems, the
Indian and the
Arab-Persian, use more than 12 intervals per octave (Burns, 1999).
The musical
systems of India are theoretically based on 22 intervals per octave.
However, the
basic scale consists of 12 tones tuned according to a form of just
The remaining 10 tones are slight variations of certain intervals,
the exact frequencies
of which depend upon the individual melodic framework (raga) being
played. The
Arab-Persian system theoretically employs intervals that bisect the
distance between
Western chromatic intervals. However, there is some controversy as to
the exact number
of possible intervals and the actual intervals produced in
performance. Most sources
list the small integer ratio tuning relationships.


On Feb 28, 2007, at 1:41 AM, Susan Allen wrote:

It is astonishing to me that all of you are talking about western
scales and  octaves!  This is not the music of the world!  This is
colonial music, discovered in the West....
The WORLD of music does not follow Pythagorean intervals!  There
are many more notes!

FORGET perfect pitch - it only has to do with relative pitch on the
piano keyboard - within the Western (colonial) paradigm!

Susan Allen PhD


On Feb 27, 2007, at 10:03 PM, Annabel Cohen wrote:

Dear Martin and Stewart and others:

I am willing to concede that sensitivity to overlapping harmonics may
not be the basis of the musical and octave sensitivity of monkeys;
what remains unclear to me is whether there is an "octave circular
pitch processor" or rather than a "small-integer / periodicity-
sensitive processor".

If there is only an "octave circular pitch processing" to account for
octave generalization, one would predict performance in monkeys on
transpositions to the perfect fifth (ratio 3/2 = 7 semitones up) to
be as poor as performance on transposition to the tritone (half
octave = 6 semitones). A study including the perfect fifth
transposition has not been carried out to the best of my knowledge.
If performance were superior for the perfect fifth, the "octave
processor" theory would be incomplete.

How also does one explain the monkey's superior performance on tonal
as opposed to atonal melodies, when tonal melodies are characterized
by tones related by small integer ratios (though typically not
octaves) as compared to tone relations in atonal melodies.


On 24 Feb 2007 at 0:43, Martin Braun wrote:

Dear Annabel, Stew, and others,

Annabel Cohen wrote:

"The evidence in this paper [
http://web.telia.com/~u57011259/Wright.htm ] for octave
generalization for tonal melodies by rhesus monkeys is impressive,
however, whether this reflects something special about sensitivity
to the octave (chroma) rather than sensitivity to the overtone
series or periodicity is still not clear from this study."

Sorry, it IS clear from this study. The authors reported that
generalization over the distance of two octaves is even stronger
than that over the distance of one octave. This finding definitely
rules out the possibility that the monkeys generalized according to
similarities in the sound spectrum (harmonics). The only remaining
possibility is that the monkeys, the same as humans, have an octave
circular pitch processing, which provides the basis for a chroma


---------------------------------------------------------------- ----
- Martin Braun Neuroscience of Music S-671 95 Klässbol Sweden web
site: http://w1.570.telia.com/~u57011259/index.htm

------- End of forwarded message -------Annabel J. Cohen, Ph. D.
Department of Psychology
University of Prince Edward Island
Charlottetown, P.E.I. C1A 4P3  CANADA
e:mail acohen@xxxxxxx
phone: (902) 628-4325  office;  (902) 628-4331  lab
fax: (902) 628-4359

Susan Allen, Ph.D. Associate Dean for Academic Affairs Instructor of Harp & Improvisation School of Music California Institute of the Arts Valencia, CA 91355 USA 661-222-2780