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Re: Pitch learning

Hi Susan,

Your message leaves the impression that non-Western tuning
systems are unrelated to the Western system and do not
follow small-integer ratio principles. But that's not quite true.
First, our modern Western tuning does not follow Pythagorean intervals, 
either. It uses equal temperament, as I'm sure you know. Second, the tuning 
systems of the rest of the world are related in many ways 
to the Western tuning system and tend to use small integer ratios (with
some exceptions, such as gamelan). From something I'm currently
working on:
The oldest Western theory of musical consonance is due to Pythagoras: 
Musical consonance is determined by the ratios of small whole numbers. 
The principle was that intervals of small integer ratios produced harmonies
 that were pleasing and mathematically pure. The Pythagorean tuning 
system is the oldest extant Western system devised explicitly according 
to this principle, and is thought to have been devised by Pythagoras himself. 
Interestingly, the available evidence suggests that a scale similar to this 
was already in use in the West before any mathematical principle was 
advanced to describe its structure. According to Iambiclus’s Life of 
Pythagoras (Guthrie, 1987), Pythagoras did not invent the Pythagorean scale, 
he discovered a principle to explain a scale that was already in use. A related 
tuning system, Just Intonation (JI), originally proposed by Ptolemy (Hunt, 1992), 
derives all interval ratios in relation to one single tonic, and chooses the smallest 
possible integer ratios that divide the octave (approximately) equally. Just 
intonation satisfies the principle of small integer ratios more nearly than the 
Pythagorean, and it is sometimes referred to as the natural scale.

The three largest non-Western tuning systems are Indian, Chinese and Arab-Persian. 
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 intonation. 
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 [
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

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