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Re: Frequency to Mel Formula

Dear Dick, Martin, and others,

I agree strongly that octave equivalence and the circular dimension  needs to be taken into account in any definition of pitch, and that Stevens' 'halving' procedure never made sense. The definition of pitch by the American National Standards Institute  as "that attribute of auditory sensation in terms of which sounds may be ordered on a scale extending from high to low" - which implicitly denies the circular component -  is simply mistaken, and should be amended.

For a study demonstrating pitch circularity in tones that constitute a full harmonic series, please see:

Deutsch, D., Dooley, K., and Henthorn, T. Pitch circularity from tones comprising full harmonic series. Journal of the Acoustical Society of America, 2008, 124, 589-597.[PDF Document] [Web Link]



Professor Diana Deutsch
Department of Psychology                          
University of California, San Diego
9500 Gilman Dr. #0109            
La Jolla, CA 92093-0109, USA

858-453-1558 (tel)
858-453-4763 (fax)

On Jul 29, 2009, at 4:45 AM, Martin Braun wrote:

Dear Dick Warren, and others,

thanks a lot for the detailed information on the psychological construct of "half-pitch" and its relation to the octave.

Perhaps it is useful to recall that asking a subject to find a "half-pitch" is something categorically different from asking for a "half-loudness" or a "half-brightness". As Dick Warren pointed out correctly, the pitch scale is already scaled by the octave phenomenon.

It is interesting that already Helmholtz saw the universality of the octave, while many later scholars seem to have missed it. Today we have plenty of further information about the octave that was unavailable in the days of Stevens.

We have multiple evidence for a general subconscious octave-based internal chroma map:


and we have multiple evidence that octave circularity is hardwired in the auditory thalamus:


So today it may no longer be useful to use the construct of "half-pitch" at all. It may be more promising to work with the physical scale of half-frequency steps and then to observe how perfect it matches the physiological octave scale, in particular on its fringes.


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

----- Original Message ----- From: "Richard M. Warren" <rmwarren@xxxxxxx>
To: <AUDITORY@xxxxxxxxxxxxxxx>
Sent: Tuesday, July 28, 2009 10:45 PM
Subject: Re: Frequency to Mel Formula