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modeling relative pitch


Dear Martin and others,

Your example of 'C4+50 cents followed by E4 + 50 cents' is dealt with in my 1969 model of interval and chord equivalence (linked below), which is not tied to any particular tuning. As I wrote in the caption to Figure 5 of this article 'Although the neurons in the primary array are identified for purposes of clarity in musical notation it is obviously assumed that intervening neurons also exist and are linked up in the same way. These are represented by C and F in the diagram'.  So any computational model based on my proposed architecture  should link up these intervening neurons also, so as to produce the impression of intervals and chords which can be treated as identical under transposition. 

Diana




On Sep 9, 2007, at 10:36 AM, Martin Braun wrote:

Dear Diana and others,

Thank you. Yes, we have computational models of relative pitch (RP), but not
yet physiological ones.

I must say I am still quite impressed by your computational model of octave
circularity and chroma from 1969. The physiological model that has emerged
during the past five years is almost congruent with your early suggestion.

As to interval equivalence, the basis of RP, I cannot see the possibility of
a similar "happy end". You see, RP listeners can spontaneously recognize a
major third, even if it appears in previously unheard sound frequencies,
such as in C4 + 50 Cent followed by E4 + 50 Cent. Models of "learning"
neural networks that are based on frequency maps cannot account for this
ability.

As to Gerald Langner's recent suggestions of a possible "pitch helix" in the
ventral nucleus of the lateral lemniscus, we first have to wait for a
publication of data. Further, even if confirmed, such a structure could - in
my view - not contribute to the extraction of interval categories.

It is also worth noting that Zhang and Kelly (2006) did not even find
periodotopic order in this nucleus in the rat.

References:

Langner G, Simonis C, Braun S, and Ochse M. Evidence for a pitch helix in
the ventral nucleus of the lateral lemniscus in the gerbil. Assoc Res
Otolaryngol Abstr 26: 173, 2003.

Langner G, Braun S, Simonis C, Benso C, and Cant N. New evidence for a pitch
helix in the ventral nucleus of the lateral lemniscus in the gerbil. Asoc
Res Otolaryngol Abstr 29: 259-260, 2006.

Zhang H., Kelly J.B. (2006) Responses of neurons in the rat's ventral
nucleus of the lateral lemniscus to amplitude-modulated tones. J
Neurophysiol. 96, 2905-2914.


Martin

---------------------------------------------------------------------
Martin Braun
Neuroscience of Music
S-671 95 Klässbol
Sweden



----- Original Message ----- From: "Diana Deutsch" <ddeutsch@xxxxxxxx>
Sent: Saturday, September 08, 2007 7:58 PM
Subject: Re: Absolute pitch discussion

Dear Martin et al,

Concerning your statement:

we do not even have the faintest trace of a hypothesis how a brain
could accomplish RP.

please see

Deutsch, D. Music recognition.  Psychological Review , 1969, 76,
300-309. [PDF Document]

for a proposed neural network that would accomplish recognition of
musical intervals and chords under transposition and inversion,
together with a discussion of the relevant neurophysiological
evidence that existed at that time.

See also my chapter 'The processing of pitch combinations' in
Deutsch, D. (Ed.) The Psychology of Music. 2nd Edition. San Diego:
Academic Press, 1999 which revisits this model with updated
references, together with the chapter 'Neural nets, temporal
composites, and tonality' by Jamshed Bharucha in the same volume.

Further at the neurophysiological level, please  also see the work of
the Gerald Langner on the ventral nucleus of the lateral lemniscus.

Diana

----------------------------------------------
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)