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Re: Cariani's question: "What is the visual analogue of pitch?"

On visual/musical formal analogues I wrote a paper published in Leonardo
Music Journal (2000) in which I used phase space diagrams to describe a
number of 'successful' non-western rhythms.

ie. rhythms that have evolved and survived over many generations of

The important distinction from other rhythmic models using phase space
representations was the application of Gestalt rules and minimum
information representations. This resulted in simple models with
mathematical consistency and strong explanatory power about rhythmic
structure. Complex metrical relations and various rhythmic permutations
were readily described.

Although the models appear largely consistent with the
expectation/realisation rhythmic models of Dessain, I have little idea
about possible neural mechanisms, and suppose that if these models do
bear some relation to brain function, it is at a high level of

I haven't put the paper on a web page but could forward it to anyone

Neil McLachlan

>>> Peter Cariani <peter@EPL.MEEI.HARVARD.EDU> 01/21/04 3:10 PM >>>
The debate between Kubovy and Neuhoff is interesting,
although it will take some time to digest.
I found that the URL for Kubovy's papers that works is:

There are a number of provocative interchanges between music and film
that always
come to mind in these discussions: the abstract films of Dadaist
Hans Richter and Eggeling's Symphonie Diagonale. This I think is the
closest visual
art comes to music, where repetition and rhythm of form and movement
strong roles. On the music as visual form front,
I taught Psychology of Music last fall and used Stephen Malinkowski's
Music Animation Machine piano roll music animations to help visualize
melodic structure.
It's worth having a look at it (and his tapes) if you're interested in
these issues.

The Gestalists certainly included melody and rhythm as examples of
coherent, relational organizations.  Melodic and rhythmic grouping
arguably form the "chunks" that cause us to parse music in particular
ways that
are then described by the cognitivists in terms of nested hierarchical

Along with Handel's Listening (1989),  I've found Snyder's book,
Music and Memory very useful in developing these notions in
musical contexts.

I agree that the relation between audition and vision is not simple.
We understand neither system well. Pitch is not frequency per se, and
form is not simply a spatial pattern of activation on the retina, but
there are
nevertheless parallels between the kinds of correlational invariances
transformations  that underlie say magnification invariance of form in
and transpositional invariance of chords and melodies in music. One
at various binocular spatial-disparity effects (stereodiagrams) and
there are
temporal analogues in the binaural system (Huggins pitch). Time delays
in the binocular
system map to depth (Pulfrich), while they map to azimuthal location in
audition. The correspondences are not those that would be predicted by
simple analogies, but neither do they seem arbitrary.

I tend to think of timbre as the auditory analogue of visual texture
and color,
and melody as an auditory analogue of visual figure or contour. Because
eye movements, a figure is constantly being presented to different
locations, such that the spatiotemporal (spike) volley pattern
associated with the
spatial form is re-presented to the system over and over again. We can
imagine circuits
that build up this invariant volley pattern as a stable object.  A
series of notes repeated likewise creates
an auditory volley pattern that is repeated, and the same kind of
would create an auditory image of the whole repeated sequence.

When the melody is transposed, we hear the similarity of the patterns,
but also the shift in pitch
(upward or downward) of the pattern as a whole: i.e. apparent movement
of an object.
Music theory is rife with all sorts of metaphors of movement (rhythmic,
tonal, thematic, etc.), which involves this combination of an invariant
pattern (object) being transformed in a manner that preserves its
essential organization (that made it a stable object in the first
The paper by Pitts & McCulloch (1947) on How We Know Universals
had the right spirit in trying to conceive of a mechanism, but their
neural coding assumptions -- re: the nature of the representations -- I
were flawed.The pattern invariants could be volley patterns of spikes,
rather than
channel patterns (rate-place profiles in auditory and visual areas).
might explain why our sensory systems so effortlessly recognize the
similarity of
the patterns even when they are transposed or translated onto completely
different sets of neural channels (different retinotopic and
cochleotopic positions in neural maps).
It's easy to move temporal patterns around in neural
systems, but much harder to move spatial patterns.
In the 1930's Lashley recognized the problems these channel-translations
pose for "switchboard models" of vision.
But today our thinking is are so enamored of features and rate-channel
that it becomes nearly impossible to conceive of anything else.

--Peter Cariani

On Tuesday, January 20, 2004, at 06:32  PM, Eliot Handelman wrote:

> John Neuhoff wrote:
>> Stephen Handel once said that an analogy between vision and audition
>> could
>> be "seductive, but misleading". In my opinion, Kubovy & Van
>> Valkenburg's
>> "Pitch is to space as audition is to vision" idea has some serious
>> drawbacks.
> I've been thinking recently about the relation of hearing to vision as
> it applies to the
> perception of music, eg the "construction" by the mind of a melody,
> such
> that when
> you listen there is a sense of a highly structured whole, or of a
> towards wholeness. In my
> work, which is about computational analysis of music, I've come to
> that a useful approach is one that
> analogizes from computer vision -- ie, hierarchically builds up larger
> entities -- "objects" -- from low level features --
> ie, things like orientational trends -- in a way that seems highly
> evocative of the patterns of computation
> that vision is known to imply. It's interesting to speculate that the
> procedures for listening to music
> might map rather gracefully from visual processes to hearing  and
> perhaps even involve certain visual specializations.
> It would be useful to know, in this regard, whether we possess
> orientation-selective cells -- which doesn't
> seem implausible. If these existed, then almost certainly some sort of
> hierarchic computations would take
> advantage of these.  I haven't seen any research that directly
> this, though.
> pitch::space = audition:vision strikes me as much too simple. If I'm
> right in thinking that music is a kind of
> auditory system analogue to vision, then there are very mny more
> factors
> that need to be accomodated. The
> most important of these, I think, are "parallelisms" -- ie,
> (in structure, for instance, and potentially
> at a very local level) that preserve a sense of "object constancy" --
> eg
> the transposiion of a rhytmically-shaped
> interval or two. Even in very simple music -- like "happy birthday" --
> these can be confoudedly complex for
> a program to work out. It gives an indication of the complexity of the
> brain the beast that regards this as a
> simple entertainment must posess.
> Ifr parallelism analysis corresponds to visual object constancy
> analysis, then surely the analogy would go something
> like this: relations-between-pitch::space =  audition:vision.
> Just a few thoughts, but I'd be glad for any feedback.
> -- eliot
> -------
> Eliot Handelman Ph.D
> Montreal, Canada