[Smt-talk] Harmonic and Melodic Scales

David Bashwiner david.bashwiner at gmail.com
Wed Dec 4 13:57:10 PST 2013


I should start off by saying I am a big fan of your work and cited it in my
dissertation. So please accept this as an invitation to continue a
conversation and to learn more, rather than any sort of a disrespectful
challenge. (It can be difficult to read between the lines in an email.)

Given my modest familiarity with your work, and with other posts on this
list, I too was surprised by the strength of your convictions with regard
to chroma maps in the brain and what these mean for musical experience. I
quote the relevant statements here:

The affinity of the [12-note harmonium] to the unknown chroma map of the
> musicians and listeners simply was too strong [for it to be successfully
> banned].

> [T]oday we know that the mammalian brain has a hard-wired octave-wide chroma
> map.

> Knowing that auditory chroma maps exist makes it easy to understand that
> scales with "augmented major seconds" can be
> quite stable in all music cultures that use 7-tone scales and fifth or fourth
> modulations.

The differences between C# and Db or between C-F and C-E# exist exclusively
> in imagination. They have no physical basis.

> If you read scores, major parts of your brain that are involved are the
> visual brain, possibly the linguistic brain, and the auditory brain. Now,
> in which of these parts of the brain varies the processing between C# and
> Db? Answer: It varies in the visual and linguistic parts, but not in the
> auditory parts. The emotional associations may also vary, but it is
> important to note that such variations are not part of the music but part
> of the ideas about music.

The origin of ... pitch class tolerance lies in the auditory brain, where
> pitch class is not represented in narrow lines, like on a ruler, but in
> wide strips, like on the back of a zebra.

The fact that even fret spacing was used 500 years ago, for music that was
> not modulated much, demonstrates the affinity of such a technique to the
> chroma map of the auditory brain.

I'll organize my comments under two topics: tonotopy vs. quantization, and
the physicality of emotion and imagination with respect to audition.

*Tonotopy vs. Quantization*
First off, I'd like to ask for a few useful references on the "chroma
map[s] of the auditory brain." Now, what everyone likely knows is that much
of the auditory brain is *tonotopically organized*, meaning organized
according to frequency. The hair cells along the basilar membrane of the
cochlea are "tuned," i.e., frequency-sensitive, with those responsive to
lower frequencies at one end and those responsive to higher frequencies at
the other end. Thus the basilar membrane is tonotopically organized, and
the lemniscal track up to the cortex retains this organization—through the
brainstem to the inferior colliculus, the ventral nucleus of the medial
geniculate complex of the thalamus, and primary auditory cortex.

Now, I say that "everyone likely knows this" because it's not really the
main issue. The main issue is not tonotopy, but rather *quantization* to a
12-note chromatic universe. I know of *one* study that suggests something
like this, Petr Janata's 2002 paper in *Nature*. It's a fascinating study
and is worth checking out for anyone who's curious. Dr. Janata has a page
with all the relevant links
By way of brief summary, he presents subjects with a melody that, over the
course of three minutes, modulates through all 24 major and minor keys. He
finds that one area of the brain especially, the medial prefrontal cortex,
tracks these different key areas tonotopically in a geometrical structure
surprisingly resembling a torus.

Nevertheless, that study does not present notes *between* the 12 pitch
classes of the octave to demonstrate that these chroma zones are quantized,
i.e., that in-between notes are perceived as (out-of-tune) representations
of the 12 standard pitch classes. In short, there's evidence that the brain
organizes sound according to frequency, but, as far as I know, there is no
evidence that there are only 12 buckets per octave for pitches to fall
into. So my first comment amounts to a request for sources demonstrating
not just tonotopy in the brain, but 12-notes-per-octave quantizing
tonotopy. I would love to read more about this and am also curious to read
about the greater representation of the notes A, C, D, E, F, and G in the
brains of Americans, Europeans, and Japanese.

*Emotion and Imagination*
The second point I'd like to address is the role played by "imagination" in
the musical experience. Marcel de Velde wrote that G# and Ab feel different
because they function differently. You responded that such differences
exist only in imagination and not in physical reality, that there would be
no difference between such tones in the auditory brain. And you wrote that
even if such differences amounted to emotional differences, audition would
not be affected, as this would not be "music" but rather only "ideas about

Any self-respecting materialist will acknowledge that imagination is a
product of the brain to some extent. And imagination certainly interacts
with audition. In my recent SMT paper, I illustrated a number of effects
that amygdala activity has upon auditory cortex, both direct and indirect.
(I'm happy to forward that if you're interested.) Directly, for instance,
amygdala activity down-regulates activity in auditory cortex (e.g., Koelsch
et al., 2013); indirectly, it affects levels of acetylcholine and
norepinephrine in auditory cortex and regulates glutamatergic innervation
from the thalamus. Amygdala activity is one of the best material indicators
we have at present for emotional activity. In any event, these interactions
demonstrate that emotions are not only the *effects of* audition, *they
also modulate audition*. (Amygdala effects are also at work in the
brainstem and inferior colliculus.)

It's not too far a stretch, I think, to suppose that "imagination,"
whatever it is, would have an effect on audition as well. Take, for
example, the case of priming. We know from the work of numerous
psychologists that subjects respond faster and more accurately to stimuli
when they know what to expect (and this "knowing" need not be conscious).
J. J. Bharucha's work in the 1980s demonstrated that listeners are faster
and more accurate at determining when a chord is in or out of tune when
they are *primed* to perceive it by means of a previous harmony. These two
harmonies could be related without sharing any tones (e.g., I and ii
chords), showing that this relatedness is "abstract." I would guess that
this level is right around the level of cognition Marcel is getting at when
he describes the felt difference between G# and Ab. If these notes are
played on a keyboard instrument, they will be played identically. In that
sense they will be physically identical, as you stated. When they reach the
cochlea, they will still be identical. However, that's where the identity
stops, at least as far as is currently known. Corticofugal influence—from
the cortex to the inferior colliculus and brainstem—extends at least to the
dorsal cochlear nucleus, the first stop after the cochlea (see for example
Jeffery Winer's 2005 article, "Decoding the Auditory Corticofugal
Influence"). It really could be that cognitive sorts of expectations like
priming affect neuronal responsivity at this deep of a level, this early in
the processing chain. *This is a physical difference*. So, as with emotion,
I see no reason why imagination couldn't be making a physical difference in
the brain *in even the most basic auditory centers*.

All this is to say that I don't think we can draw the conclusions that
you've drawn. As far as I know, there isn't evidence to say that the brain
has *quantized* 12-notes-per-octave frequency maps anywhere in the brain.
If there is more to suggest this than the Janata et al. (2002) study,
please pass on these references. Moreover, I don't think we can say that
something that is emotional or imagined is therefore not physical. Although
newly evident, it now seems clear that emotion and imagination affect even
the most physical, straightforward processes of audition. Hence, I think
Marcel's experience—of G# differing from Ab—very much *could* be physical
in a very basic way.

Very much looking forward to hearing your thoughts,

David Bashwiner

*David Bashwiner*
Assistant Professor of Music Theory
University of New Mexico
Center for the Arts, Rm 2103
MSC04 2570
1 University of New Mexico
Albuquerque, NM  87131-0001
(505) 277-4449
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