Musings On Music #41.9
sfx at 2fx.u-net.com
Sun Oct 26 16:09:32 EST 1997
*Hi there!* The following is intended to be an original and
enlightening discourse on the inner nature of music, culminating in a
summary of a theory, which, I believe, makes accurate predictions, and
resolves some fundamental paradoxes. As it draws on many subjects,
you'll probably already know more about some of this stuff than me
(I'm certainly no expert in any respect). However, I want to effectively
communicate my ideas to as many intelligent readers as possible (sorry about
the canned pork), and as such I feel it's necessary to clearly establish
my proffered grounding. Please forgive any resulting tedium, but I just
can't stand ignorant responses - as I'm sure you'll appreciate. All
critisisms gratefully acknowledged, although I'd particularly welcome
(literate) e-mail replies..... TIA :)
Right then. (Ahem)...... Music, eh? Weird, innit? Think about it. How
long does it last? - Does it only exist in the moment of perception, or
is a piece a complete whole? Aside from the obvious potential
reproductive benefits of "pop stardom", why would the development
of a species favour something so painstakingly abstract?
I mean, let's face it. Almost any way you look at it, music is unique -
a law unto itself. Like an hallucinogen, it can alter your conscious state
- yet it has no finite physical form. It is inherently mathematical, yet
arithmetic alone does not invoke motion nor emotion. Where optical
art might perhaps stir one's instinctive feelings through representation
and contrast of familiar elements within a novel context, surely raw
music cannot directly express /anything/ material? Nonetheless, it can
not only trigger almost any emotional response we are capable of, but
even seems adept at generating entirely new ones! Spooky stuff, /non?/
Most of us will spend several hours each day (if only mentally)
reciting melodies from improvisations upon repertoire. Music issues
forth incessantly from almost every audio-visual device on the planet
(and beyond). So WHY is it that for something permeating so much of
our daily lives, we so complacently accept it's enigmas? To a struggling
rationalist such as myself, it is nothing short of tragic - nay -
/infuriating/, that so many of us are still willing to dismiss music as an
"Expression Of The Soul", or musicianship as some kind of "Gift From
God". Fair enough, this may well /be/ the case, but would that
necessarily render the implied problems as being as incomprehensible as
His Will? In a nutshell - here, now, 'neath the daunting shadows of
twentieth century knowledge, are the underpinning schematics of
music _still_ intellectually insurmountable?
Everybody's heard the popular adage that we use only a fraction of
our brain's cognitive potential, and yet closer examination of this
proverb yields a whiff of /testicular/ /excreta/. Pushed beyond a critical
threshold, we would undoubtedly begin to optimise some pathways to
the detriment of others. Nature has no propensity for waste, and yet
on an evolutionary timescale, Homo Sapiens has graduated from
hunter-gatherer to interplanetary explorer in the blink of an eye. Given
the comparative lengths of our most recent phases of evolution, if a
brain that was designed to cope with such a simple lifestyle, suddenly
became as loaded with details and tasks as ours, what might keep it
from going hatstand? OTOH, is it even viable to try and isolate this
psychological ordering from elementary nervous functions?
Intriguingly, last year, researchers at BT Laboratories in Ipswich
claimed in the journal /Nature/ that any radical improvement in Human
information-processing capacity is unlikely. They believe most people
already think within 20% of their cognitive limitations. By creating
models detailing potential for axon size, insulation, blood supply and
other considerations, they found that even if the brain could
accommodate the required growth, the increased distances synapses
would have to traverse would cause an overall deterioration in
efficiency. Chris Winter, a member of the BT team, says "There is no
incremental improvement path available to the brain, which makes
[further] evolution difficult. It would be hard to improve on the fine
balance between neurons and blood vessels that has already evolved in
the Human brain".
Robert Barton, a lecturer in biological anthropology at the
University of Durham, suggests that the researchers may have
overlooked certain possibilities. "They assume that processing
information involves the whole brain, and that is not necessarily the
case." He points out that the exercise did not take into account the
possibility of new structures evolving in the brain, or the enhancement
of existing ones, both of which could improve our ability to process
information and make intelligent decisions. In light of this, coupled
with the spiralling complexity of modern Human life, one cannot help
but wonder at the implications of the observed beneficial effects of
music in juvenile and convalescing subjects; /it/ /certainly/ /poses/ /questions/
/as/ /to/ /the/ /relationship/ /between/ /music/ /and/ /"axon/ /pruning"/ /narcotics..../
_On Audiology And Motion_
Our ears are of course two distinct organs, both of which capture
vibrations at various wavelengths. The auditory apparatus contains in
particular the hammer, anvil and stirrup bones that sense frequencies
at the lower end of our hearing range. At the end of the ear canal the
eardrum, or "tympanic membrane" bows inward and outward as it absorbs
vibrations, creating minute barometric changes in the chamber behind it.
Together with hundreds of tiny hairs lining the canal, these "middle
ear" components detect mid to high range frequencies respectively.
Auditory sensors ride the waves of incoming vibrations - they resonate,
and this motion excites sensitive nerve endings. Signals from the ears
are first filtered through the cochlear nucleus, reencoded, and relayed
to part of your brainstem called the /inferior/ /colliculus,/ where
auditory signals are processed. Significantly, research has been
published showing that cells in this area respond strongly to the
precise timing of sounds. Suitable reactions are then organized in the
prefrontal cortex, where decision making and motor output is planned
and initiated, etc. etc.
The vestibular organ is found in the inner ear, or labyrinth, and
measures one's velocity changes and orientation to gravity. Notwithstanding
their aforementioned functional affinities, and considering that each of
these units has a differing physiology, what other factors might influence
their conjoined evolution? Similarly disregarding the obvious interests of
bilateral symmetry, why else would you need two of these in your skull?
Unlike eyesight, ears broaden our stereo-spatial awareness to a full
360 degrees through four dimensions. You can estimate the size, speed,
distance and direction of a sound source long before you see it, by
comparing the volumes registered from each ear. Signals carried by nerves
have inherent biological speed limits, so by evolving together these
components can cut transmission distance, enter their respective hemispheres
in close proximity and thus minimise reaction times to external stimuli.
In a life or death chase, ears provide vital information on the relative
motions of both predator and prey.
_Emancipation From The Evasion Of Predation?_
Ever since vibration detection first appeared in our earliest
prevertebrate ancestors, audio awareness has played a central role in
survival. Until the arrival of the Pleistocene, hominid interaction with
neighbouring species had been a predominantly harsh, eat-your-heart-
out David Attenborough, kill or be killed affair. The final transition
from "Ramapithecus" to Homo sapiens was by far the longest phase in
Human evolution, ending just four million years ago, during the glaciation
epochs. By the Mesolithic period, most Human communities had developed
tool and weapon making skills, and began farming, trading and wiping out
local predators /(et al.)./ So, if the precursors to modern human ears were
honed for over 600 million years to do little more than assist killing
and avoiding other animals, has our vibration analysis system's primary
function become redundant?
To stay consistent with Darwin, one would be inclined to think that
moving to the top of the food chain has not undermined our ears
functionality, but presented opportunities for new enterprises, not least
(frequency specific) verbal communication. Attack and "tactical retreat"
were, evidently, just temporary objectives. The underlying purpose of
audio processing is to facilitate the initiation of appropriate reactions
to an aural stimulus, and remains unaltered by our sudden change in
_Debunking Two Pivotal, Untenable Axioms In "Modern" Music Theory_
*1)* Currently, convention holds that rhythm is processed as
"psychological chunking" of percussive events into prime-number
based meter. Unfortunately, the vast majority of popular music is of
course in 4/4. So, we overcome this (rather worrying) inconvenience by
pretending that 4/4 is actually 2 x 2/2. It doesn't take much reflection
to conclude that this "don't seem right". 4/4 is clearly 4/4, and unless we
are equally content to fudge our mathematical definitions, four is /not/ a
Furthermore, while 3/4 structures are almost as common as 4/4, it
seems that other primes become progressively less tangible. For
example, although 5/4 is musically acceptable (at least within Western
cultures), it is comparatively far more contrived, and I would venture
to suggest that such compositions are a clever play on the "legitimate"
neurological foundations of rhythm. So, if not primes, then what?
*2)* The most widely accepted theory linking music to emotional
arousal is that proposed by the composer Leonard Meyer: "Music
activates tendencies, inhibits them, and provides meaningful and
With this approach, Meyer describes a system based almost entirely
on expectation and postponement of resolution, within a culturally
stylistic context. This view shares similarities with an idea put forward
by Hans Keller in /The/ /Listener/, whereby a tune can be considered as
contrasting between two dimensions - a logical "background", and an
"The background of a composition is both the sum total of the
expectations the composer raises in the course of a piece without
fulfilling them, and the sum total of those unborn fulfilments. The
foreground is, simply, what he does instead - what is actually in the
score. The background boils down to form, which many pieces have in
common, and which can be found in the textbooks; the foreground is
the individual structure, which happens instead of the form, unless the
music is a bore and fulfils all expectations - in which case you can
write it yourself after the first few bars: you don't need a composer
In /Music/ /and/ /The/ /Mind/, Dr. Anthony Storr raises the objection
that once a tune becomes known, expectations are no longer contradicted.
Keller responded by explaining that such prior knowledge was _intellectual_,
leaving the listener's emotions none the wiser.
NB This point is crucial. The above theory assumes a _primary intellectual_
response, and a resulting _secondary emotional_ one. I intend to show that this
model becomes nonsensical when exposed to any degree of scrutiny.
Moreover, such a dualistic interpretation perpetuates a psychological
dichotomy that must be the bane of all neurologists. In any event, much
current theory on cortical encryption points towards myriad prioritised
networks of associatively interlinked explicit neurons. Naturally, the
six-million-dollar question here is "what principles underwrite this linking?"
Francis Crick and professor Christof Koch recently published a preliminary
paper suggesting that consciousness may arise from specific oscillations in
the cerebral cortex. In this theory, subjective details are formed into an
objective whole at the exact point where their associated synaptic frequencies
become synchronized at 40Hz. Clearly, this may be integral to our experience
of music, but how?
/New/ /Scientist/ (No2105 p17) recently ran a report on the findings
of Ehud Ahissar of the Weizmann Institute of Science in Rehovot. In
1990 His team found evidence contradicting the accepted "passive" model
of the brain based upon the "one stimulus, one signal" system of impulses
between an excited nerve and the thalamus. Presaging Crick and Koch's
studies, they found clumps of neurons in monkey brains that continuously
oscillated. In Ahisar's own words: "It was not at all clear what their
role might be."
So, they have just completed a series of experiments to determine if
these oscillations were involved in neurons sensing perception from rat's
whiskers. What they discovered was that roughly one tenth of the
associated neurons had an intrinsic frequency of about 10Hz. When the
whiskers touched an object, this frequency was altered accordingly. The
team could only conclude that the brain interprets these signal variations
in much the same way as an FM radio - it measures deviation from a
NB. Personally, I find it difficult to reconcile the possibility of a truly
fundamental constant with my own hunch of a _dynamic_ "Relative
Chronological Constant", but more on this in a minute.
_On Pattern Recognition And Emotion_
Although you know from experience that, for the most part, you
can safely predict how the next few minutes will transpire, you are
constantly prepared for the unexpected - incoming sensory information
is inherently unpredictable. As the brain receives ultimately chaotic
input, it must be able to adapt to the unfolding situation rapidly.
Faced with a new visual or audio field, it first assembles a
corresponding image by screening for key details that conform to
some mnemonic template, so it can expedite advantageous reactions
from repertoire. This is "pattern recognition". Loosely speaking,
anything the brain is able to process comfortably can be called
_orderly_. Conversely, concepts that are too large, messy or unfamiliar
to cope with are _chaotic_. If you've ever seen the man in the moon,
watched developing clouds morph, or stared at bad wallpaper on acid,
you'll be getting my drift. In the continuing effort to maintain a useful
level of consciousness, your brain is literally gagging for orderly
You are continuously bombarding your brainstem with masses of
sensory data. Right at this moment in time, every nerve in your body
is feeling /something/, and this creates a lot of mental paperwork.
Instead of scrutinizing every cumbersome detail, we filter out much of
the irrelevant stuff, and only clock what seems important. To organize
this state of prioritised awareness takes time (nervous speed limits
again), and so "consciousness" only recognizes events that have already
transpired. (For clarity, there is a _marked_ delay between primary
response and "conscious" awareness.)
Recent developments in neuroscience prove that emotional responses can
occur without cognitive processing in the cortex. Beneath the temporal
region, there is a small, almond shaped widget called the /amygdala/ (from
/amygdalum/ - Latin for almond). This is the heart of our emotional appraisal
system. It appears to be able to access memories and reach conclusions on
a given set of circumstances much faster than, say, the extrastriate cortex
Earlier we noted that once a tune is familiar, it still provokes
emotional arousal, even though you know exactly what's coming.
Moreover, as Keller points out, familiarity strengthens these reactions.
One of the more unusual ailments known to neurology is "blindsight".
Here, sufferers have lost the ability to "see" their visual field, and yet
when asked to point at a target, can often do so with considerable
accuracy. In this condition, specific damage high up in the cortex has
prevented an otherwise perfect image from becoming part of conscious
awareness. Blindsight is made possible by the optic nerve branching
off to many different destinations as it enters the brain, enabling some
degree of /subconscious/ pattern recognition - albeit beyond the visual
Nerves leaving the ears are branched off in a similar way, and some
of these branches extend to the amygdala, _which processes information_
_faster than "consciousness"._ So all music, however well known, indeed,
/all incoming information,/ is emotive _before_ it is anything else.
Emotions optimise response times, and knowing what your emotions are about
to do next is a (pointedly significant) amplifying factor. What this amounts
to is a kind of psychological partial closed feedback loop. I believe that
"consciousness" resides within this delay between prioritised stages of
processing, and that this is also the state-space in which our perception of
music takes place. (In fact, I'm about to offer an explanation of how this
But elaborating on the proposals of keller and others can only explain
so much. A piece of music can be any combination of vivid, surreal,
invigorating, uplifting, depressing and literally countless other emotions
transcending those that might arise through mere surprise and gratification.
I'm not saying that the interplay between expectation and variation isn't
/important,/ but that there has to be some fairly obvious, cohesive process
that could endow such colour, depth and flair to aural imagery. Hmmm.........
_A New Methodology_
OK. OK. Right then. Get this. Here goes. Ready? I reckon I've sussed it.
It's like this:
Music is composed from two substrates - rhythm and tonality. Beats
and notes are combined to produce tunes, yeah? Well, one dark and
stormy night about a year ago, a realization came to me. At first it
seemed superficial, but I couldn't help mulling it over. It was /innocuous/.
Then, gradually, some big pieces of a puzzle I wouldn't have otherwise
been able to articulate began to dovetail. It's really very simple, just a
slightly different perspective. The broader implications however, extend
well beyond music cognition.......
Firstly, it is necessary to distinguish *beats* from *rhythms*. For the
purposes of this demonstration, a _beat_ is a /single/ percussive
frequency. A _rhythm_ is subdivided from /two/ /or/ /more/ such
frequencies - /synchronized/ /by/ /a/ /factor/ /of/ /two./ Imagine the
following simple pattern: over a _four_ second period you hear 2
snare drums, 4 kick drums and 8 closed high-hats. Now, humour me
for a second: I would propose that this is the simplest possible type of
rhythm - a standard form. Thus, _all_ rhythms are generated through
symmetrical, repetitive and causal (SRC logic) modulation of this
ubiquitous formula. D'ya get that? alrighty........
All notes are derived from subdividing *octaves.* An octave is /two/
/frequencies/ /synchronized/ /by/ /a/ /factor/ /of/ /two./ Notice anything?
_we've been here before:_ Octaves and rhythms are the same thing -
they're at different ends of the same spectrum! Conclusion?
*"Music* *is* *tonal* *and/or* *rhythmic* *modulation* *of*
*two* *or* *more* *frequencies* *synchronized* *by* *a*
*factor* *of* *two!"*
Hopefully, you will now begin to realize the point I have been
building up to; In all honesty, I don't even want to /think/ about the
amount of sleep I've lost, just trying to get my thick head around this
riddle. WTF is so special about 2 freqs. @ 2:1 that would force _all_ Humans,
all over the world (even those isolated by prehistoric continental drifts),
to construct music within this same, truly _universal_ audio field?
Why WHY *WHY?*
It appeared that, at least as far as /music/ was concerned, information
(at it's lowest level,) was somehow encoded _above and below the synaptic_
_frequency ratio of 2:1_. But if music really /is/ just an offshoot of more
primitive nervous processes..... well, you can see where this argument
is going, can't you? Is a reductionist analysis of music cognition grounds
enough on which to propose such a bold assertion? I feel the logic speaks
for itself, QED......
Eventually, I found myself reading up on complexity, and it was here
that I began to find relief. Use your imagination to try and picture this
little thought experiment: Take a handful of say, twenty rings. Drop
these on the floor, allowing them to settle into a random pattern.
Next, take a length of string, and tie it to any two rings at random.
Continuously repeat this process. As the ratio of strings to rings
increases, more and more rings get connected. Now, something
magical starts to happen. As the ratio reaches a critical point of 2:1,
nearly all the rings suddenly connect into one, giant superstructure.
Adding more strings would become increasingly pointless.
Remove any, and order declines. In this system, the most efficient
point of balance between order and chaos is therefore 2:1 (ie. 10
strings randomly tied to 20 rings makes 20 connections). This is called
a *phase transition.*
_Musicodynamics - One Up For Determinism?_
I don't do much of a neuroscientist. I've no intention of betraying the
abysmal depths of my benightedness by trying to contextualize this phenomena
in terms of concise neurobiology, and I can only speculate as to how this
may (or may not) be relevant. However, I am well aware of the fact that
this field is probably, erm, slightly more complicated than I'd like to
imagine. Admittedly, the papers I /have/ read on such topics as neurodynamics
and synaptic synchrony etc. are enough to convince me of this. Still, let's
examine some implicit, incontrovertible maxims:
1) It can be said that the brain is a complex - yet highly
efficient - thermodynamic system, from which some degree of
objective "order" arises. The /root/ of all knowledge is the
imperative biological need to identify sources of unity. Nervous
reactions are mediated largely through economical reversion to
2) Although the number of (physiological) contributory factors
is surely considerable, it is without doubt finite, and so by
no means incomprehensible.
3) We are therefore looking for a means by which - in an
admittedly reductionist context - the ratio of 2:1 might become
prominent in a thus described system. Perhaps the most obvious
naturally emerging circumstance that would promote this is the
edge-to-node ratio of 2:1 - an order/chaos phase-transition that
inexorably materializes above this precipitant threshold of
complexity (although perhaps the most important thing is that
the same laws of emergent order should apply).
I'm sure you'll agree that, notwithstanding some portentous oversights,
the indications are compelling - the elements of music cognition seem to
fit _perfectly_ into the terminology of dynamical systems theory, /a/ /la:/
piece of music = basin of attraction
brain / mind = attractor
/N/<2 freqs @ 2:1 = neuronal state-space
psychomusical event = trajectory
and so the piece is perceived as a *state-cycle.* /And that, friend, is all./
For an ironic anecdote: far from being an "expression of the soul",
IMHO music proves that we are all _mortal_ products of spontaneous
self-organization honed through natural selection, and devoid of free
will - to wit - everything, everywhere, is an inescapable "edge-of-chaos"
consequence of the initial expansion blah blah etc. etc.
OTOH, maybe it /really/ /is/ just a gift from God....... ;-)
Simon Faux <sfx at 2fx.u-net.com>
"Given that the universe is infinite, and that God is also infinite,
would you like a toasted teacake?"
TalkieToaster at RedDwarf<WhiteHole>
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