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Musings On Music #41.9

Si 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  :)

_Spooky Stuff_

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 
relevant resolutions."

  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 
unpredictable "foreground":

	"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
	for it."

  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?  

_Radio Head_

  /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
standard frequency. 


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 
might work.) 

  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.......

_On Rhythm_

  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........

_On Tonality_

  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......

_The Crunch_

  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
	   thermodynamic equilibrium. 
	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.......   ;-)

L8trN mate,



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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