Chapter 6: The Making of Vibrational Art, An Example From Music:

				Synopsis

	Biology doesn't respond very well towards irrational numbers. Irrational
values are difficult to "humanize". And yet, it is the irrational that contains
such intricate balance; and it is balance, in all of its subtle complexities,
that is the web of art we call Life. So approximation serves a purpose in
bringing fire, so to speak, down from the gods. It makes the infinite variety of
aesthetics accessible to a manner of appreciation that is both linear and
simple.
	In music, as in art in general, we have two ways of emphasizing appeal.
Both are grounded in automatic processes from physical laws. And both are repre-
sented in the body by some physical counterpart. These two ways are often called
equal and pure temperment. Equal temperment gives us scale and a sense that one
note is relative towards other notes by its pitch. It is represented by the
cochlea within the inner ear. Its shape is a logarithmic spiral whose angle of
expansion is determined by the golden ratio. The second theme is pure temper-
ment. It gives us a
sense of differences among notes, not as simply higher versus lower, but as
numerical relations that form a system of relations. It is represented by the
blood salt's approximation of the golden ratio, as discussed in chapter 5. There
is also, of course, dynamics, an integral part of interpretating what emphasis
should be placed where in a work of art. There is a human side to dynamics which
makes it difficult to analyze and quantify. I won't even attempt it. Mostly I am
going for the tonal alphabet of art. I begin with music, because it is the most
developed in a conceptually linguistic sense. When these two systems coincide
with approximating the golden ratio, then a system of music is born for our
planet. Something else must coicide though. The number of chromatic notes must
coorespond to some set or subset of the Diety Linguistic Set. It works out that
twelve chromatic semi-tones, each differing from its neighbor by a twelfth root
of two, is a scale system that epitomizes the dual nature of six Dieties as a
subclass of the primary eight. Also, the Euclidean algorithm performed on the
logarithmic value of each semi-tone gives pure temperment approximations for
nine out of twelve notes. This is an exceedingly good "match"; one that we have
come to use without knowing why. Furthermore, the diatonic scale, with its
emphasis on the major and minor modes, brings into focus the seven major
chakras; while the seven octaves of a classic music staff bears a parallel
toward the seven states of consciousness.



			Linear Versus Irrational Music.



			Pure Versus Equal Temperment

	These two approaches to analyzing music have been competitively coexis-
tent. I find them to be complimentary by virtue of their seperation from each
other. Pure temperment theory approaches music as a mathematical abstraction.
Equal temperment treats music as a concrete reality. Both are valid assumptions.
But because abstraction has no conflict with simple pragmatics, these two
theories can get along since they don't have to get along----they deal with
two adjacent planes of reality that coexist on different conceptual wavelengths,
so to speak. All that is required is that they must agree with each other for
music, and art, to occur.
	Ergo:
	When Nature selects an abstract mathematical concept to embody
operationally as a harmonic system, She selects using a definite plan of selec-
tion out of an infinite set of options. This abstraction must now be approxi-
mated in order to be actualized. Although the highbrow world of abstract mathe-
matics looks real good on paper, the reality of using aesthetics requires a
second tier to step-down some of this ethereal stuff so that it can be actually
useful. To do this, a second operational agenda comes into being to facilitate
the use of an abstraction in the "real world". In the real world, sound is
appreciated by the ear as simply a tone of lessor or greater vibration. This is
by virtue of the cochlea----a spiral shaped conch in the inner ear which gives
us this physical ability of distinguishing different tones from one another. In
addition, the human nervous system, a byproduct of evolutionary growth on this
planet, is programmed to respond to differences in vibration (intervals) that
are either directly or indirectly the product of approximating the roots of the
polynomial: x^2 +- x - 1, albeit the two beautiful quadratic golden ratios:
1.618 and 0.618. It is geared to these ratios through the use of some (genetic?)
mechanism regulating the balance of negative versus positively charged ions
whose total molecular weights must approximate the golden ratio as a ratio of
subtotaled weights. Both sodium chloride and bicarbonate are the two main
contenders in this business in the blood of mammalian bodies, while both sodium
and magnesium chlorides predominating in the oceans of the earth are the result
of some external planetary mechanism .



Evaluating the Roots of a Polynomial: The ?<Radical> Method.Creating Series Sets
--The Geometric Method.Pure Temperment Chromatic Scale Building.Approximating
Pure Temperment With the Use of Equal Temperment.The Coexistence(?Comingling) of
Both.Melody Building.The Growth of Consciousness Through its Seven Major States