From: mclaren
Subject: elaborate math & musical tunings
--
Someone finally fell into the Bengal Tiger Trap set out several
years ago in my posts.
Pity it was John Chalmers.
John mentioned some weeks back that it seemed "ironic" for me
to use exotic math and elaborate theory in constructing tunings,
while at the same time condemning the use of exotic math and
elaborate theory in constructing musical compositions.
This is a failure of logic so breathtaking as to arrest one's
attention.
The micro-level of music--namely, the tuning--is NOT AT ALL
commensurate with the macro-level of music: namely, the
formal procedures used to create large-scale order with the
pitches of a specific tuning. And no surprise. In virtually all
fields the micro-level and the macro-level are completely
& inalienably disjunct, and one level cannot be confused with the
other without producing disastrously wrong conclusions and
startling errors of logic.
In physics, concepts such as "location" and "time" and "space"
on the macro-level cannot in ANY WAY be carried down to
the micro-level. Because on the micro-level of the Planck
length (10exp[-33] meters) space and time cease to exist.
On the Planck scale of distances, space-time itself dissolves
away into a quantum foam of seething virtual particles and
the idea of "location" and "momentum" becomes meaningless
in any familiar sense. On the Planck scale of distances,the law of
conservation of energy vanishes. On that scale, particle/antiparticle
pairs appear out of the primordial ylem for incomprehensibly
brief fractions of a femtosecond & the vacuum itself
spawns mass-energy from nothing.
In the same way, it is utterly meaningless to carry upwards
concepts and procedures which prove useful on the musical
micro-level of intonation, just as it is meaningless to try to
carry downwards concepts and procedures which prove
useful on the macro-level of the symphony or the prelude.
To claim otherwise is equivalent to saying that, since the
shape of the bricks used to contruct buildings is governed by
strict laws of 3-dimensional geometry & the need to fill space
efficiently, that therefore the overall shape of a building must
necessarily be a simple geometrical solid with space-filling
characteristics.
This is obvious nonsense. Clearly, buildings can be
constructed in many shapes other than a cube or a rectangular
solid. Many such buildings have been built, even though their
constituent bricks remain space-filling rectangular solids.
This is so obvious it seems to require no explanation. But
apparently the idea hasn't seeped into the brainpans
of the modernists yet. Certainly the concept is utterly alien
to the modernist architects. After all, this group has
effectively made such an invalid and logically faulty
claim for modern architecture.
The Bauhaus ideal of modern architecture is a big
glass box. To my eyes these goddamn things are glass
filing cabinets for people. With the exception of
Mies Van der Rohe's Seagram Building and the Pan Am
building and a few others, all these wretched glass-box
skyscrapers should be dynamited as eyesores. They look like
the products of a brain-damaged infant deity who got tired
of playing with her Lego blocks and decided to drop 'em
on a hapless population.
In like wise, modernist music theorists have treated us to an
endless variety of ugly glass boxes in the compositional
realm--filing cabinets for notes.
These one-size-fits-all compositions were theoretically
different from one another, but in reality SOUNDED
tiresomely identical in all but the tiniest minutia.
Modernist music theorists like Babbitt & Forte made this
gross error because they foolishly confused procedures
meaningful on the micro-level of intonation with procedures
meaningful at the macro-level of composition.
And there is, after all, no surprise that the micro-level
of tuning should prove incommensurable with the
macro-level of a composition...just as the micro-level of
the "eightfold way" physics which governs a quark is
incompatible with--and meaningless to --
the macro-level of Newtonian laws which govern the
trajectory of a basketball. [On the macro-scale there
is, indeed, a finite probability that a baseball will diffract
through a window instead of a smashing it...but in actual
reality, this NEVER happens. The probability is just too
vanishingly small. It's theoretically possible that a pot
of coffee, when placed on a hot stove, will *freeze*--
but when did *you* ever see it happen?]
Remember: the macro-scale of a musical composition,
measured on a time-scale of minutes, involves unimaginably
many more variables and degrees of freedom than the micro-scale
of intonation measured on the time scale of cycles per second.
Thus, while this or that arcane and exotic mathematical
procedure may well usefully enrich the micro-level
of musical intonation, such rigidly mechanical math and set
theory manipulations are far far *far* too simplistic and
trivial to produce satisfying music when applied
compositionally on the macro-scale.
The value of human intuition and the necessity for audibly
ordered large-scale processes were systematically denied
by the most rabid modernists--Boulez, Cage.
They were wrong.
Time has shown that indefinables & unquantifiables (intuitive
processes, inspiration, "mood," "feeling," etc.) are absolutely
essential in taming the almost inconceivable number of
degrees of freedom entailed in composing satisfying
large-scale musical structures on the macro-level.
Notice that my argument proceeds from an information-theory,
rather than a typical reactionary "sentimental," perspective.
Forget the usual claptrap about "nice sounds" and "familiar
good ole Western triads"--instead, simply ask yourself
whether the unthinkably complex operation of the
subconscious mind called "intuition" might not be a far
more efficient method of riding herd on the near-infinite
degrees of freedom of a compositional macro-level than
some simple-minded crossword-puzzle math procedure.
Warren Burt will no doubt take issue with this point. My
judgment stands: the best algorithmic compositions seem
to me far and away those of his pieces which require the
constant intervention of the composer in making intuitive
and emotional decisions based on the "sound" of the piece
at any given point in time. The least impressive of Warren's
pieces, to these old ears, are those which use the most
rigidly mathematical and set-theoretic procedures with
the minimum of human intervention.
Incidentally, this is also my reaction to most other "new complexity"
and highly theoretical music. The music seems successful to the
exact extent that human intuitive impossible-to-describe-or-
justify decisions are involved in the production of the music.
Thus, it's *VITAL* not to confuse procedures meaningful at
the micro-level of intonation with procedures meaningful
at the macro-level of composition. Failing to do so *always*,
in my experience, produces meritricious and uninteresting music
which might *look* enormously interesting on paper but which
*sounds* like junk.
--mclaren
