beats and difference tones

There is some interesting music out there based entirely on acoustical
beating. The recent works of Alvin Lucier for various combinations of
voices, instruments, and oscillators are good examples. If you have any
doubt about the viability of beats being heard in a musical context, thenLucier's _In Memoriam, Jon Higgins_ for clarinet and oscillator should
definitely be heard. I am particularly fond of his _Navigations for
Strings_, where a four note cell within the space of a minor third is
gradually - via microtonal deviations notated in cents - diminished to a
unison, and although the attacks of the individual stringed instruments are
steady, the beating rate makes a gracious ritardando over some sixteen
minutes. Many on the list are probably familiar with Jim Tenney's _Critical
Band_, which begins with tones related as harmonics within the critical
band - thus producing beats - and broadens outside of the band to represent
lower harmonic ratios. In contrast to the Lucier, the acoustical beats are
gradually drowned out by the pulse of the players' attacks.

It is quite possible that beats between ''mistuned'' unisons are used in
Balinese music more as an aspect of musical rhythm and timbre rather thanas pitch. Some gamelan (especially gender wayang) have such steady beating
patterns throughout the instrumentation that the beats could practically be
used as a metronome.

An interesting use of difference tones may be found in Richard Maxfield'slandmark tape piece _Night Music_, which is composed entirely of difference
tones between an oscillator and the erase head of the recorder. The old
Stockhausen and David Tudor favorite, ring modulation, yields both sum and
difference tones. (I am not a Stockhausen enthusiast by any means, but his
use of ring modulation in _Mantra_ creates tonal relationship which are
quite easy for a listener to comprehend). La Monte Young's _Two Systems..._
describes a theory of harmonic controls based entirely upon avoiding
particular constellations of sums or differences. Walter Zimmermann has awonderful piece for two clarinets which play loud dyads with first order
difference tones derived from Franconian folk dances.

I think that the successful incorporation of beats and combinations tonesinto music like this illustrates well how by subtly changing the context in
which music is presented, non-traditional materials can be perceptably
integrated into a work of music. I am convinced that we know almost nothing
about the limits of our perceptual faculties and new forms of conditioning,
new ways of presentation and new technologies can extend those faculties
dramatically. This is the fundamental reason why I am always ready to
challenge compositional or analytical theories derived from psychophysical
research which is based upon narrow, culturally defined conditions. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
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