RE: Longuet-Higgins Question

Longuet-Higgins, H. Christopher.

AUTHOR: Kurenniemi, Erkki
TITLE: Divisor harmonies
SOURCE: Musiikki vol. 19, no. 1-4, 1989, p. 462-472. ISSN: 0355-1059.
LANGUAGE: English.
DOC TYPE: as -- Article in a symposium
CLASS: Theory, analysis, and composition: Harmony, counterpoint,
voice-leading
Music and related disciplines: Physics, mathematics,
acoustics, architecture
ABSTRACT: Describes a class of chords called divisor harmonies, which
lead to: (1) a new theory of harmony; (2) the denial of
octave equivalence and changes in the concepts of tonality,
scale, and rhythm; (3) a theory of microtonality; (4) and
connections between this theory and auditory neural
structures. Precursors of the theory of divisor harmonies
include Leonhard Euler's 1738 theory of harmony and
Christopher Longuet-Higgin's harmonic space. To determine a
given divisor harmony, choose any tone and call it the
fundamental. Construct the harmonic overtone series of this
fundamental. Second, choose a natural number n (1,2,3,4,...)
and select the nth harmonic of the fundamental. Call this
overtone the sampler. Third, form the descending inverted
overtone series starting at the sampler. Fourth, retain those
pitches which belong both to the overtone series and the
undertone series and discard all else. The divisor harmony Hn
consists of those overtones of the fundamental which also are
undertones of the sampler. The divisor harmonies are simply
set harmonies consist of the pitches common to the overtone
and undertone series for any given tone.
SUBJECT: > harmony--divisor theory--introduction
> Euler, Leonhard--views about harmony
> Longuet-Higgins, H. Christopher--views about harmonic space
> temperament and tuning--microtonality--role in divisor
harmony theory

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