source file: mills2.txt
Date: Wed, 18 Dec 1996 06:29:41 -0800

Subject: RE: Longuet-Higgins Question

From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

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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