Convexity and compactness as models for the preferred intonation of chords
نویسنده
چکیده
It has been argued that convexity in the Euler lattice can be interpreted in terms of consonance (Honingh and Bod 2005). In this paper, a second hypothesis is presented that states that compactness in the Euler-lattice is an indication of consonance. It will be investigated if, and to which degree convexity and compactness are in agreement with the consonance of chords according to Euler’s measure of consonance. First, some diatonic chords are observed, after which the compactness, convexity and consonance according to Euler, is calculated for all possible sets (chords) of 2, 3 and 4 notes within a bounded note name space, such that the relation between these three measures
منابع مشابه
A geometrical approach to find the preferred intonation of chords
Previous work suggested that convexity in the Euler lattice can be interpreted in terms of consonance [1]. In this paper, a second hypothesis is presented that states that compactness in the Euler lattice is an indication of consonance. The convexity and compactness of chords is used as the basis of a model for the preferred intonation of chords in isolation (without a musical context). It is i...
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