Proportion Chains

Karlheinz Schüffler
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Karlheinz Schüffler: Heinrich-Heine-Universität Düsseldorf, Mathematik

Chapter 2 in Proportions and Their Music, 2024, pp 35-82 from Springer

Abstract: Abstract In this chapter (Proportion Chains) we will decisively expand the concept of proportions in order to be able to describe the most important applications with regard to ancient music-theory. If one adds proportions to each other, then so-called chains of proportions are created. We find these chains of proportions already in ancient music-theory. Here there are three significant areas in particular the chord-theory, the scale-theory and the modology, in which the mathematics of proportion chains provides constructive answers for all structural features. The text of this chapter on chains of proportions is structured by the following sequence, in which the mathematical theory of multilevel iterations of proportions is embedded and developed: 1. The basic terms for proportion chains, 2. the composition of proportion chains, 3. reciprocal proportion chains, 4. symmetrical proportion chains, 5. the proportion chain theorem.

Date: 2024
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DOI: 10.1007/978-3-662-65336-4_2

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