Relations between multiple divisions of the octave and the traditional tonal system

Abstract

Multiple divisions of the octave are described as extensions of the traditional tonal system, by building them from chromatic and diatonic semitones with certain numbers of steps assigned to them. Except for some multiple division systems with relatively few tones per octave, this procedure always works. The number of circles of fifths in the system is equal to the largest common divisor of the numbers of steps contained in the two types of semitones. The description provides a consistent notation and a method for evaluating the qualities of the fifths and the major thirds in the systems. A list of systems with 5 up to 129 tones per octave is given, with summary references to instruments, compositions, and literature.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 3 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.