A systematic evaluation of equal temperaments through N=612

Abstract

An objective measure of how well an equal temperament can provide close approximations to harmonic intervals is introduced, and applied to temperaments with as many as 612 notes per octave. Different results are obtained depending on whether intervals involving prime factors 7 or 11 are included. These results are compared with the proposals of other authors as to which divisions of the octave offer special advantages deserving exploration by composers. While N=19 and 53 stand out as the best alternatives to N=12 for traditional music, N=31 is to be preferred when intervals involving 7 are used, and 31, 37 or 72 when the factor 11 is included.

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 — 5 citations exist upstream.

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