User:Contribution/Comma dissipation path

Definition

A comma dissipation path is a sequence of notes in a given temperament where each successive interval aims for a specific ratio. In just intonation, following these exact ratios would lead to a final note different from the starting note. However, because of the temperament used, the sequence of intervals loops back to the original note, effectively 'dissipating' the comma.

Examples

In meantone temperaments, the sequence C–G–D–A–E–C forms a comma dissipation path for the syntonic comma (81/80).

In augmented temperaments, the sequence C–E–Ab–C forms a comma dissipation path for the augmented comma (128/125).

In diminished temperaments, the sequence C–Eb–F#–A–C forms a comma dissipation path for the diminished comma (648/625).

In diaschismic temperaments, the sequence C–E–B–F#–Bb–F–C forms a comma dissipation path for the diaschisma comma (2048/2025).