Octave-splitting comma
Octave-splitting commas are rational intervals which induce fractional-octave temperaments. If tempering out the comma leads to splitting the octave into N equal parts (N > 1), the comma is an octave-splitting comma which induces an Nth-octave temperament.
This terminology was developed by Xenllium.
Examples
Below is a list of octave-splitting commas for common temperaments:
| Comma | Associated temperament |
Harmonic limit |
Splitting order |
|---|---|---|---|
| 256/243 | Blackwood | 3 | 5 |
| 2187/2048 | Whitewood | 3 | 7 |
| 531441/524288 | Compton | 3 | 12 |
| 2048/2025 | Diaschismic | 5 | 2 |
| 128/125 | Augmented | 5 | 3 |
| 648/625 | Diminished | 5 | 4 |
| 50/49 | Jubilismic | 7 | 2 |
| 250047/250000 | Landscape | 7 | 3 |
| 9801/9800 | Kalismic | 11 | 2 |
| 289/288 | Semitonismic | 17 | 2 |