Syntonic–chromatic equivalence continuum
The syntonic-chromatic equivalence continuum is a continuum of temperaments which equate a number of syntonic commas (81/80) with the chromatic semitone (2187/2048).
All temperaments in the continuum satisfy (81/80)n ~ 2187/2048. Varying n results in different temperaments such as whitewood, mavila, dicot, porcupine, tetracot, amity, gravity, and absurdity. It converges to meantone as n approaches infinity. The just value of n is 5.2861…
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| 0 | Whitewood | 2187/2048 | [-11 7⟩ |
| 1 | Mavila | 135/128 | [-7 3 1⟩ |
| 2 | Dicot | 25/24 | [-3 -1 2⟩ |
| 3 | Porcupine | 250/243 | [1 -5 3⟩ |
| 4 | Tetracot | 20000/19683 | [5 -9 4⟩ |
| 5 | Amity | 1600000/1594323 | [9 -13 5⟩ |
| 6 | Gravity | 129140163/128000000 | [-13 17 -6⟩ |
| 7 | Absurdity | 10460353203/10240000000 | [-17 21 -7⟩ |
| … | … | … | … |
| Inf | Meantone | 81/80 | [-4 4 -1⟩ |
Also fractional values of n: enipucrop (n = 1.5), seville (n = 2.3), sixix (n = 2.5), sevond (n = 3.5), brahmagupta (n = 5.25).