Syntonic–chromatic equivalence continuum: Difference between revisions

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| [[Gravity]]
| [[Gravity]]
| [[129140163/128000000]]
| [[129140163/128000000]]
| {{monzo| 13 -17 6 }}
| {{monzo| -13 17 -6 }}
|-
|-
| 7
| 7
|[[Absurdity]]
| [[Absurdity]]
| 10460353203/10240000000
| 10460353203/10240000000
| {{monzo| 17 -21 7 }}
| {{monzo| -17 21 -7 }}
|-
|-
| …
| …

Revision as of 03:54, 7 December 2020

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 satisfies (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…

Temperaments in the continuum
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