138edo: Difference between revisions
Adopt template: EDO intro; group the vals by similarity; -redundant categories; misc. cleanup |
Note it as an excellent tuning of echidna |
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Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit. | Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit. | ||
Using the 138cde val, it tempers out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 in the 5-limit; [[1728/1715]], [[10976/10935]], and [[250047/250000]] in the 7-limit; [[176/175]], [[540/539]], [[896/891]], and 85184/84375 in the 11-limit; [[351/350]], [[352/351]], [[364/363]], [[640/637]], and [[2197/2187]] in the 13-limit, | Using the 138cde val, it tempers out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 in the 5-limit; [[1728/1715]], [[10976/10935]], and [[250047/250000]] in the 7-limit; [[176/175]], [[540/539]], [[896/891]], and 85184/84375 in the 11-limit; [[351/350]], [[352/351]], [[364/363]], [[640/637]], and [[2197/2187]] in the 13-limit, [[support]]ing the [[echidna]] temperament and giving an excellent tuning. | ||
Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and {{monzo| -41 1 17 }} in the 5-limit; [[2401/2400]], [[2430/2401]], and 9765625/9633792 in the 7-limit; [[385/384]], [[1375/1372]], 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament; [[625/624]], 975/968, [[1001/1000]], and [[1188/1183]] in the 13-limit. | Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and {{monzo| -41 1 17 }} in the 5-limit; [[2401/2400]], [[2430/2401]], and 9765625/9633792 in the 7-limit; [[385/384]], [[1375/1372]], 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament; [[625/624]], 975/968, [[1001/1000]], and [[1188/1183]] in the 13-limit. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|138}} | {{Harmonics in equal|138}} | ||
[[Category:Echidna]] | |||