Bird's eye view of temperaments by accuracy: Difference between revisions
→11-limit focus: note about 16/15 violating bound |
m →7-limit focus: make formatting of gens shown consistent |
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72 for {3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 49, 63} ([[27L 45s]]) | 72 for {3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 49, 63} ([[27L 45s]]) | ||
[[Bird's eye view of temperaments by accuracy#Generator tunings|Generator tunings]]: 3\72, 4\99, 7\171, 11\270 | [[Bird's eye view of temperaments by accuracy#Generator tunings|Generator tunings]]: (3\72, 1\9), (4\99, 1\9), (7\171, 1\9), (11\270, 1\9) | ||
Ennealimmal has a 1/9-octave period representing [[27/25]], and two of them represent [[7/6]], tempering out [[4375/4374]]. It is generated by a [[~]][[36/35]] quartertone, with 3/2 being mapped to | Ennealimmal has a 1/9-octave period representing [[27/25]], and two of them represent [[7/6]], tempering out [[4375/4374]]. It is generated by a [[~]][[36/35]] quartertone, with 3/2 being mapped to 6 periods minus 2 generators, 5/4 mapped to 4 periods minus 3 generators, and 7/4 mapped to 8 periods minus 2 generators. It finds a neutral third representing [[49/40]]~[[60/49]] at 3 periods minus 1 generator, tempering out [[2401/2400]]. This temperament therefore tempers out the two smallest superparticular ratios in the [[7-limit]], 2401/2400 and 4375/4374. It is very accurate, with errors of around 0.2 cents in optimized tunings. However, due to the high note count, one may prefer lower accuracy temperaments. | ||
=== 11-limit focus === | === 11-limit focus === | ||