160edo: Difference between revisions
+as a subset of 320edo |
m Section titles |
||
| Line 2: | Line 2: | ||
{{EDO intro|160}} | {{EDO intro|160}} | ||
160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma). | 160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, [[tempering out]] [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma). | ||
Using the [[patent val]] {{val| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit. | Using the [[patent val]] {{val| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit. | ||
| Line 12: | Line 12: | ||
As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]]. | As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]]. | ||
=== | === Odd harmonics === | ||
{{Harmonics in equal|160|columns=12}} | {{Harmonics in equal|160|columns=12}} | ||
=== | === Subsets and supersets === | ||
Since 160 factors into 2<sup>5</sup> × 5, 160edo has subset edos {{EDOs| 2, 4, 5, 10, 16, 20, 32, 40, and 80 }}. | Since 160 factors into 2<sup>5</sup> × 5, 160edo has subset edos {{EDOs| 2, 4, 5, 10, 16, 20, 32, 40, and 80 }}. | ||