160edo: Difference between revisions

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'''160edo''' is the [[EDO|equal division of the octave]] into 160 parts of exact 7.5 cents each. It is closely related to [[80edo]], but the patent vals 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, 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 160bce val, it tempers out 78732/78125 and 145282683375/137438953472 in the 5-limit; 1029/1024, 2430/2401, and 390625/387072 in the 7-limit; 385/384, 441/440, 2187/2156, and 9375/9317 in the 11-limit; 351/350, 847/845, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit. Using the 160ce val, it tempers out 1638400/1594323 and 2197265625/2147483648 in the 5-limit; 875/864, 2401/2400, and 2097152/2066715 in the 7-limit; 896/891, 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

[[~~Category:Edo~~]]

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 160bce val {{val| 160 '''253''' '''371''' 449 '''553''' 592 }}, it tempers out [[78732/78125]] and 145282683375/137438953472 in the 5-limit; [[1029/1024]], [[2430/2401]], and 390625/387072 in the 7-limit; [[385/384]], 441/440, 2187/2156, and 9375/9317 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, 1573/1568, and 1875/1859 in the 13-limit.

Using the 160ce val {{val| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, [[4125/4096]], and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

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 ===

=== 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 }}.

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-'''160edo''' is the [[EDO|equal division of the octave]] into 160 parts of exact 7.5 cents each. It is closely related to [[80edo]], but the patent vals 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, 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 160bce val, it tempers out 78732/78125 and  145282683375/137438953472 in the 5-limit; 1029/1024, 2430/2401, and 390625/387072 in the 7-limit; 385/384, 441/440, 2187/2156, and 9375/9317 in the 11-limit; 351/350, 847/845, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit. Using the 160ce val, it tempers out 1638400/1594323 and 2197265625/2147483648 in the 5-limit; 875/864, 2401/2400, and 2097152/2066715 in the 7-limit; 896/891, 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edo]]
+edo 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 160bce val {{val| 160 '''253''' '''371''' 449 '''553''' 592 }}, it tempers out [[78732/78125]] and 145282683375/137438953472 in the 5-limit; [[1029/1024]], [[2430/2401]], and 390625/387072 in the 7-limit; [[385/384]], 441/440, 2187/2156, and 9375/9317 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, 1573/1568, and 1875/1859 in the 13-limit.
+Using the 160ce val {{val| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, [[4125/4096]], and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.
+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}}
+=== 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 }}.