160edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{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). | |||
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. | ||
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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. | 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]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|160|columns=12}} | {{Harmonics in equal|160|columns=12}} | ||
=== Divisors === | |||
Since 160 factors into 2<sup>5</sup> × 5, 160edo has subset edos {{EDOs| 2, 4, 5, 10, 16, 20, 32, 40, and 80 }}. | |||
Revision as of 07:55, 6 January 2023
| ← 159edo | 160edo | 161edo → |
160edo 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 ⟨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 ⟨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 ⟨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.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.04 | +3.69 | -1.33 | -1.41 | +3.68 | -0.53 | -0.77 | +0.04 | +2.49 | +1.72 | +1.73 | -0.13 |
| Relative (%) | +40.6 | +49.2 | -17.7 | -18.8 | +49.1 | -7.0 | -10.2 | +0.6 | +33.2 | +22.9 | +23.0 | -1.7 | |
| Steps (reduced) |
254 (94) |
372 (52) |
449 (129) |
507 (27) |
554 (74) |
592 (112) |
625 (145) |
654 (14) |
680 (40) |
703 (63) |
724 (84) |
743 (103) | |
Divisors
Since 160 factors into 25 × 5, 160edo has subset edos 2, 4, 5, 10, 16, 20, 32, 40, and 80.