# 160edo

 ← 159edo 160edo 161edo →
Prime factorization 25 × 5
Step size 7.5¢
Fifth 94\160 (705¢) (→47\80)
Semitones (A1:m2) 18:10 (135¢ : 75¢)
Dual sharp fifth 94\160 (705¢) (→47\80)
Dual flat fifth 93\160 (697.5¢)
Dual major 2nd 27\160 (202.5¢)
Consistency limit 5
Distinct consistency limit 5

160 equal divisions of the octave (abbreviated 160edo or 160ed2), also called 160-tone equal temperament (160tet) or 160 equal temperament (160et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 160 equal parts of exactly 7.5 ¢ each. Each step represents a frequency ratio of 21/160, or the 160th root of 2.

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.

### Odd harmonics

Approximation of odd harmonics in 160edo
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)

### Subsets and supersets

Since 160 factors into 25 × 5, 160edo has subset edos 2, 4, 5, 10, 16, 20, 32, 40, and 80.