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 2^1/160, 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.