163edo

← 162edo

163edo

164edo →

Prime factorization	163 (prime)
Step size	7.36196 ¢
Fifth	95\163 (699.387 ¢)
Semitones (A1:m2)	13:14 (95.71 ¢ : 103.1 ¢)
Dual sharp fifth	96\163 (706.748 ¢)
Dual flat fifth	95\163 (699.387 ¢)
Dual major 2nd	28\163 (206.135 ¢)
Consistency limit	5
Distinct consistency limit	5

163 equal divisions of the octave (abbreviated 163edo or 163ed2), also called 163-tone equal temperament (163tet) or 163 equal temperament (163et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 163 equal parts of about 7.36 ¢ each. Each step represents a frequency ratio of 2^1/163, or the 163rd root of 2.

163edo tempers out 15625/15552 (kleisma) and [-42 28 -1⟩ in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 413343/409600 in the 7-limit; 2187/2156, 2420/2401, 2835/2816 and 4375/4356 in the 11-limit; 351/350, 640/637, 975/968, 1188/1183, and 1573/1568 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 163edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-2.57	-3.49	+2.95	+2.22	+0.83	-1.26	+1.30	-1.89	-3.03	+0.38	-2.51
	Relative (%)	-34.9	-47.4	+40.1	+30.2	+11.3	-17.2	+17.7	-25.6	-41.2	+5.2	-34.1
Steps (reduced)		258 (95)	378 (52)	458 (132)	517 (28)	564 (75)	603 (114)	637 (148)	666 (14)	692 (40)	716 (64)	737 (85)

Subsets and supersets

163edo is the 38th prime edo.