129edo

← 128edo

129edo

130edo →

Prime factorization	3 × 43
Step size	9.30233¢
Fifth	75\129 (697.674¢) (→25\43)
Semitones (A1:m2)	9:12 (83.72¢ : 111.6¢)
Dual sharp fifth	76\129 (706.977¢)
Dual flat fifth	75\129 (697.674¢) (→25\43)
Dual major 2nd	22\129 (204.651¢)
Consistency limit	3
Distinct consistency limit	3

129 equal divisions of the octave (abbreviated 129edo or 129ed2), also called 129-tone equal temperament (129tet) or 129 equal temperament (129et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 129 equal parts of about 9.3 ¢ each. Each step represents a frequency ratio of 2^1/129, or the 129th root of 2.

129edo provides the optimal patent val for the 11-limit rank-3 clio temperament. It is the last patent val that tempers out 81/80 so as to support meantone and its higher-limit expansions. It also tempers out 1029/1024 and 1728/1715 in the 7-limit; 176/175 and 540/539 in the 11-limit; 507/500, 676/675 and 847/845 in the 13-limit; 221/220 in the 17-limit; 171/170 and 286/285 in the 19-limit.

The factorization of 129 is 3 and 43.

Odd harmonics

Approximation of odd harmonics in 129edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-4.28	+4.38	-1.38	+0.74	-2.48	-3.32	+0.10	-2.63	+0.16	+3.64	+4.28
	relative (%)	-46	+47	-15	+8	-27	-36	+1	-28	+2	+39	+46
Steps (reduced)		204 (75)	300 (42)	362 (104)	409 (22)	446 (59)	477 (90)	504 (117)	527 (11)	548 (32)	567 (51)	584 (68)