129edo

129edo is the equal division of the octave into 129 parts of 9.302 cents each. It 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.

← 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

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 (%)	-46.0	+47.1	-14.9	+8.0	-26.7	-35.7	+1.1	-28.3	+1.7	+39.1	+46.1
Steps (reduced)		204 (75)	300 (42)	362 (104)	409 (22)	446 (59)	477 (90)	504 (117)	527 (11)	548 (32)	567 (51)	584 (68)

Miscellany

The factorization of 129 is 3 and 43.