141edo

← 140edo

141edo

142edo →

Prime factorization	3 × 47
Step size	8.51064¢
Fifth	82\141 (697.872¢)
Semitones (A1:m2)	10:13 (85.11¢ : 110.6¢)
Dual sharp fifth	83\141 (706.383¢)
Dual flat fifth	82\141 (697.872¢)
Dual major 2nd	24\141 (204.255¢) (→8\47)
Consistency limit	5
Distinct consistency limit	5

141 equal divisions of the octave (abbreviated 141edo or 141ed2), also called 141-tone equal temperament (141tet) or 141 equal temperament (141et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 141 equal parts of about 8.511 ¢ each. Each step represents a frequency ratio of 2^1/141, or the 141st root of 2.

Using the patent val, it tempers out 78732/78125 (sensipent comma) and 8968066875/8589934592 (trilaquadyo comma) in the 5-limit; 1728/1715, 3645/3584, and 78125/76832 in the 7-limit; 441/440, 1350/1331, 1944/1925, and 4125/4096 in the 11-limit; 144/143, 351/350, 640/637, 975/968, and 3375/3328 in the 13-limit.

Using the 141b val, it tempers out 2109375/2097152 (semicomma) and 244140625/229582512 in the 5-limit; 875/864, 16875/16807, and 65536/64827 in the 7-limit; 100/99, 385/384, 1331/1323, and 60368/59049 in the 11-limit; 275/273, 364/363, 572/567, 640/637, and 9604/9477 in the 13-limit.

Using the 141bc val, it tempers out 1638400/1594323 (immunity comma) and 50331648/48828125 (magus comma) in the 5-limit; 245/243, 28672/28125, and 50421/50400 in the 7-limit; 176/175, 1232/1215, 1331/1323, and 79233/78125 in the 11-limit; 196/195, 325/324, 364/363, 572/567, and 15379/15360 in the 13-limit.

Using the 141def val, it tempers out 225/224, 84035/82944, and 177147/175000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 12005/11979 in the 11-limit; 351/350, 625/624, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

Using the 141ef val, it tempers out 99/98, 243/242, 385/384, and 125000/124509 in the 11-limit; 169/168, 625/624, 1001/1000, and 1188/1183 in the 13-limit.

Using the 141f val, it tempers out 169/168, 364/363, 625/624, 1287/1280, and 2025/2002 in the 13-limit.

Harnonics

Approximation of odd harmonics in 141edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-4.08	-3.33	+1.39	+0.35	+1.87	+2.03	+1.09	-2.83	+0.36	-2.70	+1.51
	relative (%)	-48	-39	+16	+4	+22	+24	+13	-33	+4	-32	+18
Steps (reduced)		223 (82)	327 (45)	396 (114)	447 (24)	488 (65)	522 (99)	551 (128)	576 (12)	599 (35)	619 (55)	638 (74)