139edo

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139edo

140edo →

Prime factorization	139 (prime)
Step size	8.63309 ¢
Fifth	81\139 (699.281 ¢)
Semitones (A1:m2)	11:12 (94.96 ¢ : 103.6 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

139edo is inconsistent to the 5-odd-limit and higher limits, with three mappings possible for the 5-limit: ⟨139 220 323] (patent val), ⟨139 221 323] (139b), and ⟨139 220 322] (139c).

Using the patent val, it tempers out 1990656/1953125 (valentine comma) and 43046721/41943040 (python comma) in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit valentine temperament; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the alternative 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit interpental temperament; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit.

Using the 139ce val, it tempers out 3125/3072 (magic comma) and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit trismegistus temperament; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit.

Using the 139bdf val, it tempers out 393216/390625 (würschmidt comma), and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 139edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-2.67	+2.18	-1.92	+3.28	+1.20	-3.12	-0.50	-1.36	-3.99	+4.04	+1.94
	Relative (%)	-31.0	+25.2	-22.2	+38.0	+13.9	-36.1	-5.8	-15.7	-46.2	+46.8	+22.5
Steps (reduced)		220 (81)	323 (45)	390 (112)	441 (24)	481 (64)	514 (97)	543 (126)	568 (12)	590 (34)	611 (55)	629 (73)