139edo
| ← 138edo | 139edo | 140edo → |
139edo is the equal division of the octave into 139 parts of 8.6331 cents each. 139edo is the 34th prime EDO.
It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323| (patent val), <139 221 323| (139b), and <139 220 322| (139c).
Commas
Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 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 139bdf val, it tempers out Würschmidt comma, 393216/390625 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.
Using the 139ce val, it tempers out the small diesis, 3125/3072 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 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 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.
Harmonics
| 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 | +25 | -22 | +38 | +14 | -36 | -6 | -16 | -46 | +47 | +22 | |
| Steps (reduced) |
220 (81) |
323 (45) |
390 (112) |
441 (24) |
481 (64) |
514 (97) |
543 (126) |
568 (12) |
590 (34) |
611 (55) |
629 (73) | |