# 151edo

 ← 150edo 151edo 152edo →
Prime factorization 151 (prime)
Step size 7.94702¢
Fifth 88\151 (699.338¢)
Semitones (A1:m2) 12:13 (95.36¢ : 103.3¢)
Consistency limit 3
Distinct consistency limit 3

151 equal divisions of the octave (abbreviated 151edo or 151ed2), also called 151-tone equal temperament (151tet) or 151 equal temperament (151et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 151 equal parts of about 7.95 ¢ each. Each step represents a frequency ratio of 21/151, or the 151st root of 2.

151edo is inconsistent to the 5-odd-limit and higher limits, with three mappings possible for the 5-limit: 151 239 351] (patent val), 151 240 351] (151b), and 151 239 350] (151c).

Using the patent val, it tempers out the mynic comma, 10077696/9765625 and the python comma, 43046721/41943040 in the 5-limit; 126/125, 1728/1715, and 31104/30625 in the 7-limit; 176/175, 243/242, 441/440, and 5314683/5242880 in the 11-limit; 1287/1280, 1573/1568, and 2200/2197 in the 13-limit.

Using the 151e val, it tempers out 1344/1331, 2187/2156, 2835/2816, and 4000/3993 in the 11-limit; 144/143, 364/363, 1001/1000, and 1716/1715 in the 13-limit.

Using the 151c val, it tempers out the sycamore comma (48828125/47775744) and graviton (129140163/128000000) in the 5-limit; 2430/2401, 3125/3087, and 33075/32768 in the 7-limit; 243/242, 385/384, 2420/2401, and 4000/3993 in the 11-limit; 275/273, 640/637, 847/845, 1573/1568, 1701/1690 in the 13-limit. Using the 151cf val, it tempers out 169/168, 325/324, 975/968, and 1287/1280 in the 13-limit.

Using the 151be val, it tempers out 15625/15552 (kleisma) and [39 -26 1 in the 5-limit; 4000/3969, 6144/6125, and 33614/32805 in the 7-limit; 1232/1215, 2401/2376, 2560/2541, and 3025/3024 in the 11-limit; 196/195, 572/567, 832/825, 1001/1000, and 2197/2178 in the 13-limit.

### Odd harmonics

Approximation of odd harmonics in 151edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -2.62 +3.09 +0.71 +2.71 -2.97 +1.86 +0.47 -1.64 -3.47 -1.91 -0.46
Relative (%) -32.9 +38.9 +8.9 +34.1 -37.4 +23.4 +6.0 -20.7 -43.7 -24.0 -5.8
Steps
(reduced)
239
(88)
351
(49)
424
(122)
479
(26)
522
(69)
559
(106)
590
(137)
617
(13)
641
(37)
663
(59)
683
(79)

### Subsets and supersets

151edo is the 36th prime edo.