151edo

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← 150edo151edo152edo →
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.