151edo: Difference between revisions
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151edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val| 151 239 351 }} ([[patent val]]), {{val| 151 '''240''' 351 }} (151b), and {{val| 151 239 '''350''' }} (151c). | |||
Using the patent val, it tempers out the | 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 | 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 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 | Using the 151be val, it tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 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 === | |||
{{Harmonics in equal|151}} | |||
=== Subsets and supersets === | |||
[[ | 151edo is the 36th [[prime edo]]. | ||
Latest revision as of 17:59, 19 February 2025
| ← 150edo | 151edo | 152edo → |
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
| 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.