151edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''151edo''' is the [[EDO|equal division of the octave]] into 151 parts of 7.9470 [[cent]]s each.
{{EDO intro}}


It is inconsistent to the 5-limit and higher limit, 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).  
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 quinbigu comma, 10077696/9765625 and the lalagu 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 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 151be val, it tempers out [[kleisma]] (15625/15552) and 2748779069440/2541865828329 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.  
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.  


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.  
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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 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.


151edo is the 36th [[prime EDO]].
=== Odd harmonics ===
{{Harmonics in equal|151}}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
=== Subsets and supersets ===
[[Category:Prime EDO]]
151edo is the 36th [[prime edo]].

Revision as of 09:20, 14 May 2024

← 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

Template:EDO intro

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 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.

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 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.

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.

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