151edo: Difference between revisions

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'''151edo''' is the [[EDO|equal division of the octave]] into 151 parts of 7.9470 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, 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 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 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 151c val, it tempers out the [[Sycamore family|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.

151edo is the ~~36th~~ [[~~prime EDO~~]].

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).

[[~~Category:Equal divisions of~~ the ~~octave~~]]

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.

[[~~Category:Prime EDO~~]]

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 ([[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 ===

=== Subsets and supersets ===

151edo is the 36th [[prime edo]].

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-'''151edo''' is the [[EDO|equal division of the octave]] into 151 parts of 7.9470 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;151 239 351| (patent val), &lt;151 240 351| (151b), and &lt;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 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 151c val, it tempers out the [[Sycamore family|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.
+{{Infobox ET}}
+{{ED intro}}
-edo is the 36th [[prime EDO]].
+edo 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).
-[[Category:Equal divisions of the octave]]
+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.
-[[Category:Prime EDO]]
+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 ([[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 ===
+edo is the 36th [[prime edo]].