156edo: Difference between revisions

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'''156edo''' is the [[EDO|equal division of the octave]] into 156 parts of 7.6923 cents each. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.

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

It [[tempering out|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.

=== Prime harmonics ===

=== Subsets and supersets ===

Sinece 156 factors into {{factorization|156}}, 156edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 13, 26, 39, 52, and 78 }}. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.

== Intervals ==

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-'''156edo''' is the [[EDO|equal division of the octave]] into 156 parts of 7.6923 cents each. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+It [[tempering out|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.
+=== Prime harmonics ===
+{{Harmonics in equal|156|intervals=prime|columns=13}}
+=== Subsets and supersets ===
+Sinece 156 factors into {{factorization|156}}, 156edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 13, 26, 39, 52, and 78 }}. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.
+== Intervals ==
+{{Interval table}}