149edo: Difference between revisions

Line 1:

'''149edo''' is the [[equal division of the octave]] into 149 equal parts of 8.054 ~~cents each. It is the smallest division which is uniquely~~ [[~~consistent~~]] through the 17-limit. It provides the [[Optimal_patent_val|optimal patent val]] for 7- 11- 13- and 17-limit [[Sensipent_family|heinz temperament]] and the rank three temperament [[Gamelismic_family|ominous]] in the 13- and 17- limits. It has a generally flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.

'''149edo''' is the [[equal division of the octave]] into 149 equal parts of 8.054 [[cent]]s each.

149edo is the 35th [[prime EDO]].

== Theory ==

149edo is the smallest division which is uniquely [[consistent]] through the [[17-odd-limit]]. It provides the [[optimal patent val]] for 7- 11- 13- and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous|ominous]] in the 13- and 17-limits. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.

149edo is the 35th [[prime EDO]].

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

[[Category:Prime EDO]]

[[Category:Theory]]

@@ Line 1: / Line 1: @@
-'''149edo''' is the [[equal division of the octave]] into 149 equal parts of 8.054 cents each. It is the smallest division which is uniquely [[consistent]] through the 17-limit. It provides the [[Optimal_patent_val|optimal patent val]] for 7- 11- 13- and 17-limit [[Sensipent_family|heinz temperament]] and the rank three temperament [[Gamelismic_family|ominous]] in the 13- and 17- limits. It has a generally flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.
+'''149edo''' is the [[equal division of the octave]] into 149 equal parts of 8.054 [[cent]]s each.
-edo is the 35th [[prime EDO]].
+== Theory ==
+edo is the smallest division which is uniquely [[consistent]] through the [[17-odd-limit]]. It provides the [[optimal patent val]] for 7- 11- 13- and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous|ominous]] in the 13- and 17-limits. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.
+edo is the 35th [[prime EDO]].
+=== Prime harmonics ===
+{{Primes in edo|149}}
 [[Category:Equal divisions of the octave]]
 [[Category:Prime EDO]]
 [[Category:Theory]]