414edo: Difference between revisions

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'''~~414EDO~~''' is the [[EDO|equal division of the octave]] into 414 parts of 2.89855 [[cent]]s each. It is closely related to [[207edo]], but the patent ~~vals~~ differ on the mapping for 5. It is consistent to the 17-limit, tempering out ~~69198046875/68719476736~~ (submajor comma) and ~~7629394531250/7625597484987~~ (~~ennealimmal comma~~) in the 5-limit; 2401/2400, 4375/4374, and 138427734375/137438953472 in the 7-limit; 3025/3024, 9801/9800, 41503/41472, and 1265625/1261568 in the 11-limit; 625/624, 729/728, 1575/1573, 2200/2197, and 26411/26364 in the 13-limit; 833/832, 1089/1088, 1225/1224, 1275/1274, and 1701/1700 in the 17-limit. It [[support]]s the 11-limit [[Ragismic microtemperaments|hemiennealimmal]] and the 13-limit [[Ragismic microtemperaments|quatracot]].

'''414edo''' is the [[EDO|equal division of the octave]] into 414 parts of 2.89855 [[cent]]s each.

414edo is closely related to [[207edo]], but the [[patent val]]s differ on the mapping for 5. It is [[consistent]] to the [[17-odd-limit]], tempering out {{monzo| -36 11 8 }} (submajor comma) and {{monzo|1 -27 18}} ([[ennealimma]]) in the 5-limit; [[2401/2400]], [[4375/4374]], and 138427734375/137438953472 in the 7-limit; [[3025/3024]], [[9801/9800]], [[41503/41472]], and 1265625/1261568 in the 11-limit; [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]], and 26411/26364 in the 13-limit; [[833/832]], [[1089/1088]], [[1225/1224]], 1275/1274, and [[1701/1700]] in the 17-limit. It [[support]]s the 11-limit [[Ragismic microtemperaments|hemiennealimmal]] and the 13-limit [[Ragismic microtemperaments|quatracot]].

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

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-'''414EDO''' is the [[EDO|equal division of the octave]] into 414 parts of 2.89855 [[cent]]s each. It is closely related to [[207edo]], but the patent vals differ on the mapping for 5. It is consistent to the 17-limit, tempering out 69198046875/68719476736 (submajor comma) and 7629394531250/7625597484987 (ennealimmal comma) in the 5-limit; 2401/2400, 4375/4374, and 138427734375/137438953472 in the 7-limit; 3025/3024, 9801/9800, 41503/41472, and 1265625/1261568 in the 11-limit; 625/624, 729/728, 1575/1573, 2200/2197, and 26411/26364 in the 13-limit; 833/832, 1089/1088, 1225/1224, 1275/1274, and 1701/1700 in the 17-limit. It [[support]]s the 11-limit [[Ragismic microtemperaments|hemiennealimmal]] and the 13-limit [[Ragismic microtemperaments|quatracot]].
+'''414edo''' is the [[EDO|equal division of the octave]] into 414 parts of 2.89855 [[cent]]s each.
+edo is closely related to [[207edo]], but the [[patent val]]s differ on the mapping for 5. It is [[consistent]] to the [[17-odd-limit]], tempering out {{monzo| -36 11 8 }} (submajor comma) and {{monzo|1 -27 18}} ([[ennealimma]]) in the 5-limit; [[2401/2400]], [[4375/4374]], and 138427734375/137438953472 in the 7-limit; [[3025/3024]], [[9801/9800]], [[41503/41472]], and 1265625/1261568 in the 11-limit; [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]], and 26411/26364 in the 13-limit; [[833/832]], [[1089/1088]], [[1225/1224]], 1275/1274, and [[1701/1700]] in the 17-limit. It [[support]]s the 11-limit [[Ragismic microtemperaments|hemiennealimmal]] and the 13-limit [[Ragismic microtemperaments|quatracot]].
+=== Prime harmonics ===
+{{Harmonics in equal|414}}
 [[Category:Equal divisions of the octave]]