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.

{{Infobox ET

| Prime factorization = 2 × 3<sup>2</sup> × 23

| Step size = 2.89855¢

| Fifth = 242\414 (701.45¢) (→ [[207edo|121\207]])

| Semitones = 38:32 (110.14¢ : 92.75¢)

| Consistency = 17

}}

The '''414 equal divisions of the octave''' ('''414edo'''), or the '''414(-tone) equal temperament''' ('''414tet''', '''414et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 414 parts of about 2.90 [[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 {{monzo| -37 4 12 1 }} 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]].

== Theory ==

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 {{monzo| -37 4 12 1 }} 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 [[hemiennealimmal]] and the 13-limit [[quatracot]].

=== Prime harmonics ===

@@ Line 1: / Line 1: @@
-'''414edo''' is the [[EDO|equal division of the octave]] into 414 parts of 2.89855 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 2 × 3<sup>2</sup> × 23
+| Step size = 2.89855¢
+| Fifth = 242\414 (701.45¢) (→ [[207edo|121\207]])
+| Semitones = 38:32 (110.14¢ : 92.75¢)
+| Consistency = 17
+}}
+The '''414 equal divisions of the octave''' ('''414edo'''), or the '''414(-tone) equal temperament''' ('''414tet''', '''414et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 414 parts of about 2.90 [[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 {{monzo| -37 4 12 1 }} 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]].
+== Theory ==
+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 {{monzo| -37 4 12 1 }} 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 [[hemiennealimmal]] and the 13-limit [[quatracot]].
 === Prime harmonics ===