612edo: Difference between revisions

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{{Infobox ET

| Prime factorization = 2<sup>2</sup> × 3<sup>2</sup> × 17

| Step size = 1.96078¢

| Fifth = 358\612 (701.961¢)

| Semitones = 58:46 (113.725¢ : 90.196¢)

| Consistency = 15

}}

The '''612 equal divisions of the octave''' ('''612edo'''), or the '''612(-tone) equal temperament''' ('''612tet''', '''612et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 612 parts of about 1.961 [[cent]]s each, a size close to [[32805/32768]], the schisma.

The '''612 equal divisions of the octave''' ('''612edo''') divides the octave into 612 equal parts of 1.961 cents each, 1/12 of a [[Pythagorean comma]] or 1/11 of a [[syntonic comma]]. It is a very strong [[5-limit]] system, a fact noted by Bosanquet and Barbour. It tempers out the sasktel comma, {{monzo| 485 -306 }}, in the 3-limit, and in the 5-limit {{monzo| -52 -17 34 }}, the septendecima, {{monzo| 1 -27 18 }}, the [[ennealimma]], {{monzo| -53 10 16 }}, the kwazy comma, {{monzo| 54 -37 2 }}, the [[monzisma]], {{monzo| -107 47 14 }}, the fortune comma, and {{monzo| 161 -84 -12 }}, the [[atom]]. In the 7-limit it tempers out [[2401/2400]] and [[4375/4374]], so that it [[support]]s the [[ennealimmal]] temperament, and in fact provides the [[optimal patent val]] for ennealimmal. The 7-limit val for 612 can be characterized as the ennealimmal commas plus the kwazy comma. In the 11-limit, it tempers out [[3025/3024]] and [[9801/9800]], so that 612 supports the [[hemiennealimmal]] temperament.

@@ Line 1: / Line 1: @@
+{{Infobox ET
+| Prime factorization = 2<sup>2</sup> × 3<sup>2</sup> × 17
+| Step size = 1.96078¢
+| Fifth = 358\612 (701.961¢)
+| Semitones = 58:46 (113.725¢ : 90.196¢)
+| Consistency = 15
+}}
+The '''612 equal divisions of the octave''' ('''612edo'''), or the '''612(-tone) equal temperament''' ('''612tet''', '''612et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 612 parts of about 1.961 [[cent]]s each, a size close to [[32805/32768]], the schisma.
 The '''612 equal divisions of the octave''' ('''612edo''') divides the octave into 612 equal parts of 1.961 cents each, 1/12 of a [[Pythagorean comma]] or 1/11 of a [[syntonic comma]]. It is a very strong [[5-limit]] system, a fact noted by Bosanquet and Barbour. It tempers out the sasktel comma, {{monzo| 485 -306 }}, in the 3-limit, and in the 5-limit {{monzo| -52 -17 34 }}, the septendecima, {{monzo| 1 -27 18 }}, the [[ennealimma]], {{monzo| -53 10 16 }}, the kwazy comma, {{monzo| 54 -37 2 }}, the [[monzisma]], {{monzo| -107 47 14 }}, the fortune comma, and {{monzo| 161 -84 -12 }}, the [[atom]]. In the 7-limit it tempers out [[2401/2400]] and [[4375/4374]], so that it [[support]]s the [[ennealimmal]] temperament, and in fact provides the [[optimal patent val]] for ennealimmal. The 7-limit val for 612 can be characterized as the ennealimmal commas plus the kwazy comma. In the 11-limit, it tempers out [[3025/3024]] and [[9801/9800]], so that 612 supports the [[hemiennealimmal]] temperament.