612edo: Difference between revisions

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== Theory ==

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.

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. In the 13-limit it tempers [[2200/2197]] and [[4096/4095]].

The 612edo has been proposed as the logarithmic [[interval size measure]] '''skisma''' (or '''sk'''), since one step is nearly the same size as the [[schisma]] (32805/32768). Since 612 is divisible by {{EDOs|2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204 and 306}}, it can readily express the step sizes of the 12, 17, 34, 68 and 72 divisions. A table of intervals approximated by 612 can be found under [[Table of 612edo intervals]].

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 == Theory ==
-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.
+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. In the 13-limit it tempers [[2200/2197]] and [[4096/4095]].
 The 612edo has been proposed as the logarithmic [[interval size measure]] '''skisma''' (or '''sk'''), since one step is nearly the same size as the [[schisma]] (32805/32768). Since 612 is divisible by {{EDOs|2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204 and 306}}, it can readily express the step sizes of the 12, 17, 34, 68 and 72 divisions. A table of intervals approximated by 612 can be found under [[Table of 612edo intervals]].