612edo: Difference between revisions

Line 1:

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 supports 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 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 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]].

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]].

@@ Line 1: / Line 1: @@
 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 supports 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 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 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]].
+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]].
 {{Primes in edo|612}}