31edo: Difference between revisions

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One step of 31edo, measuring about 38.7¢, is called a [[diesis]] because it stands in for several intervals called "dieses" (such as [[128/125]] and [[648/625]]) which are tempered out in [[12edo]]. The diesis is a defining sound of 31edo; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size. The diesis is demonstrated in [[SpiralProgressions]]. [[Zhea Erose]]'s 31edo music uses the interval frequently.

31edo is close to a circle made by stacking 31 pure [[17/13]] subfourths. A circle of 31 pure 17/13's closes with an error of only 2.74 cents ([[relative error]] 7.1%). Remarkably, 31edo tempers out [[83521/83486]], the difference between a stack of four 17/13's and a stack of one 19/13 and one 2/1, ~~which gives~~ 31edo's [[oneirotonic]] (5L 3s) mos accurate 13:17:19 chords.

31edo is close to a circle made by stacking 31 pure [[17/13]] subfourths. A circle of 31 pure 17/13's closes with an error of only 2.74 cents ([[relative error]] 7.1%). Remarkably, 31edo tempers out [[83521/83486]], the 0.7-cent difference between a stack of four 17/13's and a stack of one 19/13 and one 2/1, giving 31edo's [[oneirotonic]] (5L 3s) [[mos]] accurate 13:17:19 chords.

31edo is the 11th [[prime numbers|prime]] EDO, following [[29edo]] and coming before [[37edo]].

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 One step of 31edo, measuring about 38.7¢, is called a [[diesis]] because it stands in for several intervals called "dieses" (such as [[128/125]] and [[648/625]]) which are tempered out in [[12edo]]. The diesis is a defining sound of 31edo; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size. The diesis is demonstrated in [[SpiralProgressions]]. [[Zhea Erose]]'s 31edo music uses the interval frequently.
-edo is close to a circle made by stacking 31 pure [[17/13]] subfourths. A circle of 31 pure 17/13's closes with an error of only 2.74 cents ([[relative error]] 7.1%). Remarkably, 31edo tempers out [[83521/83486]], the difference between a stack of four 17/13's and a stack of one 19/13 and one 2/1, which gives 31edo's [[oneirotonic]] (5L 3s) mos accurate 13:17:19 chords.
+edo is close to a circle made by stacking 31 pure [[17/13]] subfourths. A circle of 31 pure 17/13's closes with an error of only 2.74 cents ([[relative error]] 7.1%). Remarkably, 31edo tempers out [[83521/83486]], the 0.7-cent difference between a stack of four 17/13's and a stack of one 19/13 and one 2/1, giving 31edo's [[oneirotonic]] (5L 3s) [[mos]] accurate 13:17:19 chords.
 edo is the 11th [[prime numbers|prime]] EDO, following [[29edo]] and coming before [[37edo]].