896/891: Difference between revisions

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The pentacircle comma can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo| 5 -3 0 0 1 -1 }}).

364/363 is the minor minthma or gentle comma, which is the difference between (14/11 × [[13/11]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)

364/363 is the minor minthma or gentle comma, which is the difference between a stack of 14/11 and [[13/11]] ([[182/121]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)

352/351 is the major minthma. Tempering it out means 13/11 is equated with the pythagorean minor third, [[32/27]]. Tempering out 352/351 also makes [[11/9]] and [[16/13]] fifth complements of each other.

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 The pentacircle comma can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo| 5 -3 0 0 1 -1 }}).
-/363 is the minor minthma or gentle comma, which is the difference between (14/11 × [[13/11]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)
+/363 is the minor minthma or gentle comma, which is the difference between a stack of 14/11 and [[13/11]] ([[182/121]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)
 /351 is the major minthma. Tempering it out means 13/11 is equated with the pythagorean minor third, [[32/27]]. Tempering out 352/351 also makes [[11/9]] and [[16/13]] fifth complements of each other.