225/224: Difference between revisions

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 The interval of '''225/224''', the '''septimal kleisma''' or '''marvel comma''' is a [[7-limit]] [[superparticular]] ratio. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]).
-It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[Meantone family#Septimal meantone|Septimal meantone]].
+It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[Meantone family#Septimal meantone|Septimal meantone]]. If we don't temper out this interval and instead repeatedly stack (and octave-reduce) it, we get [[311edo]], where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo.
 == Temperaments ==