225/224: Difference between revisions

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The interval of '''225/224''', the '''marvel comma''', otherwise known as the '''septimal kleisma''', is a [[7-limit]] [[superparticular]] [[comma]]. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]). Maybe most simply, it can be seen as the amount by which {{nowrap| [[15/8]] * [[15/8]] exceeds [[7/2]] }}, or equivalently, the amount by which {{nowrap| (15/8)/(16/15) = [[225/128]] }} exceeds 7/4.

The interval of '''225/224''', the '''marvel comma''', otherwise known as the '''septimal kleisma''', is a [[7-limit]] [[superparticular]] [[comma]]. It pops up as the difference between pairs of 7-limit ratios, for example as {{nowrap| ([[15/14]])/([[16/15]]) }} or {{nowrap| ([[45/32]])/([[7/5]]) }}. Maybe most simply, it can be seen as the amount by which {{nowrap| [[15/8]] * [[15/8]] exceeds [[7/2]] }}, or equivalently, the amount by which {{nowrap| (15/8)/(16/15) = [[225/128]] }} exceeds 7/4.

Another useful relation is as the difference between the [[25/24]], the classical chromatic semitone, and [[28/27]], the septimal third-tone. Hence, it is also the difference between [[32/25]] and [[9/7]], and between [[75/64]] and [[7/6]].

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 {{Wikipedia|Septimal kleisma}}
-The interval of '''225/224''', the '''marvel comma''', otherwise known as the '''septimal kleisma''', is a [[7-limit]] [[superparticular]] [[comma]]. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]). Maybe most simply, it can be seen as the amount by which {{nowrap| [[15/8]] * [[15/8]] exceeds [[7/2]] }}, or equivalently, the amount by which {{nowrap| (15/8)/(16/15) = [[225/128]] }} exceeds 7/4.
+The interval of '''225/224''', the '''marvel comma''', otherwise known as the '''septimal kleisma''', is a [[7-limit]] [[superparticular]] [[comma]]. It pops up as the difference between pairs of 7-limit ratios, for example as {{nowrap| ([[15/14]])/([[16/15]]) }} or {{nowrap| ([[45/32]])/([[7/5]]) }}. Maybe most simply, it can be seen as the amount by which {{nowrap| [[15/8]] * [[15/8]] exceeds [[7/2]] }}, or equivalently, the amount by which {{nowrap| (15/8)/(16/15) = [[225/128]] }} exceeds 7/4.
 Another useful relation is as the difference between the [[25/24]], the classical chromatic semitone, and [[28/27]], the septimal third-tone. Hence, it is also the difference between [[32/25]] and [[9/7]], and between [[75/64]] and [[7/6]].