225/224: Difference between revisions

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{{interwiki

| de = 225/224

| en = 225/224

| es =

| ja =

}}

{{Infobox Interval

| Name = marvel comma, septimal kleisma

| Color name = ryy-2, ruyoyo negative 2nd,<br> ~~Ruyoyo comma~~

| Color name = ryy-2, ruyoyo negative 2nd,<br>ryyM, ruyoyoma

| Comma = yes

}}

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]]).

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 a 7-limit ratio and a 5-limit ratio. For example, it's the difference between [[16/15]] and [[15/14]], and between [[7/5]] and [[45/32]]. Moreover, it can be seen as the amount by which [[8/7]] exceeds a stack of two {{nowrap|[[16/15]]'s}}, or as the amount by which a stack of two {{nowrap|[[5/4]]'s}} exceeds [[14/9]]. It's also the difference between [[75/64]] and [[7/6]], and between [[25/24]], the classical chromatic semitone, and [[28/27]], the septimal third-tone.

~~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]]~~.

As a comma with a single power of 7 in it, it is tremendously useful in terms of bringing prime 7 into the framework of [[5-limit]] [[just intonation|JI]]; tempering it out maps [[7/4]] to the classic augmented sixth, [[225/128]] and enables all of the aforementioned equivalences.

In terms of commas, it is the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[septimal meantone]]. In the 11-limit it factors neatly into ([[385/384]])([[540/539]]), and in the 13-limit, ([[351/350]])([[625/624]]) or ([[325/324]])([[729/728]]).

== Temperaments ==

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== See also ==

* [[Marvel]]

* [[Small comma]]

* [[Gallery of just intervals]]

@@ Line 1: / Line 1: @@
+{{interwiki
+| de = 225/224
+| en = 225/224
+| es =
+| ja =
+}}
 {{Infobox Interval
 | Name = marvel comma, septimal kleisma
-| Color name = ryy-2, ruyoyo negative 2nd,<br> Ruyoyo comma
+| Color name = ryy-2, ruyoyo negative 2nd,<br>ryyM, ruyoyoma
 | Comma = yes
 }}
 {{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]]).
+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 a 7-limit ratio and a 5-limit ratio. For example, it's the difference between [[16/15]] and [[15/14]], and between [[7/5]] and [[45/32]]. Moreover, it can be seen as the amount by which [[8/7]] exceeds a stack of two {{nowrap|[[16/15]]'s}}, or as the amount by which a stack of two {{nowrap|[[5/4]]'s}} exceeds [[14/9]]. It's also the difference between [[75/64]] and [[7/6]], and between [[25/24]], the classical chromatic semitone, and [[28/27]], the septimal third-tone.
-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]].
+As a comma with a single power of 7 in it, it is tremendously useful in terms of bringing prime 7 into the framework of [[5-limit]] [[just intonation|JI]]; tempering it out maps [[7/4]] to the classic augmented sixth, [[225/128]] and enables all of the aforementioned equivalences.
 In terms of commas, it is the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[septimal meantone]]. In the 11-limit it factors neatly into ([[385/384]])([[540/539]]), and in the 13-limit, ([[351/350]])([[625/624]]) or ([[325/324]])([[729/728]]).
 == Temperaments ==
@@ Line 22: / Line 28: @@
 == See also ==
+* [[Marvel]]
 * [[Small comma]]
 * [[Gallery of just intervals]]