225/224 - Revision history

Eufalesio: Marvelma as a product of schismas and garischismas

2026-06-23T09:05:00Z

Marvelma as a product of schismas and garischismas

← Older revision		Revision as of 09:05, 23 June 2026
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	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.		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]]).		In terms of commas, it is the difference between [[81/80]] and [[126/125]], is tempered out alongside these two commas in [[septimal meantone]]; and the product of two [[Schisma\|schismas]] and one [[garischisma]], equivalently of a [[schisma]] and an [[aberschisma]]. 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 ==		== Temperaments ==

TallKite: updated the comma color name

2026-04-29T04:01:52Z

updated the comma color name

← Older revision		Revision as of 04:01, 29 April 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = marvel comma, septimal kleisma		\| 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		\| Comma = yes
	}}		}}

Hstraub: Link to German

2026-02-16T10:44:59Z

Link to German

← Older revision		Revision as of 10:44, 16 February 2026
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			{{interwiki
			\| de = 225/224
			\| en = 225/224
			\| es =
			\| ja =
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = marvel comma, septimal kleisma		\| Name = marvel comma, septimal kleisma
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	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.		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]]).		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 ==		== Temperaments ==

Lériendil: mentioned augmented sixth

2025-06-06T11:31:36Z

mentioned augmented sixth

← Older revision		Revision as of 11:31, 6 June 2025
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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 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.		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.

			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]]).		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]]).

TallKite: corrected an error, also changed mathspeak like "(15/14)/(16/15)" to "the difference between 16/15 and 15/14"

2025-06-06T04:22:00Z

corrected an error, also changed mathspeak like "(15/14)/(16/15)" to "the difference between 16/15 and 15/14"

← Older revision		Revision as of 04:22, 6 June 2025
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	{{Wikipedia\|Septimal kleisma}}		{{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 {{nowrap\| (~~[[15~~/14~~]]~~)/(~~[[16/15]]~~) }} or {{nowrap\| (~~[[45/32]]~~)/(~~[[7/5]]~~) }}~~. Moreover, it can be seen as the amount by which [[~~225~~/~~128~~]], a stack of two [[15/8]]'s ~~[[octave reduction\|octave-reduced]], exceeds [[7/4]]~~, or as the amount by which ~~[[25/16]],~~ a stack of two [[5/4]]'s, exceeds [[14/9]]. ~~Hence, it is~~ also the difference between [[75/64]] and [[7/6]], and between [[25/24]], the classical chromatic semitone, and [[28/27]], the septimal third-tone.		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.

	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]]).		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]]).

FloraC: Simplify

2025-03-18T12:21:07Z

Simplify

← Older revision		Revision as of 12:21, 18 March 2025
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	{{Wikipedia\|Septimal kleisma}}		{{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 {{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.~~		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]]) }}. Moreover, it can be seen as the amount by which [[225/128]], a stack of two [[15/8]]'s [[octave reduction\|octave-reduced]], exceeds [[7/4]], or as the amount by which [[25/16]], a stack of two [[5/4]]'s, exceeds [[14/9]]. Hence, it is 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]].

	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]]).		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]]).

Godtone: add nowraps

2025-03-18T03:01:51Z

add nowraps

← Older revision		Revision as of 03:01, 18 March 2025
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	{{Wikipedia\|Septimal kleisma}}		{{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]].		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]].

Godtone: note missing equivalence

2025-03-18T03:00:35Z

note missing equivalence

← Older revision		Revision as of 03:00, 18 March 2025
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	{{Wikipedia\|Septimal kleisma}}		{{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 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.

	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]].		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]].

Godtone: it's annoying to find in my experience and regardless i really dont see what the harm in adding one more link to the "See also" (IMO also the most important/useful one there except maybe the list of superparticular intervals); the "See also" on wikipedia lets you know about related things not just broad categories and it seems a natural interpretation of the ambiguous phrase "See also"

2025-01-23T22:25:49Z

it's annoying to find in my experience and regardless i really dont see what the harm in adding one more link to the "See also" (IMO also the most important/useful one there except maybe the list of superparticular intervals); the "See also" on wikipedia lets you know about related things not just broad categories and it seems a natural interpretation of the ambiguous phrase "See also"

← Older revision		Revision as of 22:25, 23 January 2025
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	== See also ==		== See also ==
			* [[Marvel]]
	* [[Small comma]]		* [[Small comma]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

FloraC: Undo revision 176831 by Godtone (talk). Obscure? It's right there in the opening sentence of the temperaments section, which is where ppl should be looking for

2025-01-17T16:53:54Z

Undo revision 176831 by Godtone (talk). Obscure? It's right there in the opening sentence of the temperaments section, which is where ppl should be looking for

← Older revision		Revision as of 16:53, 17 January 2025
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	== See also ==		== See also ==
	* [[Marvel]]
	* [[Small comma]]		* [[Small comma]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]