2187/2176 - Revision history

Lucius Chiaraviglio: Add major thirds relation

2026-03-13T00:48:27Z

Add major thirds relation

← Older revision		Revision as of 00:48, 13 March 2026
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	Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048, which means it is the difference between [[17/1\|17th harmonic]] and a stack of seven [[3/2]] perfect fifths.		Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048, which means it is the difference between [[17/1\|17th harmonic]] and a stack of seven [[3/2]] perfect fifths.

	Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].		Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], between [[81/64]] and [[34/27]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].

	The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by [[4131/4096]], so 17/16 is represented as a minor second.		The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by [[4131/4096]], so 17/16 is represented as a minor second.

BudjarnLambeth at 00:34, 16 November 2024

2024-11-16T00:34:47Z

← Older revision		Revision as of 00:34, 16 November 2024
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	== References ==		== References ==
	<references/>		<references/>

			[[Category:Commas named for their regular temperament properties]]

FloraC: Put similar statements together to enhance reading experience

2024-05-09T14:58:59Z

Put similar statements together to enhance reading experience

← Older revision		Revision as of 14:58, 9 May 2024
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	}}		}}

	The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7{{cent}}~~. It is most intuitively described as the difference betwen the stack of 7 [[3/2]] perfect fifths and [[17/1\|17th harmonic]]~~.		The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[small comma\|small]] [[17-limit]] [[comma]] measuring about 8.7{{cent}}.

	Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048.		Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048, which means it is the difference between [[17/1\|17th harmonic]] and a stack of seven [[3/2]] perfect fifths.

	Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].		Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].

	The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by [[4131/4096]], so 17/16 is represented as a minor second.		The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by [[4131/4096]], so 17/16 is represented as a minor second.

	~~== See also ==~~
	* [[Comma]]

	== References ==		== References ==
	<references/>		<references/>

Eliora: Add an interpretation which I think should be mentioned

2024-05-08T16:46:57Z

Add an interpretation which I think should be mentioned

← Older revision		Revision as of 16:46, 8 May 2024
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	}}		}}

	The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7{{cent}}. Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048.		The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7{{cent}}. It is most intuitively described as the difference betwen the stack of 7 [[3/2]] perfect fifths and [[17/1\|17th harmonic]].

			Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048.

	Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].		Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].

Kaiveran at 18:57, 31 May 2023

2023-05-31T18:57:11Z

← Older revision		Revision as of 18:57, 31 May 2023
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	Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].		Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].

	The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by 4131/4096, so 17/16 is represented as a minor second.		The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by [[4131/4096]], so 17/16 is represented as a minor second.

	== See also ==		== See also ==

TallKite at 20:28, 11 January 2023

2023-01-11T20:28:09Z

← Older revision		Revision as of 20:28, 11 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = septendecimal schisma		\| Name = septendecimal schisma
	\| Color name = L17u-2, Lasu comma		\| Color name = L17u-2, lasu negative 2nd,<br>Lasu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

TallKite: added color name

2022-12-29T01:58:25Z

added color name

← Older revision		Revision as of 01:58, 29 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = septendecimal schisma		\| Name = septendecimal schisma
			\| Color name = L17u-2, Lasu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T14:24:17Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 14:24, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 2187/2176~~
	~~\| Monzo = -7 7 0 0 0 0 -1~~
	~~\| Cents = 8.72960~~
	\| Name = septendecimal schisma		\| Name = septendecimal schisma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name = d-2<sub>17</sub>~~
	~~\| Sound~~ =
	}}		}}

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	== References ==		== References ==
	<references/>		<references/>

	~~[[Category:17-limit]]~~
	~~[[Category:Small commas]]~~

	~~{{todo\|add color name}}~~

Fredg999: Misc. edits, categories

2022-04-05T16:29:36Z

Misc. edits, categories

← Older revision		Revision as of 16:29, 5 April 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| JI glyph =~~
	\| Ratio = 2187/2176		\| Ratio = 2187/2176
	\| Monzo = -7 7 0 0 0 0 -1		\| Monzo = -7 7 0 0 0 0 -1
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	}}		}}

	The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7 ~~cents~~. Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048.		The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7{{cent}}. Although several times in size, it shares similarities with the [[schisma]] – while the schisma is the amount by which [[16/15]] deviates from [[2187/2048]], the septendecimal schisma is the amount by which [[17/16]] deviates from 2187/2048.

	Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].		Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal comma [[4131/4096]] make a [[Pythagorean comma]].

	The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In [[Functional Just System]], however, that role is taken by 4131/4096, so 17/16 is represented as a minor second.		The septendecimal schisma is significant in [[Helmholtz-Ellis notation]] (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the [[Functional Just System]], however, that role is taken by 4131/4096, so 17/16 is represented as a minor second.

	== See also ==		== See also ==
			* [[Comma]]

	* [[Comma]]		== References ==
	* Footnotes
	<references/>		<references/>

	[[Category:17-limit]]		[[Category:17-limit]]
	[[Category:Small commas]]		[[Category:Small commas]]
	~~[[Category:Ratio]]~~
			{{todo\|add color name}}

Fredg999 category edits: Moving from Category:Small comma to Category:Small commas using Cat-a-lot

2022-03-20T21:59:55Z

Moving from Category:Small comma to Category:Small commas using Cat-a-lot

← Older revision		Revision as of 21:59, 20 March 2022
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	[[Category:17-limit]]		[[Category:17-limit]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:Ratio]]		[[Category:Ratio]]