65/64 - Revision history

VectorGraphics at 20:48, 1 June 2026

2026-06-01T20:48:48Z

← Older revision		Revision as of 20:48, 1 June 2026
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	This interval is the 13th-partial chroma (13-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "13", while its reciprocal is denoted as "{{invert\|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13.		This interval is the 13th-partial chroma (13-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "13", while its reciprocal is denoted as "{{invert\|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13.

			Tempering it out leads to the rank-2 2.5.13 '''wilsormatic''' temperament, which has a generator tuned to abut 370-375 cents that represents both 5/4 and 16/13, or the rank-5 '''wilsormic''' temperament.

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

BudjarnLambeth at 23:03, 15 November 2024

2024-11-15T23:03:41Z

← Older revision		Revision as of 23:03, 15 November 2024
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	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]
			{{todo\|research\|comment=Is it named after Erv Wilson?}}

FloraC: Expand on Johnston notation

2024-11-13T11:22:53Z

Expand on Johnston notation

← Older revision		Revision as of 11:22, 13 November 2024
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	Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.		Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.

	[[Ben Johnston's notation]] ~~denotes this interval~~ simply with the number "13", ~~and~~ its reciprocal as ~~<span style=~~"~~display: inline-block; transform: rotate(180deg)~~"~~>13</span>~~ (a turned 13).		This interval is the 13th-partial chroma (13-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "13", while its reciprocal is denoted as "{{invert\|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13.

	== See also ==		== See also ==
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[64/63]]		* [[64/63]]

			[[Category:Commas with unknown etymology]]

TallKite at 07:21, 14 January 2023

2023-01-14T07:21:11Z

← Older revision		Revision as of 07:21, 14 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = wilsorma		\| Name = wilsorma
	\| Color name = 3oy1, Thoyo comma		\| Color name = 3oy1, thoyo 1sn,<br>Thoyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

A at 03:41, 10 January 2023

2023-01-10T03:41:54Z

← Older revision		Revision as of 03:41, 10 January 2023
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	In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].		In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].

	Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.		Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.

			[[Ben Johnston's notation]] denotes this interval simply with the number "13", and its reciprocal as <span style="display: inline-block; transform: rotate(180deg)">13</span> (a turned 13).

	== See also ==		== See also ==
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[64/63]]		* [[64/63]]

TallKite: added color name

2022-12-04T02:38:15Z

added color name

← Older revision		Revision as of 02:38, 4 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = wilsorma		\| Name = wilsorma
			\| Color name = 3oy1, Thoyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:41:53Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:41, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 65/64~~
	~~\| Monzo = -6 0 1 0 0 1~~
	~~\| Cents = 26.841376~~
	\| Name = wilsorma		\| Name = wilsorma
	\| ~~FJS name = P1<sup>65</sup>~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}
	In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].		In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[64/63]]		* [[64/63]]

	~~[[Category:13-limit]]~~
	~~[[Category:Small commas]]~~
	~~[[Category:Superparticular]]~~
	~~[[Category:Octave-reduced harmonics]]~~

Fredg999: Misc. edits, categories

2022-03-23T15:42:36Z

Misc. edits, categories

← Older revision		Revision as of 15:42, 23 March 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 65/64		\| Ratio = 65/64
	\| Monzo = -6 0 1 0 0 1		\| Monzo = -6 0 1 0 0 1
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	\| Sound =		\| Sound =
	}}		}}
			In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].

	In [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8¢, nearly a quarter of a semitone or eighth of a tone. It belongs to the [[13-prime-limit]], which means that the highest prime in the ratio is 13. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].		Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.

	Tempering it out turns 5/4 and 13/8 into [[~~Octave_complement\|~~octave ~~complements~~]] of one-another. This is particularly useful in many [[13-limit]] [[~~Magic_family\|~~magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.

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

	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[64/63]]		* [[64/63]]

	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:~~Interval ratio~~]]		[[Category:Small commas]]
	[[Category:Superparticular]]		[[Category:Superparticular]]
	[[Category:~~Unison]]~~		[[Category:Octave-reduced harmonics]]
	~~[[Category:Small commas]]~~
	~~[[Category:Overtone~~]]

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

2022-03-20T21:59:57Z

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:Superparticular]]		[[Category:Superparticular]]
	[[Category:Unison]]		[[Category:Unison]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:Overtone]]		[[Category:Overtone]]

Yourmusic Productions: Effect as a comma

2021-06-12T17:29:29Z

Effect as a comma

← Older revision		Revision as of 17:29, 12 June 2021
Line 10:		Line 10:

	In [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8¢, nearly a quarter of a semitone or eighth of a tone. It belongs to the [[13-prime-limit]], which means that the highest prime in the ratio is 13. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].		In [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8¢, nearly a quarter of a semitone or eighth of a tone. It belongs to the [[13-prime-limit]], which means that the highest prime in the ratio is 13. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].

			Tempering it out turns 5/4 and 13/8 into [[Octave_complement\|octave complements]] of one-another. This is particularly useful in many [[13-limit]] [[Magic_family\|magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.

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