Tridecimal eighth-octave comma - Revision history

Hotcrystal0 at 01:25, 30 September 2026

2026-09-30T01:25:48Z

← Older revision		Revision as of 01:25, 30 September 2026
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	== Etymology ==		== Etymology ==
	17303/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, ⁸√{{Overline\|(214990848/214358881)~~³·815730721~~/800000000}}.		17303/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, ⁸√{{Overline\|([[214990848/214358881]])³·[[815730721/800000000]]}}.
	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]

Eufalesio: Blunder

2026-09-29T18:48:06Z

Blunder

← Older revision		Revision as of 18:48, 29 September 2026
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	}}		}}

	'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable 13-limit (specifically no-7 13-limit) comma. As an [[ultraparticular]], it is the difference between a stack of three [[12/11]] and [[13/10]]. In terms of commas, it is also:		'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable [[13-limit]] (specifically no-7 13-limit) comma. As an [[ultraparticular]], it is the difference between a stack of three [[12/11]] and [[13/10]]. In terms of commas, it is also:

	* ([[1331/1296]])/([[40/39]])		* ([[1331/1296]])/([[40/39]])
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	== Temperaments ==		== Temperaments ==
	As its name suggests, it is tempered out in low EDOs that are a multiple of 8 (specifically {{EDOs\|8, 16, 24, 32, 40, 56, 64, 72, 80, 96, 120…}}). As its S-expression suggests, it is tempered out in [[gariwizmic]] since all of its constituents are commas of it. It is also tempered out in [[tertiaschis]], [[tritikleismic]], [[Artoneutral (temperament)\|artoneutral]], [[Porcupinefowl\|''porcupinefowl'']] and [[wizard]] - which means the edos {{EDOs\|7, 15, 22f, 87, 94, 159, 166, 253, 270, 364…}} also temper it out by extension.		As its name suggests, it is tempered out in low EDOs that are a multiple of 8 (specifically {{EDOs\|8, 16, 24, 32, 40, 56, 64, 72, 80, 96, 120…}}).

			As its S-expression suggests, it is tempered out in [[gariwizmic]] since all of its constituents are commas of it. It is also tempered out in [[tertiaschis]], [[tritikleismic]], [[Artoneutral (temperament)\|artoneutral]], [[Porcupinefowl\|''porcupinefowl'']] and [[wizard]] - which means the edos {{EDOs\|7, 15, 22f, 87, 94, 159, 166, 253, 270, 364…}} also temper it out by extension.

	== Etymology ==		== Etymology ==
	17303/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, ~~<sup>8</sup>√~~{{Overline\|214990848/~~214358881·815730721~~/800000000}}.		17303/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, ⁸√{{Overline\|(214990848/214358881)³·815730721/800000000}}.
	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]

Eufalesio: Connecting all the dots!

2026-09-29T18:43:37Z

Connecting all the dots!

@@ Line 7: / Line 7: @@
 }}
-'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] semisixth, and is also the interval separating [[1331/1296]] from the simpler [[40/39]]. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815730721/800000000]], defining various [[8th-octave temperaments]].  However, that's not all, as it is also tempered out in EDOs such as [[159edo]].
+'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable 13-limit (specifically no-7 13-limit) comma. As an [[ultraparticular]], it is the difference between a stack of three [[12/11]] and [[13/10]]. In terms of commas, it is also:
 [[Category:Commas named for their periods per equave]]

Hotcrystal0: use correct name

2026-04-24T19:53:29Z

use correct name

← Older revision		Revision as of 19:53, 24 April 2026
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	}}		}}

	'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] semisixth, and is also the interval separating [[1331/1296]] from the simpler [[40/39]]. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[~~815830271~~/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].		'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] semisixth, and is also the interval separating [[1331/1296]] from the simpler [[40/39]]. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815730721/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].

	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]

Aura: Added information

2025-06-08T11:24:53Z

Added information

← Older revision		Revision as of 11:24, 8 June 2025
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	}}		}}

	'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] ~~supermajor third~~. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].		'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] semisixth, and is also the interval separating [[1331/1296]] from the simpler [[40/39]]. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].

	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]

BudjarnLambeth at 03:14, 4 November 2024

2024-11-04T03:14:15Z

← Older revision		Revision as of 03:14, 4 November 2024
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	'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].		'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].

			[[Category:Commas named for their periods per equave]]

BudjarnLambeth: BudjarnLambeth moved page 17303/17280 to Tridecimal eighth-octave comma: Long comma number

2024-10-22T23:44:46Z

BudjarnLambeth moved page 17303/17280 to Tridecimal eighth-octave comma: Long comma number

← Older revision	Revision as of 23:44, 22 October 2024
(No difference)

BudjarnLambeth: Named, but this time with a straightforward intuitive name

2024-10-22T23:43:55Z

Named, but this time with a straightforward intuitive name

← Older revision		Revision as of 23:43, 22 October 2024
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	\|Monzo = -7 -3 -1 0 3 1		\|Monzo = -7 -3 -1 0 3 1
	\|Color name = 3o1o<sup>3</sup>g1 <br> thotrilo-agu unison		\|Color name = 3o1o<sup>3</sup>g1 <br> thotrilo-agu unison
			\|Name = Tridecimal eighth-octave comma
	\|Comma = yes		\|Comma = yes
	}}		}}

	'''17303/17280''' is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].		'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].

BudjarnLambeth: BudjarnLambeth moved page Shelly comma to 17303/17280 over redirect: Get rid of name as discussed on Discord

2024-10-15T06:14:37Z

BudjarnLambeth moved page Shelly comma to 17303/17280 over redirect: Get rid of name as discussed on Discord

← Older revision	Revision as of 06:14, 15 October 2024
(No difference)

BudjarnLambeth: Remove name

2024-10-15T06:14:03Z

Remove name

← Older revision		Revision as of 06:14, 15 October 2024
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	\|Ratio = 17303/17280		\|Ratio = 17303/17280
	\|Monzo = -7 -3 -1 0 3 1		\|Monzo = -7 -3 -1 0 3 1
	~~\|Name = Shelly comma~~
	\|Color name = 3o1o<sup>3</sup>g1 <br> thotrilo-agu unison		\|Color name = 3o1o<sup>3</sup>g1 <br> thotrilo-agu unison
	\|Comma = yes		\|Comma = yes
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	'''17303/17280''' is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].		'''17303/17280''' is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as it is also tempered out in EDOs such as [[159edo]].

	~~Previously known, but unnamed, [[Budjarn Lambeth]] named it the '''shelly comma''' in 2024, after asteroid 17280 Shelly.~~