2601/2600 - Revision history

FloraC: Update data

2026-03-29T07:40:28Z

Update data

← Older revision		Revision as of 07:40, 29 March 2026
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	: mapping generators: ~2, ~3, ~5, ~51/20		: mapping generators: ~2, ~3, ~5, ~51/20

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.~~9252~~{{c}}, ~5/4 = 386.~~3777~~{{c}}, ~51/40 = 420.~~3045~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0165{{c}}, ~3/2 = 701.9109{{c}}, ~5/4 = 386.3400{{c}}, ~51/40 = 420.2767{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9128{{c}}, ~5/4 = 386.3554{{c}}, ~51/40 = 420.2871{{c}}

	{{Optimal ET sequence\|legend=1\| ~~12,~~ 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg }}		{{Optimal ET sequence\|legend=1\| 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg }}

			[[Badness]] (Sintel): 0.0654

	=== Sextantonismic ===		=== Sextantonismic ===
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 2 \|\| 1 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 2 \|\| 1 \|\| ]]
	\|}		\|}

	: mapping generators: ~2, ~3, ~5, ~7, ~11, ~51/20		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~51/20

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.~~9252~~{{c}}, ~5/4 = 386.~~3777~~{{c}}, ~7/4, ~11/8, ~51/40 = 420.~~3045~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0165{{c}}, ~3/2 = 701.9109{{c}}, ~5/4 = 386.3400{{c}}, ~7/4 = 968.7969{{c}}, ~11/8 = 551.2685{{c}}, ~51/40 = 420.2767{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9128{{c}}, ~5/4 = 386.3554{{c}}, ~7/4 = 968.8019{{c}}, ~11/8 = 551.2883{{c}}, ~51/40 = 420.2871{{c}}

	{{Optimal ET sequence\|legend=1\| 17cg, 22f, 26, 29g, 31, 38df, 43, 46, 60e, 65d, 68, 72, 103, 111, 140, 171, 183, 217, 243e, 282, 311, 354, 400, 422, 460, 494, 742, 814, 954, 1236, 1696, 2190g, 4069g }}<nowiki>*</nowiki>		{{Optimal ET sequence\|legend=1\| 17cg, 22f, 26, 29g, 31, 38df, 43, 46, 60e, 65d, 68, 72, 103, 111, 140, 171, 183, 217, 243e, 282, 311, 354, 400, 422, 460, 494, 742, 814, 954, 1236, 1696, 2190g, 4069g }}<nowiki>*</nowiki>

	<nowiki>*</nowiki> [[optimal patent val]]: [[2932edo\|2932]]		<nowiki>*</nowiki> [[optimal patent val]]: [[2932edo\|2932]]

			[[Badness]] (Sintel): 0.689

	== Etymology ==		== Etymology ==

FloraC: Expand on etymology. Misc. cleanup

2026-03-29T07:34:02Z

Expand on etymology. Misc. cleanup

← Older revision		Revision as of 07:34, 29 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''2601/2600''', the '''sextantonisma''', is a [[17-limit]] (also 2.3.5.13.17 [[subgroup]]) [[superparticular]] [[comma]] measuring about 0.67 [[cent]]s. It may be properly described as the ''septendecimal sixth-tones comma'', since it is the difference between [[51/50]] and [[52/51]], the two 17-limit sixth-tones. ~~Another prominent identity is~~ the little gap between [[18/13]] and a stack of two [[20/17]]'s.		'''2601/2600''', the '''sextantonisma''', is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] (also 2.3.5.13.17-[[subgroup]]) [[superparticular]] [[comma]] measuring about 0.666 [[cent]]s. It may be properly described as the ''septendecimal sixth-tones comma'', since it is the difference between [[51/50]] and [[52/51]], the two 17-limit sixth-tones. It also represents the little gap between [[18/13]] and a stack of two [[20/17]]'s.

	== Commatic relations ==		== Commatic relations ==
	In terms of commas, it is the difference between the following pairs:		In terms of commas, it is the difference between the following pairs:
	* [[289/288]] and [[325/324]] ~~(both of these commas are also within the 2.3.5.13.17 subgroup, while most others listed here are not)~~		* [[289/288]] and [[325/324]] *
	* [[561/560]] and [[715/714]]		* [[561/560]] and [[715/714]]
	* [[833/832]] and [[1225/1224]]		* [[833/832]] and [[1225/1224]]
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	* [[2401/2400]] and [[31213/31212]]		* [[2401/2400]] and [[31213/31212]]
	* [[2431/2430]] and [[37180/37179]]		* [[2431/2430]] and [[37180/37179]]

			<nowiki/>* relation within the 2.3.5.13.17 subgroup

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit results in the rank-6 '''sextantonismic ~~temperament~~''', or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic ~~temperament~~'''. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and ~~enables the~~ [[sextantonismic chords]]. If [[140625/140608]] is also added to the comma list, the sixth-tone above becomes literally a sixth of [[9/8]] and is tuned exactly middle of 51/50 and 52/51. This temperament, however, strongly suggests also tempering out [[9801/9800]] and/or [[12376/12375]] since 2601/2600 = (9801/9800)(12376/12375)<sup>2</sup>(140625/140608).		[[Tempering out]] this comma in the 17-limit results in the rank-6 '''sextantonismic''' temperament, or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic''' temperament. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and [[sextantonismic chords]] are enabled.

			If [[140625/140608]] is also added to the comma list, the sixth-tone above becomes literally a sixth of [[9/8]] and is tuned exactly middle of 51/50 and 52/51. This temperament, however, strongly suggests also tempering out [[9801/9800]] and/or [[12376/12375]] since 2601/2600 = (9801/9800)⋅(12376/12375)<sup>2</sup>(140625/140608).

	=== Sextantonic ===		=== Sextantonic ===
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	{{Mapping\|legend=2\| 1 0 0 2 1 \| 0 1 0 0 -1 \| 0 0 0 0 1 \| 0 0 0 2 1 }}		{{Mapping\|legend=2\| 1 0 0 2 1 \| 0 1 0 0 -1 \| 0 0 0 0 1 \| 0 0 0 2 1 }}
			: mapping generators: ~2, ~3, ~5, ~51/20

	~~: sval mapping generators: ~2, ~3, ~5, ~51/20~~		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9252{{c}}, ~5/4 = 386.3777{{c}}, ~51/40 = 420.3045{{c}}

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.9252, ~5/4 = 386.3777, ~51/40 = 420.3045

	{{Optimal ET sequence\|legend=1\| 12, 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg }}		{{Optimal ET sequence\|legend=1\| 12, 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg }}
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	: mapping generators: ~2, ~3, ~5, ~7, ~11, ~51/20		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~51/20

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.9252, ~5/4 = 386.3777, ~7/4, ~11/8, ~51/40 = 420.3045		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9252{{c}}, ~5/4 = 386.3777{{c}}, ~7/4, ~11/8, ~51/40 = 420.3045{{c}}

	{{Optimal ET sequence\|legend=1\| 17cg, 22f, 26, 29g, 31, 38df, 43, 46, 60e, 65d, 68, 72, 103, 111, 140, 171, 183, 217, 243e, 282, 311, 354, 400, 422, 460, 494, 742, 814, 954, 1236, 1696, 2190g, 4069g }}<nowiki>*</nowiki>		{{Optimal ET sequence\|legend=1\| 17cg, 22f, 26, 29g, 31, 38df, 43, 46, 60e, 65d, 68, 72, 103, 111, 140, 171, 183, 217, 243e, 282, 311, 354, 400, 422, 460, 494, 742, 814, 954, 1236, 1696, 2190g, 4069g }}<nowiki>*</nowiki>
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	== Etymology ==		== Etymology ==
	The sextantonisma was named by [[Flora Canou]] in 2023. It is a contraction of ''~~septendecimal~~ sixth-tones comma'' into a single word consisting of Latin ''sextans'' ("sixth") and ''tonus'' ("tone").		The sextantonisma was named by [[Flora Canou]] in 2023. It is a contraction of ''sixth-tones comma'' into a single word consisting of Latin ''sextans'' ("sixth") and ''tonus'' ("tone"). This comma was chosen as the sixth-tones comma because the sixth-tones it separates lie in the middle of the harmonic series segment of sixth-tones, 48::54.

	== See also ==		== See also ==
	* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Sextantonismic]]		[[Category:Sextantonismic]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]

BudjarnLambeth at 02:01, 16 November 2024

2024-11-16T02:01:38Z

← Older revision		Revision as of 02:01, 16 November 2024
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	[[Category:Sextantonismic]]		[[Category:Sextantonismic]]
			[[Category:Commas named for the intervals they stack]]

Dummy index: mark the subgroup-strict decomposition ((51/50)/(52/51) is obvious)

2024-05-12T06:48:31Z

mark the subgroup-strict decomposition ((51/50)/(52/51) is obvious)

← Older revision		Revision as of 06:48, 12 May 2024
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	== Commatic relations ==		== Commatic relations ==
	In terms of commas, it is the difference between the following pairs:		In terms of commas, it is the difference between the following pairs:
	* [[289/288]] and [[325/324]]		* [[289/288]] and [[325/324]] (both of these commas are also within the 2.3.5.13.17 subgroup, while most others listed here are not)
	* [[561/560]] and [[715/714]]		* [[561/560]] and [[715/714]]
	* [[833/832]] and [[1225/1224]]		* [[833/832]] and [[1225/1224]]

FloraC: /* Temperaments */ swap them to impress the reader of the "simpler" temp first

2024-03-28T10:24:30Z

Temperaments: swap them to impress the reader of the "simpler" temp first

@@ Line 19: / Line 19: @@
 == Temperaments ==
 Tempering out this comma in the 17-limit results in the rank-6 '''sextantonismic temperament''', or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic temperament'''. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and enables the [[sextantonismic chords]]. If [[140625/140608]] is also added to the comma list, the sixth-tone above becomes literally a sixth of [[9/8]] and is tuned exactly middle of 51/50 and 52/51. This temperament, however, strongly suggests also tempering out [[9801/9800]] and/or [[12376/12375]] since 2601/2600 = (9801/9800)(12376/12375)<sup>2</sup>(140625/140608).
 === Sextantonismic ===
@@ Line 46: / Line 57: @@
 <nowiki>*</nowiki> [[optimal patent val]]: [[2932edo|2932]]
 == Etymology ==

FloraC: +commatic relation

2023-09-05T15:22:08Z

+commatic relation

← Older revision		Revision as of 15:22, 5 September 2023
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	* [[1701/1700]] and [[4914/4913]]		* [[1701/1700]] and [[4914/4913]]
	* [[2401/2400]] and [[31213/31212]]		* [[2401/2400]] and [[31213/31212]]
			* [[2431/2430]] and [[37180/37179]]

	== Temperaments ==		== Temperaments ==

FloraC: /* Temperaments */ note about tuning exact sixth-tones

2023-08-13T14:12:17Z

Temperaments: note about tuning exact sixth-tones

← Older revision		Revision as of 14:12, 13 August 2023
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit results in the rank-6 '''sextantonismic temperament''', or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic temperament'''. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and enables the [[sextantonismic chords]].		Tempering out this comma in the 17-limit results in the rank-6 '''sextantonismic temperament''', or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic temperament'''. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and enables the [[sextantonismic chords]]. If [[140625/140608]] is also added to the comma list, the sixth-tone above becomes literally a sixth of [[9/8]] and is tuned exactly middle of 51/50 and 52/51. This temperament, however, strongly suggests also tempering out [[9801/9800]] and/or [[12376/12375]] since 2601/2600 = (9801/9800)(12376/12375)<sup>2</sup>(140625/140608).

	=== Sextantonismic ===		=== Sextantonismic ===

FloraC: /* Temperaments */ correct ET sequence (I forgot to turn off patent val)

2023-08-13T13:40:30Z

Temperaments: correct ET sequence (I forgot to turn off patent val)

← Older revision		Revision as of 13:40, 13 August 2023
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	=== Sextantonic ===		=== Sextantonic ===
	[[Subgroup]]: 2.3.5~~.7.11~~.13.17		[[Subgroup]]: 2.3.5.13.17

	{{Mapping\|legend=2\| 1 0 0 2 1 \| 0 1 0 0 -1 \| 0 0 0 0 1 \| 0 0 0 2 1 }}		{{Mapping\|legend=2\| 1 0 0 2 1 \| 0 1 0 0 -1 \| 0 0 0 0 1 \| 0 0 0 2 1 }}
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	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9252, ~5/4 = 386.3777, ~51/40 = 420.3045		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9252, ~5/4 = 386.3777, ~51/40 = 420.3045

	{{Optimal ET sequence\|legend=1\| 12, 25, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848 }}		{{Optimal ET sequence\|legend=1\| 12, 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg }}

	== Etymology ==		== Etymology ==

FloraC: /* Temperaments */ +data

2023-08-13T13:34:34Z

Temperaments: +data

@@ Line 17: / Line 17: @@
 == Temperaments ==
 Tempering out this comma in the 17-limit results in the rank-6 '''sextantonismic temperament''', or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic temperament'''. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and enables the [[sextantonismic chords]].
 == Etymology ==

FloraC at 09:58, 23 February 2023

2023-02-23T09:58:21Z

← Older revision		Revision as of 09:58, 23 February 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~septendecimal sixth-tones comma~~		\| Name = sextantonisma
	\| Color name = 17oo3ugg2, sosothugugu 2nd,<br>Sosothugugu comma		\| Color name = 17oo3ugg2, sosothugugu 2nd,<br>Sosothugugu comma
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''2601/2600''' is a [[17-limit]] (also 2.3.5.13.17 subgroup) [[superparticular]] [[comma]] measuring about 0.67 [[cent]]s. It may be properly described as the ''septendecimal sixth-tones comma'', since it is the difference between [[51/50]] and [[52/51]], the two 17-limit sixth-tones. Another prominent identity is the little gap between [[18/13]] and a stack of two [[20/17]]'s.		'''2601/2600''', the '''sextantonisma''', is a [[17-limit]] (also 2.3.5.13.17 [[subgroup]]) [[superparticular]] [[comma]] measuring about 0.67 [[cent]]s. It may be properly described as the ''septendecimal sixth-tones comma'', since it is the difference between [[51/50]] and [[52/51]], the two 17-limit sixth-tones. Another prominent identity is the little gap between [[18/13]] and a stack of two [[20/17]]'s.

			== Commatic relations ==
	In terms of commas, it is the difference between the following pairs:		In terms of commas, it is the difference between the following pairs:
	* [[289/288]] and [[325/324]]		* [[289/288]] and [[325/324]]
Line 16:		Line 17:

	== Temperaments ==		== Temperaments ==
	Tempering out this comma results in [[26/25]] ~~being~~ split into two equal parts, each representing 51/50~52/51, and enables the ~~related essentially tempered~~ chords.		Tempering out this comma in the 17-limit results in the rank-6 '''sextantonismic temperament''', or in the 2.3.5.13.17 subgroup, the rank-4 '''sextantonic temperament'''. In either case [[26/25]] is split into two equal parts, each representing 51/50~52/51, and enables the [[sextantonismic chords]].

			== Etymology ==
			The sextantonisma was named by [[Flora Canou]] in 2023. It is a contraction of ''septendecimal sixth-tones comma'' into a single word consisting of Latin ''sextans'' ("sixth") and ''tonus'' ("tone").

	== See also ==		== See also ==
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			[[Category:Sextantonismic]]