120/119 - Revision history

FloraC at 14:40, 21 March 2026

2026-03-21T14:40:11Z

← Older revision		Revision as of 14:40, 21 March 2026
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic ~~temperament~~'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic ~~temperament~~'''. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.		[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic''' temperament. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic''' temperament. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

	Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[char]], though it loses accuracy when compared to marvel.		Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[char]], though it loses accuracy when compared to marvel.

FloraC: /* Temperaments */

2026-03-21T12:49:10Z

Temperaments

← Older revision		Revision as of 12:49, 21 March 2026
Line 9:		Line 9:
	[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.		[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

	Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[~~Marvel family #Char\|~~char]], though it loses accuracy when compared to marvel.		Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[char]], though it loses accuracy when compared to marvel.

	=== Lynchic ===		=== Lynchic ===

FloraC: Update data

2026-03-21T10:19:29Z

Update data

← Older revision		Revision as of 10:19, 21 March 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}

	'''120/119''', the '''lynchisma''', is a [[small comma\|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]].		'''120/119''', the '''lynchisma''', is a [[small comma\|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]].

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	Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[Marvel family #Char\|char]], though it loses accuracy when compared to marvel.		Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[Marvel family #Char\|char]], though it loses accuracy when compared to marvel.

			=== Lynchic ===
			[[Subgroup]]: 2.3.5.7.17

			{{Mapping\|legend=2\| 1 0 0 0 3 \| 0 1 0 0 1 \| 0 0 1 0 1 \| 0 0 0 1 -1 }}
			: mapping generators: ~2, ~3, ~5, ~7

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}

			{{Optimal ET sequence\|legend=1\| 10, 12, 19, 22, 27g, 31, 41, 53, 198ddggg }}

			[[Badness]] (Sintel): 0.220

	=== Lynchismic ===		=== Lynchismic ===
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
	\|}		\|}
	: ~~Mapping~~ generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	~~[[Optimal tuning]]:~~
	* [[TE]]: ~2 = 1198.953, ~3 = 1901.078, ~5 = 2784.431, ~7 = 3371.578
	* [[CTE]]: ~2 = 1200.000 (1<span style="font-family:'Arial', sans-serif">\</span>1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340

	~~=== Lynchic ===~~
	~~Subgroup: 2.3.5.7.17~~

	~~Mapping: {{mapping\| 1 0 0 0 3 \| 0 1 0 0 1 \| 0 0 1 0 1 \| 0 0 0 1 -1 }}~~

	: ~~Mapping generators~~: ~2, ~3, ~5, ~7		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}, ~11/8 = 554.4584{{c}}, ~13/8 = 843.6671{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}, ~11/8 = 553.3440{{c}}, ~13/8 = 842.6949{{c}}

	Optimal ~~tuning (CTE): ~2~~ = ~~1200.000 (~~1~~<span style="font-family:'Arial'~~, ~~sans-serif">\</span>1)~~, ~~~3/2 = 700.835~~, ~~~5/4 = 383.910~~, ~~~7/4 = 972.340~~		{{Optimal ET sequence\|legend=1\| 19, 22, 26, 27eg, 31, 41, 49fg, 53, 65d, 84g, 92defg, 106g, 123dfgg, 128dg, 137gg, 145dgg, 171dgg }}

	~~{{Optimal ET sequence\|legend=~~0~~\| 10, 12, 19, 22, 26, 31, 41, 53 }}~~		[[Badness]] (Sintel): 0.603

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

			[[Category:Lynchismic]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

Overthink: /* Temperaments */ note the name

2026-02-25T00:01:21Z

Temperaments: note the name

← Older revision		Revision as of 00:01, 25 February 2026
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	[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.		[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

	Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] ~~temperaments~~ that ~~includes~~ prime 17, though ~~at the cost of~~ accuracy.		Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[Marvel family #Char\|char]], though it loses accuracy when compared to marvel.

	=== Lynchismic ===		=== Lynchismic ===

FloraC: Cleanup

2026-01-27T10:38:52Z

Cleanup

← Older revision		Revision as of 10:38, 27 January 2026
Line 5:		Line 5:
	}}		}}

	'''120/119''', the '''lynchisma''' is ~~the~~ [[17-limit]] [[superparticular]] comma of about 14.49 ~~cents~~. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.		'''120/119''', the '''lynchisma''', is a [[small comma\|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]].

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. Since 120/119 factors as [[225/224]]*[[256/255]], it would make sense to temper them both out, so lynchic can be ~~used as~~ a simple extension of [[marvel]] temperaments ~~to include~~ prime 17, though at the cost of accuracy.		[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. In either case, it allows you to assign [[10:12:15:17]] as the inverse of [[4:5:6:7]], an otonal chord that would otherwise be [[70:84:105:120]]. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

			Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] temperaments that includes prime 17, though at the cost of accuracy.

	=== Lynchismic ===		=== Lynchismic ===
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	== See also ==		== See also ==
	* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

Overthink: /* Temperaments */ add factoring

2026-01-27T05:22:48Z

Temperaments: add factoring

← Older revision		Revision as of 05:22, 27 January 2026
Line 8:		Line 8:

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''.		Tempering out this comma in the 17-limit leads to the rank-6 '''lynchismic temperament'''. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 '''lynchic temperament'''. Since 120/119 factors as [[225/224]]*[[256/255]], it would make sense to temper them both out, so lynchic can be used as a simple extension of [[marvel]] temperaments to include prime 17, though at the cost of accuracy.

	=== Lynchismic ===		=== Lynchismic ===

Xenllium at 22:34, 20 April 2025

2025-04-20T22:34:00Z

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = lynchisma
-| Color name = 17ury-2, suruyo negative 2nd,<br>Suruyo comma
+| Color name = 17ury-2, suruyo negative 2nd, <br>Suruyo comma
 | Comma = yes
 }}
@@ Line 7: / Line 7: @@
 '''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's thoughts on septimal harmony and 22edo|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.
-By tempering it out is defined the '''lynchismic temperament''', which enables the [[lynchismic chords]]. EDOs supporting this temperament includes {{EDOs|10, 12, 19, 22, 26, 31, 41}} and [[53edo|53]].
+== Temperaments ==
 [[Category:Commas named after composers]]
 [[Category:Commas named after music theorists]]

ArrowHead294: Update link

2024-11-19T14:24:01Z

Update link

← Older revision		Revision as of 14:24, 19 November 2024
Line 5:		Line 5:
	}}		}}

	'''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's ~~Thoughts~~ on ~~Septimal Harmony~~ and ~~22 EDO~~\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.		'''120/119''', the '''lynchisma''' is the [[17-limit]] [[superparticular]] comma of about 14.49 cents. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. [[William Lynch's thoughts on septimal harmony and 22edo\|William Lynch]] calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

	By tempering it out is defined the '''lynchismic temperament''', which enables the [[lynchismic chords]]. EDOs supporting this temperament includes {{EDOs\|10, 12, 19, 22, 26, 31, 41}} and [[53edo\|53]].		By tempering it out is defined the '''lynchismic temperament''', which enables the [[lynchismic chords]]. EDOs supporting this temperament includes {{EDOs\|10, 12, 19, 22, 26, 31, 41}} and [[53edo\|53]].

BudjarnLambeth at 00:26, 16 November 2024

2024-11-16T00:26:50Z

← Older revision		Revision as of 00:26, 16 November 2024
Line 8:		Line 8:

	By tempering it out is defined the '''lynchismic temperament''', which enables the [[lynchismic chords]]. EDOs supporting this temperament includes {{EDOs\|10, 12, 19, 22, 26, 31, 41}} and [[53edo\|53]].		By tempering it out is defined the '''lynchismic temperament''', which enables the [[lynchismic chords]]. EDOs supporting this temperament includes {{EDOs\|10, 12, 19, 22, 26, 31, 41}} and [[53edo\|53]].

			[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

TallKite at 03:02, 4 December 2022

2022-12-04T03:02:11Z

← Older revision		Revision as of 03:02, 4 December 2022
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = lynchisma		\| Name = lynchisma
	\| Color name = suruyo negative 2nd, ~~17ury-2~~		\| Color name = 17ury-2, suruyo negative 2nd,<br>Suruyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}