561/560 - Revision history

FloraC: /* Temperaments */

2026-03-22T10:25:44Z

Temperaments

← Older revision		Revision as of 10:25, 22 March 2026
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	[[Subgroup]]: 2.3.5.7.11.17		[[Subgroup]]: 2.3.5.7.11.17

	[[~~Mapping~~]]: <br>		[[Subgroup val\|Subgroup-val]] [[mapping]]: <br>
	{\| class="right-all"		{\| class="right-all"
	\|-		\|-

FloraC: Expand

2026-03-22T10:23:19Z

Expand

← Older revision		Revision as of 10:23, 22 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''561/560''', the '''monardisma''' is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]].		'''561/560''', the '''monardisma''' is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] of about 3.09 [[cent]]s. It is the difference between the pentacircle minor third, [[33/28]], and the diatismic minor third, [[20/17]], on account of it being the difference between the diatisma, [[136/135]], and the pentacircle comma, [[896/891]]. It also represents the difference between the supraminor thirds of [[17/14]] and [[40/33]], and between the quartertones of [[33/32]] and [[35/34]].

	== Temperaments ==		== Temperaments ==

FloraC: Complete & update data

2026-03-22T10:10:39Z

Complete & update data

← Older revision		Revision as of 10:10, 22 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}

	'''561/560''', the '''monardisma''' is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]].		'''561/560''', the '''monardisma''' is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]].

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 2.3.5.7.11.17 [[subgroup]] ~~results in~~ the '''monardic ~~temperament~~'''~~, or in the full 17-limit, the '''monardismic~~ temperament~~'''~~, enabling [[monardismic chords]]. This temperament has a number of notable properties:		[[Tempering out]] this comma in the full 17-limit results in the rank-6 '''monardismic''' temperament, or in the 2.3.5.7.11.17 [[subgroup]], the rank-5 '''monardic''' temperament, enabling [[monardismic chords]]. This temperament has a number of notable properties:

	* [[14/11]] and [[20/17]] become [[fifth complement]]s;		* [[14/11]] and [[20/17]] become [[fifth complement]]s;
	* [[11/10]] and [[17/14]] become [[fourth complement]]s.		* [[11/10]] and [[17/14]] become [[fourth complement]]s.

			=== Monardic ===
			[[Subgroup]]: 2.3.5.7.11.17

			[[Mapping]]: <br>
			{\| class="right-all"
			\|-
			\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 4 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| -1 \|\| ]]
			\|}
			: mapping generators: ~2, ~3, ~5, ~7, ~11

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.2042{{c}}, ~3/2 = 701.6222{{c}}, ~5/4 = 386.1804{{c}}, ~7/4 = 968.8197{{c}}, ~11/8 = 550.0934{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6204{{c}}, ~5/4 = 386.3575{{c}}, ~7/4 = 968.9591{{c}}, ~11/8 = 550.2059{{c}}

			{{Optimal ET sequence\|legend=1\| 12, 14c, 15, 17cg, 19g, 22, 31, 41g, 43, 46, 58, 68, 72, 118, 183, 255, 301, 373g, 674eg, 768egg, 1290beeeggg }}

			[[Badness]] (Sintel): 0.204

	=== Monardismic ===		=== Monardismic ===
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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]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = 1200.~~0000~~, ~3/2 = 701.~~7805~~, ~5/4 = 386.~~6883~~, ~7/4 = ~~969~~.~~3735~~, ~11/8 = 550.~~4865~~, ~13/8 = ~~840~~.~~5277~~		* [[WE]]: ~2 = 1200.2042{{c}}, ~3/2 = 701.6222{{c}}, ~5/4 = 386.1804{{c}}, ~7/4 = 968.8197{{c}}, ~11/8 = 550.0934{{c}}, ~13/8 = 839.9145{{c}}
	* [[CWE]]: ~2 = 1200.0000, ~3/2 = 701.6204, ~5/4 = 386.3575, ~7/4 = 968.9591, ~11/8 = 550.2059, ~13/8 = 840.0917		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6204{{c}}, ~5/4 = 386.3575{{c}}, ~7/4 = 968.9591{{c}}, ~11/8 = 550.2059{{c}}, ~13/8 = 840.0917{{c}}

	{{Optimal ET sequence\|legend=1\| 12f, 14cf, 15, 17cg, 19g, 22, 26, 29g, 31, 38df, 41g, 43, 46, 58, 72, 103, 111, 130, 140, 183, 243e, 301, 373g, 886eefgg, 1362bdeeefgggg }}*		{{Optimal ET sequence\|legend=1\| 12f, 14cf, 15, 17cg, 19g, 22, 26, 29g, 31, 38df, 41g, 43, 46, 58, 72, 103, 111, 130, 140, 183, 243e, 301, 373g, 886eefgg, 1362bdeeefgggg }} *

	<nowiki/>* [[optimal patent val]]: [[484edo\|484]]		<nowiki/>* [[optimal patent val]]: [[484edo\|484]]

			[[Badness]] (Sintel): 0.398

	== Etymology ==		== Etymology ==

Xenllium: /* Temperaments */

2025-04-11T23:37:57Z

Temperaments

← Older revision		Revision as of 23:37, 11 April 2025
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 2.3.5.7.11.17 [[subgroup]] results in the '''monardic temperament''', or in the full 17-limit, the '''monardismic temperament''', enabling [[monardismic chords]].		[[Tempering out]] this comma in the 2.3.5.7.11.17 [[subgroup]] results in the '''monardic temperament''', or in the full 17-limit, the '''monardismic temperament''', enabling [[monardismic chords]]. This temperament has a number of notable properties:

			* [[14/11]] and [[20/17]] become [[fifth complement]]s;
			* [[11/10]] and [[17/14]] become [[fourth complement]]s.

	=== Monardismic ===		=== Monardismic ===
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	\|}		\|}

	: ~~mapping~~ generators: ~2, ~3, ~5, ~7, ~11, ~13		: Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: +etymology

2025-02-25T14:53:40Z

+etymology

← Older revision		Revision as of 14:53, 25 February 2025
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	<nowiki/>* [[optimal patent val]]: [[484edo\|484]]		<nowiki/>* [[optimal patent val]]: [[484edo\|484]]

			== Etymology ==
			This comma was named by [[Scott Dakota]] in 2023 after the [[Monarda]] scale, a 12-tone scale of [[tannic]], where this is one of the commas being tempered out.

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

FloraC: -"tsaharuk comma" (tempering out this comma alone doesn't lead to tsaharuk

2025-02-25T14:48:53Z

-"tsaharuk comma" (tempering out this comma alone doesn't lead to tsaharuk

← Older revision		Revision as of 14:48, 25 February 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = monardisma~~, <br>tsaharuk comma~~		\| Name = monardisma
	\| Color name = 17o1org1, <br>solorugu unison, <br>Solorugu comma		\| Color name = 17o1org1, <br>solorugu unison, <br>Solorugu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	'''561/560''', the '''monardisma''' ~~or '''tsaharuk~~ comma~~''' is a~~ [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]].		'''561/560''', the '''monardisma''' is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]].

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

	[[Category:Monardismic]]		[[Category:Monardismic]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

FloraC: Rework; +temperament data

2025-02-25T14:46:06Z

Rework; +temperament data

@@ Line 5: / Line 5: @@
 }}
-'''561/560''', the '''monardisma''' or '''tsaharuk comma''' is a [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]]. Tempering it out defines the '''[[monardismic temperament]]''', which enables [[monardismic chords]].
+'''561/560''', the '''monardisma''' or '''tsaharuk comma''' is a [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]].
 == See also ==

MisterShafXen at 13:34, 25 February 2025

2025-02-25T13:34:01Z

← Older revision		Revision as of 13:34, 25 February 2025
Line 5:		Line 5:
	}}		}}

	'''561/560''', the '''monardisma''' or '''tsaharuk comma''' is a [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]]. Tempering it out defines the '''monardismic temperament''', which enables [[monardismic chords]].		'''561/560''', the '''monardisma''' or '''tsaharuk comma''' is a [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]]. Tempering it out defines the '''[[monardismic temperament]]''', which enables [[monardismic chords]].

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

BudjarnLambeth at 01:49, 16 November 2024

2024-11-16T01:49:51Z

← Older revision		Revision as of 01:49, 16 November 2024
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	[[Category:Monardismic]]		[[Category:Monardismic]]
			[[Category:Commas with unknown etymology]]

BudjarnLambeth: Undo revision 156112 by BudjarnLambeth (talk)

2024-09-22T09:10:24Z

Undo revision 156112 by BudjarnLambeth (talk)

← Older revision		Revision as of 09:10, 22 September 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = monardisma, tsaharuk comma		\| Name = monardisma, <br>tsaharuk comma
	\| Color name = 17o1org1, solorugu unison, Solorugu comma		\| Color name = 17o1org1, <br>solorugu unison, <br>Solorugu comma
	\| Comma = yes		\| Comma = yes
	}}		}}