273/272 - Revision history

FloraC: /* Temperaments */

2026-03-22T10:25:01Z

Temperaments

← Older revision		Revision as of 10:25, 22 March 2026
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	[[Comma list]]: 273/272		[[Comma list]]: 273/272

	{{Mapping\|legend=1\| 1 0 0 0 -4 \| 0 1 0 0 1 \| 0 0 1 0 1 \| 0 0 0 1 1 }}		{{Mapping\|legend=2\| 1 0 0 0 -4 \| 0 1 0 0 1 \| 0 0 1 0 1 \| 0 0 0 1 1 }}
	: mapping generators: ~2, ~3, ~7, ~13		: mapping generators: ~2, ~3, ~7, ~13

FloraC: + see also

2026-03-22T10:02:50Z

+ see also

← Older revision		Revision as of 10:02, 22 March 2026
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	== Etymology ==		== Etymology ==
	This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma naming standard as it would induce ''tannic'' as a temperament that tempers out the comma alone in its minimal prime subgroup, 2.3.7.13.17 {273/272}, for which Scott's 17-limit tannic is a weak extension and cannot share the same time. ''Prototannisma'' has thus been proposed as an alternative name.		This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma naming standard as it would induce ''tannic'' as a temperament that tempers out the comma alone in its minimal prime subgroup, 2.3.7.13.17 {273/272}, for which Scott's 17-limit tannic is a weak extension and cannot share the same time. ''Prototannisma'' has thus been proposed as an alternative name.

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

	== References ==		== References ==

FloraC: Update data

2026-03-22T10:00:49Z

Update data

@@ Line 31: / Line 31: @@
 == Temperaments ==
 [[Tempering out]] this comma in the 17-limit leads to the rank-6 '''prototannismic''' temperament, or in the 2.3.7.13.17 subgroup, the rank-4 '''prototannic''' temperament, both characterized by the equivalences introduced above, and lead to a type of [[essentially tempered chord]]s called [[prototannismic chords]]. The prototannic temperament has a notable [[weak extension]] to the full 17-limit called [[tannic]]. According to [[Scott Dakota]], tannic is of similar overall utility to [[marvel]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.
 === Prototannismic ===
@@ Line 54: / Line 70: @@
 : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.5638{{c}}, ~5/4, ~7/4 = 967.5985{{c}}, ~11/8, ~13/8 = 838.3951{{c}}
+[[Optimal tuning]]s:
 {{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }}
-=== Prototannic ===
+[[Badness]] (Sintel): 0.678
 == Etymology ==

FloraC: Cleanup/rework

2026-03-22T09:55:21Z

Cleanup/rework

← Older revision		Revision as of 09:55, 22 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
			'''273/272''', the '''tannisma''', or the '''prototannisma''', is a [[small comma\|small]] [[17-limit]] (also 2.3.7.13.17-[[subgroup]]) [[comma]] with a value of roughly 6.35 [[cent]]s. It forms the difference between [[21/17]] and [[16/13]], and the difference between [[39/32]] and [[17/14]], as well as the difference between [[17/13]] and [[21/16]].
	'''273/272''', the '''tannisma''', or the '''prototannisma''', is a [[small comma\|small]] [[17-limit]] (also 2.3.7.13.17 [[subgroup]]) [[comma]] with a value of roughly 6.35 [[cent]]s. It forms the difference between [[21/17]] and [[16/13]], and the difference between [[39/32]] and [[17/14]], as well as the difference between [[17/13]] and [[21/16]].

	== Commatic relations ==		== Commatic relations ==
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit leads to the rank-6 '''prototannismic ~~temperament~~''', or in the 2.3.7.13.17 subgroup, the rank-4 '''prototannic ~~temperament~~''', both characterized by the equivalences introduced above, and lead to a type of essentially tempered ~~chords~~ called [[prototannismic chords]]. The prototannic temperament has a notable [[~~extension\|~~weak extension]] to the full 17-limit called [[tannic]]. ~~However, that is not all, as according~~ to [[Scott Dakota]], tannic is ~~actually~~ of similar overall utility to [[marvel ~~temperament~~]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.		[[Tempering out]] this comma in the 17-limit leads to the rank-6 '''prototannismic''' temperament, or in the 2.3.7.13.17 subgroup, the rank-4 '''prototannic''' temperament, both characterized by the equivalences introduced above, and lead to a type of [[essentially tempered chord]]s called [[prototannismic chords]]. The prototannic temperament has a notable [[weak extension]] to the full 17-limit called [[tannic]]. According to [[Scott Dakota]], tannic is of similar overall utility to [[marvel]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.

	=== Prototannismic ===		=== Prototannismic ===
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]
	\|}		\|}

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

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.5638, ~5/4, ~7/4 = 967.5985, ~11/8, ~13/8 = 838.3951		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.5638{{c}}, ~5/4, ~7/4 = 967.5985{{c}}, ~11/8, ~13/8 = 838.3951{{c}}

	{{Optimal ET sequence\|legend=1\| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }}		{{Optimal ET sequence\|legend=1\| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }}
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	{{Mapping\|legend=1\| 1 0 0 0 -4 \| 0 1 0 0 1 \| 0 0 1 0 1 \| 0 0 0 1 1 }}		{{Mapping\|legend=1\| 1 0 0 0 -4 \| 0 1 0 0 1 \| 0 0 1 0 1 \| 0 0 0 1 1 }}

	: mapping generators: ~2, ~3, ~7, ~13		: mapping generators: ~2, ~3, ~7, ~13

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.5638, ~7/4 = 967.5985, ~13/8 = 838.3951		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.5638{{c}}, ~7/4 = 967.5985{{c}}, ~13/8 = 838.3951{{c}}

	{{Optimal ET sequence\|legend=1\| 10, 17g, 24, 26, 31, 36, 113, 149 }}		{{Optimal ET sequence\|legend=1\| 10, 17g, 24, 26, 31, 36, 113, 149 }}

	== Etymology ==		== Etymology ==
	This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma ~~logging~~ standard ~~that a comma name "X-isma" should not be associated to~~ a temperament ~~"X-ic" if "X-ic" is a weak extension of the temperament induced by~~ the comma, ~~since 17-limit tannic is a weak extension of~~ 2.3.7.13.17[273/272~~] (see above)~~. ''Prototannisma'' has thus been proposed as an alternative name.		This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma naming standard as it would induce ''tannic'' as a temperament that tempers out the comma alone in its minimal prime subgroup, 2.3.7.13.17 {273/272}, for which Scott's 17-limit tannic is a weak extension and cannot share the same time. ''Prototannisma'' has thus been proposed as an alternative name.

	== References ==		== References ==

Squib: /* Commatic relations */

2026-03-13T15:34:53Z

Commatic relations

← Older revision		Revision as of 15:34, 13 March 2026
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	* [[325/324]] and [[1701/1700]]		* [[325/324]] and [[1701/1700]]
	* [[289/288]] and [[4914/4913]]		* [[289/288]] and [[4914/4913]]

			It also factors neatly into three superparticular commas: [[715/714]], [[833/832]], and [[936/935]].

	== Temperaments ==		== Temperaments ==

BudjarnLambeth at 00:39, 16 November 2024

2024-11-16T00:39:22Z

← Older revision		Revision as of 00:39, 16 November 2024
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	[[Category:Prototannismic]]		[[Category:Prototannismic]]
			[[Category:Commas with unknown etymology]]

Inthar: /* Etymology */ style

2023-08-01T00:50:19Z

Etymology: style

← Older revision		Revision as of 00:50, 1 August 2023
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	== Etymology ==		== Etymology ==
	This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" if "X-ic" is a weak extension of the temperament ~~that~~ the comma ~~induces~~, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272] (see above). ''Prototannisma'' has thus been proposed as an alternative name.		This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" if "X-ic" is a weak extension of the temperament induced by the comma, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272] (see above). ''Prototannisma'' has thus been proposed as an alternative name.

	== References ==		== References ==

Inthar: /* Temperaments */

2023-07-28T12:11:12Z

Temperaments

← Older revision		Revision as of 12:11, 28 July 2023
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit leads to the rank-6 '''prototannismic temperament''', or in the 2.3.7.13.17 subgroup, the rank-4 '''prototannic temperament''', both characterized by the equivalences introduced above, and lead to a type of essentially tempered chords called [[prototannismic chords]]. The prototannic temperament has a notable [[extension\|weak extension]] to the full 17-limit called [[tannic]]. However, that is not all, as according to [[Scott Dakota]], tannic is actually of similar overall utility to ~~those that temper out the~~ [[marvel ~~comma~~]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.		Tempering out this comma in the 17-limit leads to the rank-6 '''prototannismic temperament''', or in the 2.3.7.13.17 subgroup, the rank-4 '''prototannic temperament''', both characterized by the equivalences introduced above, and lead to a type of essentially tempered chords called [[prototannismic chords]]. The prototannic temperament has a notable [[extension\|weak extension]] to the full 17-limit called [[tannic]]. However, that is not all, as according to [[Scott Dakota]], tannic is actually of similar overall utility to [[marvel temperament]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.

	=== Prototannismic ===		=== Prototannismic ===

Inthar: /* Etymology */

2023-07-28T11:56:57Z

Etymology

← Older revision		Revision as of 11:56, 28 July 2023
Line 72:		Line 72:

	== Etymology ==		== Etymology ==
	This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" ~~that~~ is a weak extension of the temperament that the comma induces, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272] (see above). ''Prototannisma'' has thus been proposed as an alternative name.		This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" if "X-ic" is a weak extension of the temperament that the comma induces, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272] (see above). ''Prototannisma'' has thus been proposed as an alternative name.

	== References ==		== References ==

Inthar: /* Etymology */

2023-07-28T11:55:17Z

Etymology

← Older revision		Revision as of 11:55, 28 July 2023
Line 72:		Line 72:

	== Etymology ==		== Etymology ==
	This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" that is a weak extension of the temperament that the comma induces, since 17-limit tannic is a weak extension of 2.3.7.13.17 ~~prototannic~~ (see above). ''Prototannisma'' has thus been proposed as an alternative name.		This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" that is a weak extension of the temperament that the comma induces, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272] (see above). ''Prototannisma'' has thus been proposed as an alternative name.

	== References ==		== References ==