5767168/5767125 - Revision history

Eufalesio: Threading it all together...

2026-07-10T12:05:01Z

Threading it all together...

← Older revision		Revision as of 12:05, 10 July 2026
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	Badness (Sintel): 0.241		Badness (Sintel): 0.241

			For the [[19-limit]] weak extension, see [[insatinismic]].

	== Etymology ==		== Etymology ==

Eufalesio: More expressions

2026-07-10T09:14:07Z

More expressions

← Older revision		Revision as of 09:14, 10 July 2026
Line 7:		Line 7:

	As an ultraparticular, it is the difference between [[22/21]] and ([[65/64]])<sup>3</sup>. It also splits the [[olympia]] in three and the [[ibnsinma]] in two, each for 4096/4095~4225/4224.		As an ultraparticular, it is the difference between [[22/21]] and ([[65/64]])<sup>3</sup>. It also splits the [[olympia]] in three and the [[ibnsinma]] in two, each for 4096/4095~4225/4224.

			In terms of commas, it is also ([[1990656/1990625]])/([[123201/123200]]).

	== Temperaments ==		== Temperaments ==

Eufalesio: Fixed temp layout

2026-06-22T15:46:44Z

Fixed temp layout

@@ Line 16: / Line 16: @@
 [[Subgroup]]: 2.3.5.7.11.13
-[[Comma list]]: [[5767168/5767125]]
+[[Comma list]]: 5767168/5767125
 Mapping generators: ~2, ~3, ~5, ~7, ~65/128

Eufalesio: Added the temp

2026-06-19T17:24:52Z

Added the temp

← Older revision		Revision as of 17:24, 19 June 2026
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	== Temperaments ==		== Temperaments ==
	This comma is trivially tempered out in [[olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan\|here]] for a compendium of temperaments and edos that temper out this comma due to being ~~olympian~~.		This comma is trivially tempered out in [[olympic\|(tridecimal) olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan\|here]] for a compendium of temperaments and edos that temper out this comma due to being olympic.

	Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs\| 35, 40, 49 }}, and some hyperfine edos like [[3395edo\|3395]] and [[8539edo\|8539]].		Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs\| 35, 40, 49 }}, and some hyperfine edos like [[3395edo\|3395]] and [[8539edo\|8539]].

			=== Insanismic ===
			[[Subgroup]]: 2.3.5.7.11.13

			[[Comma list]]: [[5767168/5767125]]

			[[Mapping]]: [⟨ 1 0 0 0 2 7 ], ⟨ 0 1 0 0 0 0 ], ⟨ 0 0 1 0 0 -1 ], ⟨ 0 0 0 1 1 0 ], ⟨ 0 0 0 0 3 1 ]]

			Mapping generators: ~2, ~3, ~5, ~7, ~65/128

			[[Optimal tuning\|Optimal tunings]]:

			: [[WE]]: ~2 = 1199.999558¢, ~3/2 = 701.955501¢, ~5/4 = 386.314974¢, ~7/4 = 968.826974¢, ~65/128 = -1173.1542¢
			: error map: -0.000442 0.000058 0.000376 0.000183 -0.000278 0.000955
			: [[CWE]]: ~2 = 1200.¢, ~3/2 = 701.955606¢, ~5/4 = 386.315031¢, ~7/4 = 968.827097¢, ~65/128 = -1173.154680¢
			: error map: 0.000000 0.000605 0.001318 0.001190 0.000720 0.002627

			[[Optimal ET sequence]]: [[7edo\|7]], [[10edo\|10e]], [[12edo\|12e]], [[30edo\|30b]], [[31edo\|31e]], [[34edo\|34]], [[36edo\|36]], [[41edo\|41]], [[46edo\|46]], [[53edo\|53]], [[84edo\|84]], [[87edo\|87]], [[130edo\|130]], [[183edo\|183]], [[217edo\|217]], [[224edo\|224]], [[270edo\|270]], [[494edo\|494]], [[764edo\|764]], [[935edo\|935]], [[1075edo\|1075]], [[1205edo\|1205]], [[1609edo\|1609]], [[1696edo\|1696]], [[1920edo\|1920]], [[2190edo\|2190]], [[2684edo\|2684]], [[3395edo\|3395]], [[5144edo\|5144]], [[5585edo\|5585]], [[6079edo\|6079]], [[8269edo\|8269]], [[8539edo\|8539]], [[11664edo\|11664]], [[14124edo\|14124]], [[14348edo\|14348]], [[14618edo\|14618]], [[20203edo\|20203]]

			Badness (Sintel): 0.241

	== Etymology ==		== Etymology ==
	This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails an ''insane'' level of precision.		This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails a ''insane'' level of precision.

	[[Category:Insanismic]]		[[Category:Insanismic]]
	[[Category:Commas named for other reasons]]		[[Category:Commas named for other reasons]]

Eufalesio: etymology

2026-06-05T18:40:47Z

etymology

← Older revision		Revision as of 18:40, 5 June 2026
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	== Etymology ==		== Etymology ==
	This comma was named by [[Eufalesio]] in 2026.		This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails an ''insane'' level of precision.

	[[Category:Insanismic]]		[[Category:Insanismic]]
	[[Category:Commas named for other reasons]]		[[Category:Commas named for other reasons]]

FloraC: + etymology & misc. cleanup

2026-06-05T04:33:24Z

+ etymology & misc. cleanup

← Older revision		Revision as of 04:33, 5 June 2026
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	{{Infobox Interval\|Name=insanisma\|Color name=satrithu-alorutriguma, s3u^31org^3M\|Comma=yes}}5767168/5767125, the insanisma is a 13-limit interval, one of the smallest 13-limit ~~commas~~. It is an [[ultraparticular]], the difference between [[4096/4095]] and [[4225/4224]], or S64/S65 [[S-expression\|S-expressed]].		{{Infobox Interval
			\| Name = insanisma
			\| Color name = satrithu-alorutriguma, s3u^31org^3M
			\| Comma = yes
			}}
			'''5767168/5767125''', the '''insanisma''', is a [[13-limit]] interval, one of the smallest 13-limit [[comma]]s. It is an [[ultraparticular]], the difference between [[4096/4095]] and [[4225/4224]], or S64/S65 [[S-expression\|S-expressed]].

	As an ultraparticular, it is the difference between ~~66/63 =~~ [[22/21]] and (65/64)^3. It also splits the [[olympia]] in three and the [[ibnsinma]] in two 4096/4095~4225/4224.		As an ultraparticular, it is the difference between [[22/21]] and ([[65/64]])<sup>3</sup>. It also splits the [[olympia]] in three and the [[ibnsinma]] in two, each for 4096/4095~4225/4224.

	== Temperaments ==		== Temperaments ==
	It is trivially tempered out in [[olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan\|here]] for a compendium of temperaments and edos that temper out this comma due to being olympian.		This comma is trivially tempered out in [[olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan\|here]] for a compendium of temperaments and edos that temper out this comma due to being olympian.

	Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs\|35, 40, 49}}, and some hyperfine edos like [[3395edo\|3395]] and [[8539edo\|8539]].		Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs\| 35, 40, 49 }}, and some hyperfine edos like [[3395edo\|3395]] and [[8539edo\|8539]].

			== Etymology ==
			This comma was named by [[Eufalesio]] in 2026.

			[[Category:Insanismic]]
			[[Category:Commas named for other reasons]]

Eufalesio: Birth

2026-06-04T22:05:14Z

Birth

New page

{{Infobox Interval|Name=insanisma|Color name=satrithu-alorutriguma, s3u^31org^3M|Comma=yes}}5767168/5767125, the insanisma is a 13-limit interval, one of the smallest 13-limit commas. It is an [[ultraparticular]], the difference between [[4096/4095]] and [[4225/4224]], or S64/S65 [[S-expression|S-expressed]].

As an ultraparticular, it is the difference between 66/63 = [[22/21]] and (65/64)^3. It also splits the [[olympia]] in three and the [[ibnsinma]] in two 4096/4095~4225/4224.

== Temperaments ==
It is trivially tempered out in [[olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan|here]] for a compendium of temperaments and edos that temper out this comma due to being olympian.

Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs|35, 40, 49}}, and some hyperfine edos like [[3395edo|3395]] and [[8539edo|8539]].