User:Eufalesio/Insatinismic - Revision history

Eufalesio: It's ULTRAOLYMPIC not ultraolympic!

2026-06-30T11:16:12Z

It's ULTRAOLYMPIC not ultraolympic!

← Older revision		Revision as of 11:16, 30 June 2026
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	A redundant accidental, the [[mercator comma]], can be introduced to keep the amount of pythagorean commas needed less than two, since it is the difference between 4 pythagorean commas and one limma. 17/16 is a type of '''major''' second. Using a mercator comma allows it to be respelled as a minor second + pythagorean comma - mercator comma... etc.		A redundant accidental, the [[mercator comma]], can be introduced to keep the amount of pythagorean commas needed less than two, since it is the difference between 4 pythagorean commas and one limma. 17/16 is a type of '''major''' second. Using a mercator comma allows it to be respelled as a minor second + pythagorean comma - mercator comma... etc.

	=== Eufalesio's ULTRAOLYMPIC notation ===		=== Eufalesio's ULTRAOLYMPIC [sic] notation ===
	Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations. This has the benefit of being a natural representation of olympic, keeping the representations of primes 2-13,19 as simple as possible.		Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations. This has the benefit of being a natural representation of olympic, keeping the representations of primes 2-13,19 as simple as possible.
	[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]		[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]

Eufalesio: /* Eufalesio's ULTRAOLYMPIC notation */

2026-06-30T11:15:02Z

Eufalesio's ULTRAOLYMPIC notation

← Older revision		Revision as of 11:15, 30 June 2026
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	=== Minimal Insatinismic notation ===		=== Minimal Insatinismic notation ===
	~~Requires~~ 5 pairs of accidentals:		This notation is a direct mapping retrieved from sintel's temperament evaluator [https://sintel.pythonanywhere.com/result?subgroup=19&reduce=spine&weights=unweighted&target=&edos=53%2C94%2C270%2C3395%2C8539&submit_edo=submit&commas= here], shuffling the generators to have them be in decreasing order of size. Either way, it requires 5 pairs of accidentals:

	* Sharps/Flats		* Sharps/Flats
	* Pythagorean commas		* Pythagorean commas
Line 54:		Line 53:
	* 17/16: '''major''' second - 4 pythagorean commas + 2 schismas - 8 kevolismas		* 17/16: '''major''' second - 4 pythagorean commas + 2 schismas - 8 kevolismas
	* 19/16: minor third + schisma - 2 garischismas + 8 kevolismas		* 19/16: minor third + schisma - 2 garischismas + 8 kevolismas
	A redundant accidental, the mercator comma, can be introduced to keep the amount of pythagorean commas needed less than two, since it is the difference between 4 pythagorean commas and one limma. 17/16 is a type of '''major''' second. Using a mercator comma allows it to be respelled as a minor second + pythagorean comma - mercator comma... etc.		The notation can be equivalently and naively described as using:

			*Sharps/Flats
			*'''Septimal commas'''
			*Pythagorean commas
			* '''Syntonic commas'''
			* Kevolismas

			Any of the above expressions can be rewritten by converting syntonic comma = pythagorean comma - schisma; septimal comma = pythagorean comma + garischisma.

			A redundant accidental, the [[mercator comma]], can be introduced to keep the amount of pythagorean commas needed less than two, since it is the difference between 4 pythagorean commas and one limma. 17/16 is a type of '''major''' second. Using a mercator comma allows it to be respelled as a minor second + pythagorean comma - mercator comma... etc.

	=== Eufalesio's ULTRAOLYMPIC notation ===		=== Eufalesio's ULTRAOLYMPIC notation ===
	Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations.		Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations. This has the benefit of being a natural representation of olympic, keeping the representations of primes 2-13,19 as simple as possible.
	[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]		[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]
	Buzzardmas are to ULTRAOLYMPIC notation what mercator commas are to minimal. They are the difference between 4 arrow-unison and a minor second, only that the arrow here is a septimal comma, not a pythagorean one.		Buzzardmas are to ULTRAOLYMPIC notation what mercator commas are to minimal. They are the difference between 4 arrow-unison and a minor second, only that the arrow here is a septimal comma, not a pythagorean one.

Eufalesio at 02:15, 29 June 2026

2026-06-29T02:15:20Z

← Older revision		Revision as of 02:15, 29 June 2026
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	* 7/4: minor seventh - septimal comma		* 7/4: minor seventh - septimal comma
	* 11/8: fourth + 2 septimal commas - 3 minas		* 11/8: fourth + 2 septimal commas - 3 minas
	* 13/8: minor sixth + 2 septimal commas - mina		* 13/8: minor sixth + 2 septimal commas - aberschisma - mina
	* 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina		* 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina
	* 19/16: minor third + schisma + 3 minas + tina		* 19/16: minor third + schisma + 3 minas + tina

	And any interval between them can be found by subtracting each accidental independently.		And any interval between them can be found by subtracting each accidental independently.

Eufalesio at 02:12, 29 June 2026

2026-06-29T02:12:12Z

← Older revision		Revision as of 02:12, 29 June 2026
Line 59:		Line 59:
	Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations.		Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations.
	[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]		[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]
	Buzzardmas are to ULTRAOLYMPIC notation what mercator commas are to minimal. They are the difference between 4 arrow-unison and a minor second.		Buzzardmas are to ULTRAOLYMPIC notation what mercator commas are to minimal. They are the difference between 4 arrow-unison and a minor second, only that the arrow here is a septimal comma, not a pythagorean one.

	Thus, as seen in the notation, octave reduced harmonics can be described as follows:		Thus, as seen in the notation, octave reduced harmonics can be described as follows:

Eufalesio: Infobox is broken :sad:

2026-06-28T22:33:24Z

Infobox is broken :sad:

← Older revision		Revision as of 22:33, 28 June 2026
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	~~{{Infobox regtemp\|Title=~~Insatinismic\|~~Subgroups=2~~.3.5~~.7.11.13.17,~~ 2~~.3.5.7.11.13.19,~~ 2.3.5.7.11.13.17.19~~\|Comma basis=(17-limit)~~ [[5767168/5767125]]~~, 200931874/200930625<br>(19-limit) 165376/165375, 709632/709631~~, [[633556/633555]]~~\|Edo join 1=53\|Edo join 2=94\|Edo join 3=270\|~~Mapping=1; 1 0 0 1 0 2 1; 0 1 0 0 -1 2 1; 0 0 0 1 1 0 0 2; 0 0 0 9 3 -8 8\|~~Generators~~=3/2; 5/4~~\|Generators tuning~~=~~701.955847,~~ 386.~~315423~~, 968.~~827501~~, -791.~~051331\|Optimization method=CWE\|Pergen=???\|Color name=Satrithu~~-~~alorutrigu & Satriso~~-~~athothololobirugugu (17~~-~~limit)<br>Satrithu~~-~~alorutrigu & Satrino-athotriluru-agugu (~~2.3.5.7.11.13.~~19)<br>Sanosorurutrigu & Nusutrithu-alozo & Nunusothutrilo-azogu (19-limit)~~\|~~Mistuning 1=???\|Complexity 1=???\|Edo join 4=~~3395~~\|Edo join 5=~~8539~~\|Odd-limit 1=19~~}}~~Insatinismic is a [[rank~~-~~5 temperament]] that is a [[weak extension]] of [[5767168/5767125#Insanismic\|insanismic]] and a detemperament of [[cassaschismic]]. It is not a member of any known temperament family~~ or ~~clan~~.		Insatinismic is a [[rank-5 temperament]] that is a [[weak extension]] of [[5767168/5767125#Insanismic\|insanismic]] and a detemperament of [[cassaschismic]]. It is not a member of any known temperament family or clan.

			Data below is given because infobox regtemp doesn't work with rank-5 temperaments:{{Databox\|Temperament data\|2=[[Subgroup]]: 2.3.5.7.11.13.17.19
			[[Comma list]]: 5767168/5767125, [[11413376/11413325]], [[633556/633555]]

			[[Mapping]]: [⟨ 1 0 0 0 5 8 -9 0 ],
			⟨ 0 1 0 0 0 0 -2 1 ],
			⟨ 0 0 1 0 0 -1 -2 1 ],
			⟨ 0 0 0 1 1 0 0 2 ],
			<nowiki>⟨ 0 0 0 0 -9 -3 8 -8 ]]</nowiki>

			Mapping generators: ~2, ~3, ~5, ~7, ~608/385

			[[Optimal tuning\|Optimal tunings]]

			: [[WE]]: ~2 = 1199.999542¢, ~3/2 = 701.955847¢, ~5/4 = 386.315423¢, ~7/4 = 968.827501¢, ~385/608 = -791.051331¢
			: error map: -0.000458 0.000388 0.000793 0.000678 -0.000238 0.000173 -0.000847 -0.000598
			: [[CWE]]: ~2 = 1199.999542¢, ~3/2 = 701.955948¢, ~5/4 = 386.315507¢, ~7/4 = 968.827700¢, ~385/608 = -791.051640¢
			: error map: 0.000000 0.000947 0.001794 0.001794 0.00095 0.001912 0.000618 0.000724


			Optimal ET sequence: {{EDOs\|41g, 53, 94, 176g, 217, 270, 311, 487, 581, 1115g, 1385, 1696, 1966, 2597, 2814, 3084, 3178, 3395, 5144, 6573, 7958, 8269, 8539, 11934, 16808, 20203}}.

			Badness (Sintel): 0.279}}Ploidacots, pergens, MOS scales and odd-limit detunings are unapplicable or too convoluted to be descriptive.

	As a detemperament of cassaschismic, it does the following:		As a detemperament of cassaschismic, it does the following:

Eufalesio: BIG changes

2026-06-28T22:17:12Z

BIG changes

← Older revision		Revision as of 22:17, 28 June 2026
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	== Notation ==		== Notation ==
	Because this is a rank-5 temperament, there is no good way of visualizing intervals in a neatly compressed lattice~~. However~~, ~~a somewhat accessible notation of differently sized accidentals~~ can be ~~devised by reusing~~ the accidentals ~~of cassaschismic and adding a couple more. Namely~~:		Because this is a rank-5 temperament, there is no good way of visualizing intervals in a neatly compressed lattice, however, it can be somewhat easily notated with the following accidentals:

	* Apotomes		=== Minimal Insatinismic notation ===
	* Septimal commas		Requires 5 pairs of accidentals:
	* ~~Aberschismas~~
	* ~~''Buzzardmas*''~~		* Sharps/Flats
			* Pythagorean commas
	* Garischismas		* Garischismas
	* ~~Minas~~		* Schismas
	* ~~Tinas~~		* [[1540/1539\|Kevolismas]]

			Through this notation, octave reduced harmonics can be described as follows:
			* 2/1: octave
			* 3/2: fifth
			* 5/4: major third - pythagorean comma + schisma
			* 7/4: minor seventh - pythagorean comma - garischisma
			* 11/8: fourth + 2 pythagorean commas + 3 garischismas - 9 kevolismas
			* 13/8: minor sixth + 2 pythagorean commas - schisma - 3 kevolismas
			* 17/16: '''major''' second - 4 pythagorean commas + 2 schismas - 8 kevolismas
			* 19/16: minor third + schisma - 2 garischismas + 8 kevolismas
			A redundant accidental, the mercator comma, can be introduced to keep the amount of pythagorean commas needed less than two, since it is the difference between 4 pythagorean commas and one limma. 17/16 is a type of '''major''' second. Using a mercator comma allows it to be respelled as a minor second + pythagorean comma - mercator comma... etc.

	~~<nowiki>*</nowiki>buzzardmas are not strictly necessary~~, ~~but they reduce~~ the ~~amount of septimal~~ commas ~~needed considerably~~. ~~In cassaschismic and insatinismic, 17/16 is a major second - '''~~4~~''' septimal commas + 2 aberschismas (~~- ~~garischisma - 3 minas - tina). By using a buzzardma, 17/16 can be spelt as~~ a minor second ~~- buzzardma +1 septimal comma... etc~~.		=== Eufalesio's ULTRAOLYMPIC notation ===
			Eufalesio had devised a somewhat accessible notation of differently sized accidentals can be devised by reusing the suit of accidentals that is used for 12e, cassandra, and cassaschismic, and expanding upon them to accomodate the minuscule alterations.
			[[File:ULTRAOLYMPIANsymbolset.jpg\|center\|thumb\|960x960px]]
			Buzzardmas are to ULTRAOLYMPIC notation what mercator commas are to minimal. They are the difference between 4 arrow-unison and a minor second.

	Thus, octave reduced harmonics can be described as follows:		Thus, as seen in the notation, octave reduced harmonics can be described as follows:

	* 2/1: octave		* 2/1: octave
Line 32:		Line 47:
	* 13/8: minor sixth + 2 septimal commas - mina		* 13/8: minor sixth + 2 septimal commas - mina
	* 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina		* 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina
	* 19/16: minor third + schisma + 2 minas + tina		* 19/16: minor third + schisma + 3 minas + tina

	And any interval between them can be found by subtracting each accidental independently.		And any interval between them can be found by subtracting each accidental independently.

Eufalesio: Birth (possible proposal to add this to the whole wiki)

2026-06-28T19:13:24Z

Birth (possible proposal to add this to the whole wiki)

New page

{{Infobox regtemp|Title=Insatinismic|Subgroups=2.3.5.7.11.13.17, 2.3.5.7.11.13.19, 2.3.5.7.11.13.17.19|Comma basis=(17-limit) [[5767168/5767125]], 200931874/200930625<br>(19-limit) 165376/165375, 709632/709631, [[633556/633555]]|Edo join 1=53|Edo join 2=94|Edo join 3=270|Mapping=1; 1 0 0 1 0 2 1; 0 1 0 0 -1 2 1; 0 0 0 1 1 0 0 2; 0 0 0 9 3 -8 8|Generators=3/2; 5/4|Generators tuning=701.955847, 386.315423, 968.827501, -791.051331|Optimization method=CWE|Pergen=???|Color name=Satrithu-alorutrigu & Satriso-athothololobirugugu (17-limit)<br>Satrithu-alorutrigu & Satrino-athotriluru-agugu (2.3.5.7.11.13.19)<br>Sanosorurutrigu & Nusutrithu-alozo & Nunusothutrilo-azogu (19-limit)|Mistuning 1=???|Complexity 1=???|Edo join 4=3395|Edo join 5=8539|Odd-limit 1=19}}Insatinismic is a [[rank-5 temperament]] that is a [[weak extension]] of [[5767168/5767125#Insanismic|insanismic]] and a detemperament of [[cassaschismic]]. It is not a member of any known temperament family or clan.

As a detemperament of cassaschismic, it does the following:

* It decouples the septimal comma from the chain of fifths (observing the garischisma),
* It observes 4096/4095 and 4225/4224 but tempers them together (observing the olympia and ibsinma too), as seen in insanismic

As a weak extension of insanismic, it does the following:

* The fifth generator is trisected for primes 11 and 13, and can be instead taken to be ~1540/1539, or a redundant pair of 4096/4095~4225/4224 and 10241/10240. 10241/10240 is used to reached 17/16 and 19/16.

== Notation ==
Because this is a rank-5 temperament, there is no good way of visualizing intervals in a neatly compressed lattice. However, a somewhat accessible notation of differently sized accidentals can be devised by reusing the accidentals of cassaschismic and adding a couple more. Namely:

* Apotomes
* Septimal commas
* Aberschismas
* ''Buzzardmas*''
* Garischismas
* Minas
* Tinas

<nowiki>*</nowiki>buzzardmas are not strictly necessary, but they reduce the amount of septimal commas needed considerably. In cassaschismic and insatinismic, 17/16 is a major second - '''4''' septimal commas + 2 aberschismas (- garischisma - 3 minas - tina). By using a buzzardma, 17/16 can be spelt as a minor second - buzzardma +1 septimal comma... etc.

Thus, octave reduced harmonics can be described as follows:

* 2/1: octave
* 3/2: fifth
* 5/4: major third - septimal comma + aberschisma
* 7/4: minor seventh - septimal comma
* 11/8: fourth + 2 septimal commas - 3 minas
* 13/8: minor sixth + 2 septimal commas - mina
* 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina
* 19/16: minor third + schisma + 2 minas + tina

And any interval between them can be found by subtracting each accidental independently.