Eufalesio: Little things

2026-07-08T11:37:17Z

Little things

← Older revision		Revision as of 11:37, 8 July 2026
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	* It decouples the septimal comma from the chain of fifths (observing the garischisma),		* 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		* It observes [[4096/4095]] and [[4225/4224]] but tempers them together (observing the [[olympia]] and [[2080/2079\|ibnsinma]] too), as seen in insanismic

	As a weak extension of insanismic, it does the following:		As a weak extension of insanismic, it does the following:
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	=== Minimal Insatinismic notation{{Idiosyncratic}} ===		=== Minimal Insatinismic notation{{Idiosyncratic}} ===
	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:		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 to notate fully
	* Sharps/Flats		* Sharps/Flats
	* Pythagorean commas		* Pythagorean commas
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	=== Eufalesio's ULTRAOLYMPIC [sic] 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, 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.

	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: Public birth, now to make it less idiosyncratic, more neutral!

2026-07-07T21:20:02Z

Public birth, now to make it less idiosyncratic, more neutral!

New page

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:

* 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, it can be somewhat easily notated with the following accidentals:

=== Minimal Insatinismic notation{{Idiosyncratic}} ===
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
* Pythagorean commas
* Garischismas
* Schismas
* [[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
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 [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.
[[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.

Thus, as seen in the notation, 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 - aberschisma - mina
* 17/16: minor second + septimal comma - buzzardma + aberschisma + 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.

Insatinismic - Revision history

Eufalesio: Little things

Eufalesio: Public birth, now to make it less idiosyncratic, more neutral!