User:Eufalesio/Insatinismic: Difference between revisions
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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: | ||
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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: | 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 === | === 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 | * Sharps/Flats | ||
* Pythagorean commas | * Pythagorean commas | ||
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* 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 [sic] notation{{Idiosyncratic}} === | ||
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. | 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: | ||
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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. | ||