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.

Insatinismic is a [[rank-5 temperament]] for the add-29-19-limit 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

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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.

Badness (Sintel): 0.279<br>

[[Subgroup]]: 2.3.5.7.11.13.17.19.29<br>[[Comma list]]: 5767168/5767125, [[11413376/11413325]], [[633556/633555]], [[176176/176175]]

[[Mapping]]: [⟨ 1 0 0 0 5 8 -9 0 19 ],

⟨ 0 1 0 0 0 0 -2 1 -3 ],

⟨ 0 0 1 0 0 -1 -2 1 -3 ],

⟨ 0 0 0 1 1 0 0 2 3 ],

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

[[Optimal tuning|Optimal tunings]]

: [[WE]]: ~2 = 1199.999454¢, ~3/2 = 701.955619¢, ~5/4 = 386.314591¢, ~7/4 = 968.825991¢, ~385/608 = -791.051281¢

: error map: -0.000546 0.000618 0.000877 0.000084 -0.000591 -0.000463 0.00017 -0.001072 0.001239

Badness (Sintel): 0.354}}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

* 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:

* 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.

* The fifth generator is trisected for primes 11, 13 and 29, 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 ==

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=== 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=2.3.5.7.11.13.17.19.29&reduce=spine&weights=weil&target=&edos=53%2C94%2C217%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 fully notate on a score.

* Sharps/Flats

* Pythagorean commas

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* 17/16: '''major''' second - 4 pythagorean commas + 2 schismas - 8 kevolismas

* 19/16: minor third + schisma - 2 garischismas + 8 kevolismas

* 29/16: '''major sixth''' + 5 pythagorean commas - 3 schismas - 3 garischismas + 21 kevolismas

The notation can be equivalently and naively described as using:

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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.

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. Same with 29/16, which instead of being spelt a major sixth can be spelt a minor seventh + 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.

[[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]]

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:

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* 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina

* 19/16: minor third + schisma + 3 minas + tina

* 29/16: minor seventh + septimal comma + buzzardma - aberschisma - 2 schismas - 7 minas <br>OR minor seventh + septimal comma + buzzardma - 3 aberschismas + 10 minas - 3 tinas

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, keeping in mind that an excess of septimal commas can be converted into buzzardmas.

@@ Line 1: / Line 1: @@
-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]] for the add-29-19-limit 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
@@ Line 22: / Line 22: @@
 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.
+Badness (Sintel): 0.279<br>
+[[Subgroup]]: 2.3.5.7.11.13.17.19.29<br>[[Comma list]]: 5767168/5767125, [[11413376/11413325]], [[633556/633555]], [[176176/176175]]
+[[Mapping]]: [⟨	1	0	0	0	5	8	-9	0	19	],
+⟨	0	1	0	0	0	0	-2	1	-3	],
+⟨	0	0	1	0	0	-1	-2	1	-3	],
+⟨	0	0	0	1	1	0	0	2	3	],
+<nowiki>⟨	0	0	0	0	-9	-3	8	-8	-21	]]</nowiki>
+Mapping generators: ~2, ~3, ~5, ~7, ~608/385
+[[Optimal tuning|Optimal tunings]]
+: [[WE]]: ~2 = 1199.999454¢, ~3/2 = 701.955619¢, ~5/4 = 386.314591¢, ~7/4 = 968.825991¢, ~385/608 = -791.051281¢
+: error map: -0.000546  0.000618  0.000877  0.000084 -0.000591 -0.000463  0.00017  -0.001072  0.001239
+Badness (Sintel): 0.354}}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
+* 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:
-* 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.
+* The fifth generator is trisected for primes 11, 13 and 29, 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 ==
@@ Line 37: / Line 54: @@
 === 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=2.3.5.7.11.13.17.19.29&reduce=spine&weights=weil&target=&edos=53%2C94%2C217%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 fully notate on a score.
 * Sharps/Flats
 * Pythagorean commas
@@ Line 53: / Line 70: @@
 * 17/16: '''major''' second - 4 pythagorean commas + 2 schismas - 8 kevolismas
 * 19/16: minor third + schisma - 2 garischismas + 8 kevolismas
+* 29/16: '''major sixth''' + 5 pythagorean commas - 3 schismas - 3 garischismas + 21 kevolismas
 The notation can be equivalently and naively described as using:
@@ Line 63: / Line 81: @@
 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.
+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. Same with 29/16, which instead of being spelt a major sixth can be spelt a minor seventh + 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.
+[[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]]
-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:
@@ Line 80: / Line 98: @@
 * 17/16: minor second + septimal comma - buzzardma + aberschisma + schisma - 3 minas - tina
 * 19/16: minor third + schisma + 3 minas + tina
+* 29/16: minor seventh + septimal comma + buzzardma - aberschisma - 2 schismas - 7 minas <br>OR minor seventh + septimal comma + buzzardma - 3 aberschismas + 10 minas - 3 tinas
-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, keeping in mind that an excess of septimal commas can be converted into buzzardmas.