User:Eufalesio/Insatinismic: Difference between revisions

(5 intermediate revisions by the same user not shown)

Line 36:

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}} ===

~~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

* Pythagorean commas

Line 54:

Line 53:

* 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.

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]]

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.

Line 68:

Line 77:

* 7/4: minor seventh - septimal comma

* 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

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

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

@@ Line 36: / Line 36: @@
 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}} ===
-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
 * Pythagorean commas
@@ Line 54: / Line 53: @@
 * 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.
+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]]
 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.
@@ Line 68: / Line 77: @@
 * 7/4: minor seventh - septimal comma
 * 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
 * 19/16: minor third + schisma + 3 minas + tina
 And any interval between them can be found by subtracting each accidental independently.