User:Eufalesio/Insatinismic
| Insatinismic |
(19-limit) 165376/165375, 709632/709631, 633556/633555
Satrithu-alorutrigu & Satrino-athotriluru-agugu (2.3.5.7.11.13.19)
Sanosorurutrigu & Nusutrithu-alozo & Nunusothutrilo-azogu (19-limit)
Insatinismic is a rank-5 temperament that is a weak extension of 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, it can be somewhat easily notated with the following accidentals:
Minimal Insatinismic notation
Requires 5 pairs of accidentals:
- Sharps/Flats
- Pythagorean commas
- Garischismas
- Schismas
- 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.
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.
Buzzardmas are to ULTRAOLYMPIC notation what mercator commas are to minimal. They are the difference between 4 arrow-unison and a minor second.
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 - 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.