User:Eufalesio/Insatinismic

Insatinismic

Subgroups	2.3.5.7.11.13.17, 2.3.5.7.11.13.19, 2.3.5.7.11.13.17.19
Comma basis	(17-limit) 5767168/5767125, 200931874/200930625 (19-limit) 165376/165375, 709632/709631, 633556/633555
Reduced mapping	⟨1; 1 0 0 1 0 2 1; 0 1 0 0 -1 2 1; 0 0 0 1 1 0 0 2; 0 0 0 9 3 -8 8]
ET join	53 & 94 & 270 & 3395
Generators (CWE)	~3/2 = 701.955847 ¢, ~5/4 = 386.315423 ¢
MOS scales	n/a
Ploidacot	n/a
Pergen	???
Color name	Satrithu-alorutrigu & Satriso-athothololobirugugu (17-limit) Satrithu-alorutrigu & Satrino-athotriluru-agugu (2.3.5.7.11.13.19) Sanosorurutrigu & Nusutrithu-alozo & Nunusothutrilo-azogu (19-limit)
Minimax error	-odd-limit: ??? ¢
Target scale size	-odd-limit: ??? notes

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, a somewhat accessible notation of differently sized accidentals can be devised by reusing the accidentals of cassaschismic and adding a couple more. Namely:

• Apotomes
• Septimal commas
• Aberschismas
• Buzzardmas*
• Garischismas
• Minas
• Tinas

*buzzardmas are not strictly necessary, but they reduce the amount of septimal commas needed considerably. In cassaschismic and insatinismic, 17/16 is a major second - 4 septimal commas + 2 aberschismas (- garischisma - 3 minas - tina). By using a buzzardma, 17/16 can be spelt as a minor second - buzzardma +1 septimal comma... etc.

Thus, 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 + 2 minas + tina

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