User:Eliora/Schismic-parakleismic equivalence continuum

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The schismic–parakleismic equivalence continuum is a continuum of 5-limit temperaments which equate a number of schismas (32805/32768) with parakleisma (. This continuum is theoretically interesting in that the temperaments associated with its various commas are all 5-limit microtemperaments.

All temperaments in the continuum satisfy (32805/32768)ⁿ = [8 14 -13⟩. Varying n results in different temperaments listed in the table below. It converges to parakleismic as n approaches infinity. If we allow non-integer and infinite n, the continuum describes the set of all 5-limit temperaments supported by 118edo (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of n is approximately 2.70854..., and temperaments having n near this value tend to be the most accurate ones.

Temperaments with integer n

n	Temperament	Comma
		Ratio	Monzo
0	Schismic	32805/32768	[-15 8 1⟩
1	Vishnu		[23 6 -14⟩
2	Luna		[38 -2 -15⟩
3	Kwazy		[-53 10 16⟩
4	Vavoom		[-68 18 17⟩
5	10 & 118		[-83 26 18]
6
7
8
9
…	…	…	…
∞	Parakleismic		[8 14 -13⟩