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.
| 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⟩ | |