User:Overthink/Dicot–kleismic equivalence continuum
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The dicot–kleismic equivalence continuum is a continuum of 5-limit temperaments which equate a number of classical chromatic semitones (25/24) with the Pythagorean major second (9/8). As such, it can also be called the dicot–antitonic equivalence continuum.
All temperaments in the continuum satisfy (25/24)n ~ 9/8. Varying n results in different temperaments listed in the table below. It converges to dicot as n approaches infinity. If we allow non-integer and infinite n, the continuum describes the set of all 5-limit temperaments supported by 4edo 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 2.8853…, and temperaments having n near this value tend to be the most accurate ones.
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| 0 | Antitonic | 9/8 | [-3 2⟩ |
| 1 | Bug | 27/25 | [0 3 -2⟩ |
| 2 | Diminished | 648/625 | [3 4 -4⟩ |
| 3 | Kleismic | 15625/15552 | [-6 -5 6⟩ |
| 4 | Doublewide | 390625/373248 | [-9 -6 8⟩ |
| … | … | … | … |
| ∞ | Dicot | 25/24 | [-3 -1 2⟩ |
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| 5/2 | Mynic | 10077696/9765625 | [9 9 -10⟩ |
| 7/2 | Quasitemp | 6103515625/5804752896 | [-15 -11 14⟩ |