Semaphore–chromatic equivalence continuum
The semaphore-chromatic equivalence continuum is a continuum of 7-limit rank-3 temperament families which equate a number of semaphore commas (49/48) with a classic chromatic semitone (25/24). This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by decimal temperament.
All temperaments in the continuum satisfy (49/48)n ~ 25/24. Varying n results in different temperament families listed in the table below. It converges to semaphore as n approaches infinity. If we allow non-integer and infinite n, the continuum describes the set of all 7-limit temperament families supported by decimal (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of n is approximately 1.9797965913603088..., and temperaments having n near this value will be more accurate. As this value is so close to 2, temperaments tempering out the breedsma (2401/2400) are unusually accurate.
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| -1 | 10 & 4 & 12d | 1225/1152 | [-7 -2 2 2⟩ |
| 0 | Dicot | 25/24 | [-3 -1 2 0⟩ |
| 1 | Jubilismic | 50/49 | [1 0 2 -2⟩ |
| 2 | Breed | 2401/2400 | [-5 -1 -2 4⟩ |
| 3 | 46 & 60 & 50 | 117649/115200 | [-9 -2 -2 6⟩ |
| … | … | … | … |
| ∞ | Semaphore | 49/48 | [-4 -1 0 2⟩ |