Chromatisma
| Ratio | 640 000 000 000 000 000 / 635 585 924 776 181 463 |
| Factorization | 222 × 3-32 × 516 × 7-3 |
| Monzo | [22 -32 16 -3⟩ |
| Size in cents | 11.981675¢ |
| Names | chromatisma, 218EDO comma |
| Color name | s3r3y16-3, trisa-triru-aquadquadyo negative 3rd |
| FJS name | [math]\text{5d}{-3}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}_{7,7,7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 118.292 |
| Weil height (log2 max(n, d)) | 118.302 |
| Wilson height (sopfr (nd)) | 241 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.96106 bits |
| Comma size | small |
| open this interval in xen-calc | |
The chromatisma, [22 -32 16 -3⟩ = (10/9)16/(7/4)3 is a 7-limit comma measuring about 12 cents. It is the difference between a stack of three 7/4s and a stack of sixteen 10/9s. It is also known as 218EDO comma, because 218EDO tempers it out in the 2.9.5.7 subgroup (not in the full 7-limit = 2.3.5.7 subgroup). The name chromatisma was named after the chromat temperament by Xenllium.
Temperaments
Tempering out this comma leads a number of regular temperaments including chromat. Chromatismic rank three temperament can be described as the 99&159&277 temperament, which has a generator tuned about 61 cents, three of which gives ~10/9 and sixteen gives ~7/4.
7-limit chromatismic (99&159&277)
Comma: [22 -32 16 -3⟩
Mapping: [⟨1 0 -1 2], ⟨0 1 2 0], ⟨0 0 3 16]]
POTE generators: ~3/2 = 702.261, ~413343/400000 = 60.566
Optimal ET sequence: 60, 99, 159, 258, 277, 357, 376, 436, 535