Chromatisma

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 640000000000000000/635585924776181463
Monzo [22 -32 16 -3
Size in cents 11.98167
Name(s) chromatisma,
218EDO comma
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
Vals: 60, 99, 159, 258, 277, 357, 376, 436, 535

See also