Chromatisma: Difference between revisions
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The '''chromatisma''', {{monzo|22 -32 16 -3}} = (10/9)<sup>16</sup>/(7/4)<sup>3</sup> is a [[7-limit]] [[comma]] measuring about 12 cents. It is the difference between a stack of three [[7/4]]s and a stack of sixteen [[10/9]]s. It is also known as '''[[218edo|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 '''chromatisma''', {{monzo|22 -32 16 -3}} = (10/9)<sup>16</sup>/(7/4)<sup>3</sup> is a [[7-limit]] [[comma]] measuring about 12 cents. It is the difference between a stack of three [[7/4]]s and a stack of sixteen [[10/9]]s. It is also known as '''[[218edo|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 [[Hemimage temperaments #Chromat|chromat]] temperament by [[User:Xenllium|Xenllium]]. | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma leads a number of regular temperaments including | 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. | ||
'''<font style="font-size: 1.15em">7-limit chromatismic (99&159&277)</font>'''<br> | '''<font style="font-size: 1.15em">7-limit chromatismic (99&159&277)</font>'''<br> | ||
Revision as of 00:34, 5 May 2021
| Interval information |
218EDO comma
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, ~5/4 = 60.566
Vals: Template:Val list