Chromatisma: Difference between revisions
Jump to navigation
Jump to search
Created page with "{{Infobox Interval | Icon = | Ratio = 640000000000000000 / 635585924776181463 | Monzo = 22 -32 16 -3 | Cents = 11.98167 | Name = chromatisma, <br>218EDO comma | Color name =..." |
mNo edit summary |
||
| (7 intermediate revisions by 6 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 640 000 000 000 000 000 /<br/>635 585 924 776 181 463 | |||
| Ratio = | |||
| Monzo = 22 -32 16 -3 | | Monzo = 22 -32 16 -3 | ||
| Name = chromatisma, 218EDO comma | |||
| Name = chromatisma, | | Color name = s<sup>3</sup>r<sup>3</sup>y<sup>16</sup>-3, trisa-triru-aquadquadyo negative 3rd | ||
| Color name = | | Comma = yes | ||
| | |||
}} | }} | ||
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> | ||
Comma: {{monzo|22 -32 16 -3}}<br> | Comma: {{monzo|22 -32 16 -3}}<br> | ||
Mapping: [{{val|1 0 -1 2}}, {{val|0 1 2 0}}, {{val|0 0 3 16}}]<br> | Mapping: [{{val|1 0 -1 2}}, {{val|0 1 2 0}}, {{val|0 0 3 16}}]<br> | ||
POTE generators: ~3/2 = 702.261, ~ | POTE generators: ~3/2 = 702.261, ~413343/400000 = 60.566<br> | ||
{{Optimal ET sequence|legend=1| 60, 99, 159, 258, 277, 357, 376, 436, 535 }}<br><br> | |||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
[[Category: | [[Category:Commas with unknown etymology]] | ||
Latest revision as of 12:29, 3 November 2024
| Interval information |
635 585 924 776 181 463
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, ~413343/400000 = 60.566
Optimal ET sequence: 60, 99, 159, 258, 277, 357, 376, 436, 535