Chromatisma: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 640 000 000 000 000 000 / 635 585 924 776 181 463

| Ratio = ~~640000000000000000~~ / ~~635585924776181463~~

| Monzo = 22 -32 16 -3

~~| Cents = 11.98167~~

| Name = chromatisma, 218EDO comma

| Name = chromatisma, ~~ ~~218EDO comma

| Color name = s3r3y16-3, trisa-triru-aquadquadyo negative 3rd

| Color name =

| Comma = yes

| ~~FJS name =~~

~~| Sound~~ =

}}

The '''chromatisma''', {{monzo|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 [[7/4]]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)16/(7/4)3 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 ==

Tempering out this comma leads a number of regular temperaments including ~~[[Hemimage temperaments #Chromat|~~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.

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: {{monzo|22 -32 16 -3}}

Mapping: [{{val|1 0 -1 2}}, {{val|0 1 2 0}}, {{val|0 0 3 16}}]

POTE generators: ~3/2 = 702.261, ~5/4 = 60.566

POTE generators: ~3/2 = 702.261, ~413343/400000 = 60.566

~~Vals:~~ {{~~Val list~~| 60, 99, 159, 258, 277, 357, 376, 436, 535 }}

{{Optimal ET sequence|legend=1| 60, 99, 159, 258, 277, 357, 376, 436, 535 }}

== See also ==

* [[Small comma]]

~~[[Category:7-limit]]~~

[[Category:~~Small comma~~]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Ratio = 640 000 000 000 000 000 /<br/>635 585 924 776 181 463
-| Ratio = 640000000000000000 / 635585924776181463
 | Monzo = 22 -32 16 -3
-| Cents = 11.98167
+| Name = chromatisma, 218EDO comma
-| Name = chromatisma, <br>218EDO comma
+| Color name = s<sup>3</sup>r<sup>3</sup>y<sup>16</sup>-3, trisa-triru-aquadquadyo negative 3rd
-| Color name =
+| Comma = yes
-| FJS name =
-| Sound =
 }}
-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 ==
-Tempering out this comma leads a number of regular temperaments including [[Hemimage temperaments #Chromat|chromat]]. Chromatismic rank three temperament can be described as the 99&amp;159&amp;277 temperament, which has a generator tuned about 61 cents, three of which gives ~10/9 and sixteen gives ~7/4.
+Tempering out this comma leads a number of regular temperaments including chromat. Chromatismic rank three temperament can be described as the 99&amp;159&amp;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&amp;159&amp;277)</font>'''<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>
-POTE generators: ~3/2 = 702.261, ~5/4 = 60.566<br>
+POTE generators: ~3/2 = 702.261, ~413343/400000 = 60.566<br>
-Vals: {{Val list| 60, 99, 159, 258, 277, 357, 376, 436, 535 }}<br><br>
+{{Optimal ET sequence|legend=1| 60, 99, 159, 258, 277, 357, 376, 436, 535 }}<br><br>
 == See also ==
 * [[Small comma]]
-[[Category:7-limit]]
-[[Category:Small comma]]
+[[Category:Commas with unknown etymology]]