1225/1224: Difference between revisions

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== Commatic relations ==

~~In terms of commas, it~~ is the difference between the following superparticular pairs:

This comma is the difference between the following superparticular pairs:

* [[273/272]] and [[351/350]]

* [[325/324]] and [[442/441]]

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== Temperaments ==

Tempering out this comma in the 17-limit results in the '''noellismic temperament''', ~~where~~ [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support ~~this temperament~~ below.

Tempering out this comma in the 17-limit results in the rank-6 '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

=== Noellic ===

[[Subgroup]]: 2.3.5.7.17

{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }}

: sval mapping generators: ~2, ~3, ~5, ~7

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

{{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}

=== Noellismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Mapping]]:

[[Mapping]]:

[~~{{val~~| 1 0 0 0 0 0 -3 }}

{| class="right-all"

~~ {{val~~| 0 1 0 0 0 0 -2 }}

|-

~~ {{val~~| 0 0 1 0 0 0 2 }}

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -3 || ],

~~ {{val~~| 0 0 0 1 0 0 2 }}

|-

~~ {{val~~| 0 0 0 0 1 0 0 }}

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -2 || ],

~~ {{val~~| 0 0 0 0 0 1 0 }}

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 2 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 2 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

~~Mapping generators~~: ~2, ~3, ~5, ~7, ~11, ~13

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277

{{~~Val list~~|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}

{{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}

== Etymology ==

The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.

The noellisma was named by [[Flora Canou]] in 2022. The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.

== See also ==

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[[Category:Noellismic]]

[[Category:Commas referencing a famous use of a number]]

@@ Line 7: / Line 7: @@
 == Commatic relations ==
-In terms of commas, it is the difference between the following superparticular pairs:
+This comma is the difference between the following superparticular pairs:
 * [[273/272]] and [[351/350]]
 * [[325/324]] and [[442/441]]
@@ Line 25: / Line 25: @@
 == Temperaments ==
-Tempering out this comma in the 17-limit results in the '''noellismic temperament''', where [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support this temperament below.
+Tempering out this comma in the 17-limit results in the rank-6 '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.
+=== Noellic ===
+[[Subgroup]]: 2.3.5.7.17
+{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }}
+: sval mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468
+{{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}
+=== Noellismic ===
 [[Subgroup]]: 2.3.5.7.11.13.17
-[[Mapping]]:
+[[Mapping]]: <br>
-<br>[{{val| 1 0 0 0 0 0 -3 }}
+{| class="right-all"
-<br>{{val| 0 1 0 0 0 0 -2 }}
+|-
-<br>{{val| 0 0 1 0 0 0 2 }}
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -3 || ],
-<br>{{val| 0 0 0 1 0 0 2 }}
+|-
-<br>{{val| 0 0 0 0 1 0 0 }}
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -2 || ],
-<br>{{val| 0 0 0 0 0 1 0 }}
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277
-{{Val list|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
+{{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
 == Etymology ==
-The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.
+The noellisma was named by [[Flora Canou]] in 2022. The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.
 == See also ==
@@ Line 49: / Line 71: @@
 [[Category:Noellismic]]
+[[Category:Commas referencing a famous use of a number]]