5832/5831: Difference between revisions

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| Comma = yes

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'''5832/5831''', the '''chlorisma''', is an [[unnoticeable comma|exceptionally small]] [[17-limit]] (also 2.3.7.17-[[subgroup]]) [[unnoticeable comma]] of about 0.297 [[cent]]s. It is amount by which a stack of three [[9/7]]'s exceeds [[17/8]], or the amount by which a stack of three [[7/6]]'s falls short of [[27/17]]. Equivalently, it is the difference between [[18/17]] and [[343/324]], or between [[24/17]] and [[343/243]].

'''5832/5831''', the '''chlorisma''', is an exceptionally small [[17-limit]] (also 2.3.7.17 [[subgroup]]) [[unnoticeable comma]] of ~~less than~~ 0.~~3 cents~~. It is the difference between [[18/17]] and [[343/324]].

In [[Sagittal notation]], this is the default comma represented by two [[tina]]s.

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== Commatic relations ==

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

* [[540/539]] and [[595/594]]

* [[729/728]] and [[833/832]]

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* [[4914/4913]] and [[31213/31212]]

It factors into the following ~~suparparticular pairs~~:

It factors into the following superparticular pair:

* [[9801/9800]] and [[14400/14399]]

== Temperaments ==

Tempering out this comma in the 17-limit results in the rank-6 '''chlorismic ~~temperament~~''', or in the 2.3.7.17 subgroup, the rank-3 '''chloric ~~temperament~~'''. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves.

[[Tempering out]] this comma in the 17-limit results in the rank-6 '''chlorismic''' temperament, or in the 2.3.7.17 subgroup, the rank-3 '''chloric''' temperament. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves. [[80edo]] represents both 9/7 and 17/8 within 0.1 cents, so it and many [[80th-octave temperaments]] temper out the chlorisma.

=== Chloric ===

[[Subgroup]]: 2.3.7.17

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

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~7/4 = 968.8729{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~7/4 = 968.8712{{c}}

{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 99, 130, 135, 171, 364, 400, 571, 971, 2378, 2549, 2949, 3920 }}

[[Badness]] (Sintel): 0.0174

=== Chlorismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Mapping]]: <br>

{| class="right-all"

|-

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

|-

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 6 || ],

|-

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

|-

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

|-

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

|-

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

|}

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

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~5/4 = 386.3232{{c}}, ~7/4 = 968.8729{{c}}, ~11/8 = 551.3322{{c}}, ~13/8 = 840.5419{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~5/4 = 386.3194{{c}}, ~7/4 = 968.8712{{c}}, ~11/8 = 551.3264{{c}}, ~13/8 = 840.5367{{c}}

{{Optimal ET sequence|legend=1| 19, 22, 27eg, 41, 49fg, 50, 58, 72, 121, 149, 166g, 171, 193, 198g, 224g, 243e, 270, 364, 373g, 400, 422, 494, 742, 764, 814, 935, 1084, 1106, 1178, 1236, 1506, 2000, 2414, 2684, 3178, 3920, 4684, 5498, 10182d, 14102dg, 14174d, 15680dg, 19600dg }} *

<nowiki/> * [[optimal patent val]]: [[14916edo|14916]]

[[Badness]] (Sintel): 1.13

== Etymology ==

The chlorisma was named by [[User:Jerdle|Jerdle]] in 2021.

The chlorisma was named by [[User:Jerdle|Jerdle]] in 2021. Despite the similar name, it has no relation to the previously-named [[chlorine]] temperament.

== See also ==

* [[List of superparticular intervals]]

* [[Unnoticeable comma]]

[[Category:Chlorismic]]

[[Category:Commas with unknown etymology]]

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
+'''5832/5831''', the '''chlorisma''', is an [[unnoticeable comma|exceptionally small]] [[17-limit]] (also 2.3.7.17-[[subgroup]]) [[unnoticeable comma]] of about 0.297 [[cent]]s. It is amount by which a stack of three [[9/7]]'s exceeds [[17/8]], or the amount by which a stack of three [[7/6]]'s falls short of [[27/17]]. Equivalently, it is the difference between [[18/17]] and [[343/324]], or between [[24/17]] and [[343/243]].
-'''5832/5831''', the '''chlorisma''', is an exceptionally small [[17-limit]] (also 2.3.7.17 [[subgroup]]) [[unnoticeable comma]] of less than 0.3 cents. It is the difference between [[18/17]] and [[343/324]].
 In [[Sagittal notation]], this is the default comma represented by two [[tina]]s.
@@ Line 11: / Line 10: @@
 == Commatic relations ==
 In terms of commas, it is the difference between the following superparticular pairs:
 * [[540/539]] and [[595/594]]
 * [[729/728]] and [[833/832]]
@@ Line 18: / Line 16: @@
 * [[4914/4913]] and [[31213/31212]]
-It factors into the following suparparticular pairs:
+It factors into the following superparticular pair:
 * [[9801/9800]] and [[14400/14399]]
 == Temperaments ==
-Tempering out this comma in the 17-limit results in the rank-6 '''chlorismic temperament''', or in the 2.3.7.17 subgroup, the rank-3 '''chloric temperament'''. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves.
+[[Tempering out]] this comma in the 17-limit results in the rank-6 '''chlorismic''' temperament, or in the 2.3.7.17 subgroup, the rank-3 '''chloric''' temperament. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves. [[80edo]] represents both 9/7 and 17/8 within 0.1 cents, so it and many [[80th-octave temperaments]] temper out the chlorisma.
+=== Chloric ===
+[[Subgroup]]: 2.3.7.17
+{{Mapping|legend=2| 1 0 0 3 | 0 1 0 6 | 0 0 1 -3 }}
+: mapping generators: ~2, ~3, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~7/4 = 968.8729{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~7/4 = 968.8712{{c}}
+{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 99, 130, 135, 171, 364, 400, 571, 971, 2378, 2549, 2949, 3920 }}
+[[Badness]] (Sintel): 0.0174
+=== Chlorismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 6 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -3 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~5/4 = 386.3232{{c}}, ~7/4 = 968.8729{{c}}, ~11/8 = 551.3322{{c}}, ~13/8 = 840.5419{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~5/4 = 386.3194{{c}}, ~7/4 = 968.8712{{c}}, ~11/8 = 551.3264{{c}}, ~13/8 = 840.5367{{c}}
+{{Optimal ET sequence|legend=1| 19, 22, 27eg, 41, 49fg, 50, 58, 72, 121, 149, 166g, 171, 193, 198g, 224g, 243e, 270, 364, 373g, 400, 422, 494, 742, 764, 814, 935, 1084, 1106, 1178, 1236, 1506, 2000, 2414, 2684, 3178, 3920, 4684, 5498, 10182d, 14102dg, 14174d, 15680dg, 19600dg }} *
+<nowiki/> * [[optimal patent val]]: [[14916edo|14916]]
+[[Badness]] (Sintel): 1.13
 == Etymology ==
-The chlorisma was named by [[User:Jerdle|Jerdle]] in 2021.
+The chlorisma was named by [[User:Jerdle|Jerdle]] in 2021. Despite the similar name, it has no relation to the previously-named [[chlorine]] temperament.
 == See also ==
 * [[List of superparticular intervals]]
-* [[Unnoticeable comma]]
 [[Category:Chlorismic]]
+[[Category:Commas with unknown etymology]]