24576/24565: Difference between revisions

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{{Infobox Interval

~~| Ratio = 24576/24565~~

| Name = mavka comma, archagallisma

~~| Monzo = 13, 1, -1, 0, 0, 0, -3~~

| Color name = 17u3g-2, Trisu-agu comma

~~| Cents = 0.77505~~

| Comma = yes

| Name = mavka comma

| Color name = ~~trisu~~-agu ~~negative 2nd~~

| ~~FJS name~~ = ~~d-25,17,17,17~~

}}

'''24576/24565''', the '''mavka comma,''' is an unnoticeable 17-limit ~~interval that represents~~ the difference between ~~two adjacent square superparticulars -~~ [[289/288]] ~~and~~ [[~~256/255~~]]~~. By extension~~, ~~tempering~~ it ~~out also makes~~ a ~~chain~~ of ~~18/17 -~~ 17/16 ~~- 16~~/15 into ~~equidistant intervals~~.

'''24576/24565''', the '''mavka comma''' or '''archagallisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] measuring about 0.775 [[cents]]. It is the difference between [[256/255]] and [[289/288]] – two adjacent [[square superparticular]]s, making it an [[ultraparticular]], and identifies itself as the amount by which a stack of three [[17/16]]'s fall short of a [[6/5]] minor third. It can be factored into ([[4096/4095]])⋅([[4914/4913]]).

== ~~Theory~~ ==

== Temperaments ==

~~By tempering it~~ out, the rank 6 ~~mavka~~ temperament is ~~defined~~.

[[Tempering out]] this comma in the full [[17-limit]] results in the rank-6 '''mavka''' a.k.a. '''archagallismic''' temperament, or in the 2.3.5.17 subgroup, the rank-3 '''archagallic''' temperament. You may find a list of good equal temperaments supporting them below. The rank-6 temperament can be thought of as being equivalent to the [[17-limit]] with the exception that 5/4 is reached by going down by 17/16 three times, starting at 3/2. In other words, [[5/4]] = ([[3/2]])/([[17/16]])3. Similarly, archagallic can be thought of as the 2.3.5.17 subgroup with that same equivalence (so that it is essentially being expressed through 2.3.17).

~~Mapping:~~

If we retract it to the 2.75.85 subgroup, we get the rank-2 [[MVP archagall]] temperament, which can be extended to the 2.75.9/7.85 subgroup as [[archagall]]. This has its own, more complex mapping of prime 5 at +13 charismic fourths ([[85/64]]'s) octave reduced, resulting in [[prime archagall]], an extension of [[fifthplus]].

[ ~~⟨ 1 0 1 0 0 0 4~~ ]

Finally, tempering out 256/255 and/or 289/288 results in a lower-accuracy temperament, [[srutal archagall]], of the [[diaschismic family]].

~~⟨ 0 1 1 0 0 0 0~~ ]

=== Archagallic ===

[[Subgroup]]: 2.3.5.17

~~⟨ 0 0 3 0 0 0 -1~~ ]

[[Comma list]]: 24576/24565

~~⟨ 0 0~~ 0 1 0 0 0 ]

: mapping generators: ~2, ~3, ~17/16

~~⟨ 0 0 0 0 1 0 0~~ ]

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9692{{c}}, ~3/2 = 701.9798{{c}}, ~17/16 = 105.1973{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9799{{c}}, ~17/16 = 105.2003{{c}}

~~⟨ 0 0 0 0 0~~ 1 ~~0 ] ⟩~~

{{Optimal ET sequence|legend=1| 10, 12, 22, 34, 80, 103, 115, 125, 137, 159, 171, 354, 376, 388, 559, 1882, 2441g, 3000g, 6559gg, 9559cggg }}

~~Vals~~: ~~{{EDOs|581, 764, 742, 422, 183, 400, 935, 354, 1506, 217}}~~.

[[Badness]] (Sintel): 0.127

[[Category:~~Unnoticeable comma~~]]

=== Mavka a.k.a. archagallismic ===

[[Category:~~17-limit~~]]

[[Subgroup]]: 2.3.5.7.11.13.17

[[Comma list]]: 24576/24565

{| class="right-all"

|-

| [⟨ || 1 || 0 || 1 || 0 || 0 || 0 || 4 || ],

|-

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

|-

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

|-

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

|-

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

|}

: mapping generators: ~2, ~3, ~17/16, ~7, ~11, ~13

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9692{{c}}, ~3/2 = 701.9798{{c}}, ~17/16 = 105.1973{{c}}, ~7/4 = 968.8875{{c}}, ~11/8 = 551.4103{{c}}, ~13/8 = 840.6200{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9799{{c}}, ~17/16 = 105.2003{{c}}, ~7/4 = 968.8842{{c}}, ~11/8 = 551.3897{{c}}, ~13/8 = 840.6045{{c}}

{{Optimal ET sequence|legend=1| 46, 58, 80, 103, 137, 149, 159, 171, 183, 217, 296, 320, 342f, 354, 400, 422, 525, 571, 581, 742, 764, 935, 1084, 1106, 1323, 1506, 3593g, 3947eg, 5053fgg, 6559defgg, 8065cdefggg, 10152cdeffgggg }}.

[[Badness]] (Sintel): 15.8

== Etymology ==

The mavka comma was named by [[Eliora]] in 2022. Its other name ''archagallismic comma'' derives from ''archagall'', the esoteric subgroup temperament named by [[Scott Dakota]] earlier.

[[Category:Mavka]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 24576/24565
+| Name = mavka comma, archagallisma
-| Monzo = 13, 1, -1, 0, 0, 0, -3
+| Color name = 17u<sup>3</sup>g-2, Trisu-agu comma
-| Cents = 0.77505
+| Comma = yes
-| Name = mavka comma
-| Color name = trisu-agu negative 2nd
-| FJS name = d-2<sub>5,17,17,17</sub>
 }}
-'''24576/24565''', the '''mavka comma,''' is an unnoticeable 17-limit interval that represents the difference between two adjacent square superparticulars - [[289/288]] and [[256/255]]. By extension, tempering it out also makes a chain of 18/17 - 17/16 - 16/15 into equidistant intervals.
+'''24576/24565''', the '''mavka comma''' or '''archagallisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] measuring about 0.775 [[cents]]. It is the difference between [[256/255]] and [[289/288]] – two adjacent [[square superparticular]]s, making it an [[ultraparticular]], and identifies itself as the amount by which a stack of three [[17/16]]'s fall short of a [[6/5]] minor third. It can be factored into ([[4096/4095]])⋅([[4914/4913]]).
-== Theory ==
+== Temperaments ==
-By tempering it out, the rank 6 mavka temperament is defined.
+[[Tempering out]] this comma in the full [[17-limit]] results in the rank-6 '''mavka''' a.k.a. '''archagallismic''' temperament, or in the 2.3.5.17 subgroup, the rank-3 '''archagallic''' temperament. You may find a list of good equal temperaments supporting them below. The rank-6 temperament can be thought of as being equivalent to the [[17-limit]] with the exception that 5/4 is reached by going down by 17/16 three times, starting at 3/2. In other words, [[5/4]] = ([[3/2]])/([[17/16]])<sup>3</sup>. Similarly, archagallic can be thought of as the 2.3.5.17 subgroup with that same equivalence (so that it is essentially being expressed through 2.3.17).
-Mapping:
+If we retract it to the 2.75.85 subgroup, we get the rank-2 [[MVP archagall]] temperament, which can be extended to the 2.75.9/7.85 subgroup as [[archagall]]. This has its own, more complex mapping of prime 5 at +13 charismic fourths ([[85/64]]'s) octave reduced, resulting in [[prime archagall]], an extension of [[fifthplus]].
-[ ⟨	1	0	1	0	0	0	4	]
+Finally, tempering out 256/255 and/or 289/288 results in a lower-accuracy temperament, [[srutal archagall]], of the [[diaschismic family]].
-⟨	0	1	1	0	0	0	0	]
+=== Archagallic ===
+[[Subgroup]]: 2.3.5.17
-⟨	0	0	3	0	0	0	-1	]
+[[Comma list]]: 24576/24565
-⟨	0	0	0	1	0	0	0	]
+{{Mapping|legend=2| 1 1 2 4 | 0 1 1 0 | 0 0 -3 1 }}
+: mapping generators: ~2, ~3, ~17/16
-⟨	0	0	0	0	1	0	0	]
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9692{{c}}, ~3/2 = 701.9798{{c}}, ~17/16 = 105.1973{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9799{{c}}, ~17/16 = 105.2003{{c}}
-⟨	0	0	0	0	0	1	0	] ⟩
+{{Optimal ET sequence|legend=1| 10, 12, 22, 34, 80, 103, 115, 125, 137, 159, 171, 354, 376, 388, 559, 1882, 2441g, 3000g, 6559gg, 9559cggg }}
-Vals: {{EDOs|581, 764, 742, 422, 183, 400, 935, 354, 1506, 217}}.
+[[Badness]] (Sintel): 0.127
-[[Category:Unnoticeable comma]]
+=== Mavka a.k.a. archagallismic ===
-[[Category:17-limit]]
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Comma list]]: 24576/24565
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 1 || 0 || 0 || 0 || 4 || ],
+|-
+| ⟨ || 0 || 1 || 1 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || -3 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~17/16, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9692{{c}}, ~3/2 = 701.9798{{c}}, ~17/16 = 105.1973{{c}}, ~7/4 = 968.8875{{c}}, ~11/8 = 551.4103{{c}}, ~13/8 = 840.6200{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9799{{c}}, ~17/16 = 105.2003{{c}}, ~7/4 = 968.8842{{c}}, ~11/8 = 551.3897{{c}}, ~13/8 = 840.6045{{c}}
+{{Optimal ET sequence|legend=1| 46, 58, 80, 103, 137, 149, 159, 171, 183, 217, 296, 320, 342f, 354, 400, 422, 525, 571, 581, 742, 764, 935, 1084, 1106, 1323, 1506, 3593g, 3947eg, 5053fgg, 6559defgg, 8065cdefggg, 10152cdeffgggg }}.
+[[Badness]] (Sintel): 15.8
+== Etymology ==
+The mavka comma was named by [[Eliora]] in 2022. Its other name ''archagallismic comma'' derives from ''archagall'', the esoteric subgroup temperament named by [[Scott Dakota]] earlier.
+[[Category:Mavka]]
+[[Category:Commas with unknown etymology]]