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{{Infobox Interval | {{Infobox Interval | ||
| Name = mavka comma, archagallisma | |||
| Color name = 17u<sup>3</sup>g-2, Trisu-agu comma | |||
| Comma = yes | |||
| Name = mavka comma | |||
| Color name = | |||
| | |||
}} | }} | ||
'''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]]). | |||
''' | == Temperaments == | ||
[[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). | |||
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]]. | |||
Finally, tempering out 256/255 and/or 289/288 results in a lower-accuracy temperament, [[srutal archagall]], of the [[diaschismic family]]. | |||
=== Archagallic === | |||
[[Subgroup]]: 2.3.5.17 | |||
[[Comma list]]: 24576/24565 | |||
== | {{Mapping|legend=2| 1 1 2 4 | 0 1 1 0 | 0 0 -3 1 }} | ||
: mapping generators: ~2, ~3, ~17/16 | |||
[[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}} | |||
{{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 }} | |||
[[Badness]] (Sintel): 0.127 | |||
[ | === Mavka a.k.a. archagallismic === | ||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Comma list]]: 24576/24565 | |||
⟨ 0 0 3 0 0 0 -1 ] | {| 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:Mavka]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 16:08, 22 July 2026
| Interval information |
archagallisma
24576/24565, the mavka comma or archagallisma, is an unnoticeable 17-limit comma measuring about 0.775 cents. It is the difference between 256/255 and 289/288 – two adjacent square superparticulars, 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).
Temperaments
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).
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.
Finally, tempering out 256/255 and/or 289/288 results in a lower-accuracy temperament, srutal archagall, of the diaschismic family.
Archagallic
Subgroup: 2.3.5.17
Comma list: 24576/24565
Subgroup-val mapping: [⟨1 1 2 4], ⟨0 1 1 0], ⟨0 0 -3 1]]
- mapping generators: ~2, ~3, ~17/16
- WE: ~2 = 1199.9692 ¢, ~3/2 = 701.9798 ¢, ~17/16 = 105.1973 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9799 ¢, ~17/16 = 105.2003 ¢
Optimal ET sequence: 10, 12, 22, 34, 80, 103, 115, 125, 137, 159, 171, 354, 376, 388, 559, 1882, 2441g, 3000g, 6559gg, 9559cggg
Badness (Sintel): 0.127
Mavka a.k.a. archagallismic
Subgroup: 2.3.5.7.11.13.17
Comma list: 24576/24565
| [⟨ | 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
- WE: ~2 = 1199.9692 ¢, ~3/2 = 701.9798 ¢, ~17/16 = 105.1973 ¢, ~7/4 = 968.8875 ¢, ~11/8 = 551.4103 ¢, ~13/8 = 840.6200 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9799 ¢, ~17/16 = 105.2003 ¢, ~7/4 = 968.8842 ¢, ~11/8 = 551.3897 ¢, ~13/8 = 840.6045 ¢
Optimal ET sequence: 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.