Subgroup temperaments: Difference between revisions

= Composite subgroup temperaments =

=== Darian calendar ===

Darian calendar is described as 24 & 668 temperament in the 2.3.11.19 [[subgroup]] and is named after a certain calendar layout by the same name. The generator is close to the [[36/35]] quartertone, and this allows an extension to the 2.3.35.11.19 subgroup. 5 of them make [[11/8]], 8 of them make [[3/2]], and 6 of them make [[32/19]].

[[Support]]ing [[ET]]s: {{EDOs|24, 668}}, ...

See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].  

{{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}

=== Glacial ===

{{See also| Chromatic pairs #Glacial }}

* ''[[Thundersnow]]'' - [[Sevish]] (2021)

=== Mabon ===

Derived from a [http://individual.utoronto.ca/kalendis/leap/index.htm#se calendar leap cycle built for the autumn equinox], hence the name. Defined as the 11 & 62 temperament.

{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}

=== Apparatus ===

[[Subgroup]]: 2.9.7.11

Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]

=== Novisept ===

Badness (Dirichlet): 0.142

=== Demon ===

Demon is a temperament which equates 3 [[11/9]] with [[16/9]], or equivalently 3 [[18/11]] with [[9/8]], tempering out [[1331/1296]]. This results in [[11/9]] being tuned flat to a supraminor third, and [[27/22]] being tuned sharp to a submajor third. It was discovered by [[User:CompactStar|CompactStar]] while searching for temperaments assosciated with the [[7L 4s]] ("daemotonic") MOS, known for its lack of representation of simple temperaments. The optimal tuning for demon temperament is near the basic tuning of 7L 4s (13\18), and indeed [[18edo]] supports demon temperament.

{{Optimal ET sequence|legend=1|9, 11, 24, 59, 83, 142, 225, 367}}[-11], 592[-11], 959[-9, --11], 1326[-9, --11]

=== Stacks (a.k.a. 2magic) ===

Stacks, the 11 & 30 temperament in the 2.9.15.7.11.13 subgroup, is every other step of [[magic]].  

RMS error: 1.540 cents

=== A-team ===

A-team is every other step of [[slendric]]; the 2.9.5.21.11 extension below specifically restricts [[mothra]].  

{{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }}

=== Archagall ===

{{See also| Fifthplus }}

{{Optimal ET sequence|legend=0| 5, 12, 17, 22, 83, 105, 127, 403, 530, 657, 784, 1441* }}

=== Tetrahanson ===

{{Main| Tetrahanson }}

[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}

=== Meanquad ===

{{Main| Meanquad }}

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=== Meansquared ===

[[Subgroup]]: 4.9.25

[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]

=== Archsquared ===  

[[Subgroup]]: 4.9.49

[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49

=== Sixscared ===

Sixscared is a tuning which still maintains some consonance, while eviscerating the rules of conventional 12-tone harmony. The familiar major, minor and perfect intervals are nowhere to be found, and octaves are far and few between, so the seventh harmonic becomes the backbone of harmony. Approximating the harmonics 7, 8, 9, Sixscared is named for the classic dad joke: "Why was six scared? Because seven ate nine."