Quartismic family

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The quartismic family is built up from temperaments that temper out the quartisma- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of [24 -6 0 1 -5. Among the members of this family are Quartismatic, Altierran, Meanquarter, Coin, Escapismic, Dietismic, Kleirtismic, and Doublefour.

Quartismic

The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of 117440512/117406179 and a monzo of [24 -6 0 1 -5⟩. As the quartisma is an unnoticeable comma, this rank-4 temperament is a microtemperament.

Comma: 117440512/117406179

POTE generators: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748

Map: [<1 0 0 1 5|, <0 1 0 1 -1|, <0 0 1 0 0|, <0 0 0 5 1|]

Wedgie: <<<<5 1 0 -6 -24||||

EDOs: 21, 22, 24, 25, 43, 45, 46, 67, 68, 89, 90, 91, 92, 110, 111, 113, 114, 132, 134, 135, 138, 156, 157, 159, 178, 179, 180, 181, 202, 224, 270, 313, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 3125, 7419

Badness: 0.274 × 10-6

13-limit

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Quartismatic

There are some temperaments in the quartismic family in which the quartisma is tempered out, but without any sort of five-limit representation. This particular temperament is the parent temperament of all such no-fives children, and is referred to as Saquinlu-azo temperament in color notation.

Comma: 117440512/117406179

POTE generators: ~3/2 = 701.9826, ~33/32 = 53.3748

Map: [<1 0 1 5|, <0 1 1 -1|, <0 0 5 1|]

Wedgie:

EDOs: 21, 22, 24, 43, 46, 89, 135, 270, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 7419

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The following unnamed rank-2 quartismic temperament MOS scales have been found

13-limit

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Altierran

The Altierran clan is the temperament clan consisting of those temperaments in which both the schisma and the quartisma are tempered out.

Commas: 32805/32768, 117440512/117406179

POTE generators: ~3/2 = 701.7299, ~33/32 = 53.3889

Map: [<1 0 15 1 5|, <0 1 -8 1 -1|, <0 0 0 5 1|]

Wedgie: <<-102 24 -15 75 6 -8 40 1 -5 0||

EDOs: 135, 159, 224, 248, 313, 472

Badness:

13-limit

Commas: 10985/10976, 32805/32768, 117440512/117406179

POTE generators: ~11/10 = 166.0628, ~33/32 = 53.4151

Map: [<1 2 -1 3 3 5|, <0 -3 24 -3 3 -11|, <0 0 0 5 1 5|]

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17-limit

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Meanquarter

The Meanquarter clan is the temperament clan consisting of those temperaments in which both the meantone comma and the quartisma are tempered out. Meanquarter can easily be extended to a form of godzilla, though not all possible tunings for Meanquarter lend themselves to this sort of thing.

Commas: 81/80, 117440512/117406179

POTE generators: ~3/2 = 697.3325, ~33/32 = 54.1064

Map: [<1 0 -4 1 5|, <0 1 4 1 -1|, <0 0 5 1|]

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EDOs: 24, 43, 45, 67

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Coin

The Coin clan is the temperament clan consisting of those temperaments in which both the magic comma and the quartisma are tempered out.

Commas: 3125/3072, 117440512/117406179

POTE generators: ~5/4 = 380.3623, ~9/7 = 433.3120

Map: [<1 0 2 1 5|, <0 5 1 0 -6|, <0 0 0 5 1|]

EDOs: 22, 25, 139cdd

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Escapismic

The Escapisimic clan is the temperament clan consisting of those temperaments in which both the escapade comma and the quartisma are tempered out, thus, it is essentially an Escapade extension.

Commas: 117440512/117406179, 4294967296/4271484375

POTE generators: ~33/32 = 55.3538

Map: [<1 2 2 3 3|, <0 -9 7 -4 10|]

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EDOs: 21, 22, 43

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Dietismic

The Dietismic clan is the temperament clan consisting of those temperaments in which both the diaschisma and the quartisma are tempered out. Dietismic can easily be extended to a form of shrutar, and in fact, it is rather unusual to find a Dietismic temperament that is not also some form of shrutar.

Commas: 2048/2025, 117440512/117406179

POTE generators: ~33/32 = 52.6800

Map: [<2 3 5 5 7|, <0 2 -4 7 -1|]

Wedgie:

EDOs: 22, 24, 38cdde, 46, 68, 114

Badness:

Rank 2 scale (52.6800, 2/1), 13|9

Rank 2 scale (53.3742, 2/1), 13|9

Kleirtismic

The Kleirtismic clan is the temperament clan consisting of those temperaments in which both the kleisma and the quartisma are tempered out. The "kleir-" in "Kleirtismic" is pronounced the same as "Clair"

Commas: 15625/15552, 117440512/117406179

POTE generators: ~6/5 = 317.0291, ~68/55 370.2940

Map: [<1 0 1 1 5|, <0 6 5 1 -7|, <0 0 0 5 1|]

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EDOs: 159, 178, 246

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Doublefour

The Doublefour clan is the temperament clan consisting of those temperaments in which both the tetracot comma and the quartisma are tempered out.

Commas: 20000/19683, 117440512/117406179

POTE generators: ~425/384 = 175.9566, ~33/32 = 52.9708

Map: [<1 1 1 2 4|, <0 4 9 4 -4|, <0 0 0 5 1|]

Wedgie:

EDOs: 48d, 68, 89c

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