Orwellismic family

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The orwellismic family of rank three temperaments tempers out the orwellisma, 1728/1715.

Comma: 1728/1715

7- and 9-limit minimax

[<1 0 0 0|, <0 1 0 0|, <3/2 3/4 3/4 -3/4|,

<3/2 3/4 -1/4 1/4|]

Eigenmonzos: 2, 4/3, 7/5

Lattice basis: 7/6 0.7526 3/2 1.3931

Angle(7/6, 3/2) = 97.5081

Map to lattice: [<0 0 -3 1|, <0 1 0 1|]

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

Generators: 2, 3, 12/7

Edos: 9, 14, 17, 18, 22, 26, 27, 31, 49, 53, 58, 80, 84, 111, 142, 164d, 306d, 417cd

Badness: 0.000187

Projection pair: 5 1728/343 to 2.3.7

Scales: orwellismic9

Orwellian

Commas: 99/98, 385/384

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

EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee

Badness: 0.000715

Guanyin

Commas: 176/175, 540/539

11-limit minimax

[<1 0 0 0 0|, <-2/9 0 -5/9 5/9 4/9|, <4/3 0 1/3 -1/3 1/3|,

<4/3 0 -2/3 2/3 1/3|, <0 0 0 0 1|]

Eigenmonzos: 2, 11/8, 7/5

Lattice basis: 7/6 0.5167 3/2 1.3055

Angle(7/6, 3/2) = 79.0940

Map to lattice: [<0 0 -3 1 -5|, <0 1 0 1 1|]

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

Generators: 2, 3, 12/7

EDOs: 9, 22, 31, 53, 58, 80, 111, 280cd, 391cd

Badness: 0.000411

Projection pairs: 5 1728/343 11 186624/16807 to 2.3.7

Scales: guanyin22

Music:

Trio for SoftSaturn, NebulaSing and TromBonehead play by Gene Ward Smith

13-limit

Commas: 176/175, 351/350, 540/539

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

EDOs: 22, 31, 53, 58, 80, 111, 280cdf, 391cdf

Badness: 0.000758

Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7

Georgian

Commas: 144/143, 176/175, 196/195

Map: [<1 0 0 2 -2 6|, <0 1 0 1 1 1|, <0 0 3 -1 5 -5|]

EDOs: 9, 31, 46f, 48c, 58

Badness: 0.000904

Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7