Sensamagic clan

The sensamagic clan tempers out the sensamagic comma, 245/243, a triprime comma with no factors of 2, ⟨0 -5 1 2] to be exact. There are a number of linear temperaments in the clan (magic, father, sensi, godzilla, superpyth, octacot, rodan, hedgehog, clyde, shrutar, sidi) but they've mostly been discussed elsewhere. Tempering out 245/243 alone leads to a rank three temperament for which 283edo is the optimal patent val.

Bohpier

Comma: 1220703125/1162261467

POTE generator: ~27/25 = 146.476

Map: [<1 0 0|, <0 13 19|]

EDOs: 8, 41, 131, 172, 213c

Badness: 0.8605

7-limit

Commas: 245/243, 3125/3087

POTE generator: ~27/25 = 146.474

Map: [<1 0 0 0|, <0 13 19 23|]

Wedgie: <<13 19 23 0 0 0||

EDOs: 41, 49, 90, 131

EDTs: 13

Badness: 0.0682

11-limit

Commas: 100/99, 245/243, 1344/1331

POTE generator: ~12/11 = 146.545

Map: [<1 0 0 0 2|, <0 13 19 23 12|]

EDOs: 41, 90e, 131e

Badness: 0.0339

13-limit

Commas: 100/99, 144/143, 196/195, 275/273

POTE generator: ~12/11 = 146.603

Map: [<1 0 0 0 2 2|, <0 13 19 23 12 14|]

EDOs: 41, 90ef, 131ef, 221bdeff

Badness: 0.0249

Music

by Chris Vaisvil:

• bophier-1.mp3
• bophier-12equal-six-octaves.mp3

Sensa (Escaped)

See also: Escapade family § Escaped

Commas: 245/243, 65625/65536

POTE generator: ~28/27 = 55.122

Map: [<1 2 2 4|, <0 -9 7 -26|]

Wedgie: <<9 -7 26 -32 16 80||

EDOs: 22, 43d, 65, 87, 109, 196, 283

Badness: 0.0887

11-limit

Commas: 245/243, 385/384, 4000/3993

POTE generator: ~28/27 = 55.126

Map: [<1 2 2 4 3|, <0 -9 7 -26 10|]

EDOs: 22, 43d, 65, 87, 109, 196, 283

Badness: 0.0358

13-limit

Commas: 245/243, 352/351, 385/384, 625/624

POTE generator: ~28/27 = 55.138

Map: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|]

EDOs: 22, 65, 87, 109, 196, 283

Badness: 0.0317

Salsa

See also: Schismatic family

Commas: 245/243, 32805/32768

POTE generator: ~128/105 = 351.049

Map: [<1 1 7 -1|, <0 2 -16 13|]

Wedgie: <<2 -16 13 -30 15 75||

EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd

Badness: 0.08015

11-limit

Commas: 243/242, 245/242, 385/384

POTE generator: ~11/9 = 351.014

Map: [<1 1 7 -1 2|, <0 2 -16 13 5|]

EDOs: 17, 24, 41, 106d, 147d

Badness: 0.0394

13-limit

Commas: 105/104, 144/143, 243/242, 245/242

POTE generator: ~11/9 = 351.025

Map: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]

EDOs: 17, 24, 41, 106df, 147df

Badness: 0.0310

Pycnic

The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.

Commas: 245/243, 525/512

POTE generator: ~45/32 = 567.720

Map: [<1 3 -1 8|, <0 -3 7 -11|]

Wedgie: <<3 -7 11 -18 9 45||

EDOs: 17, 19, 36c, 55c, 74cd, 93cdd

Badness: 0.0737

Cohemiripple

See also: Mint temperaments § Ripple

Commas: 245/243, 1323/1250

POTE generator: ~7/5 = 549.944

Map: [<1 7 11 12|, <0 -10 -16 -17|]

Wedgie: <<10 16 17 2 -1 -5||

EDOs: 11cd, 13cd, 24

Badness: 0.1902

11-limit

Commas: 77/75, 243/242, 245/242

POTE generator: ~7/5 = 549.945

Map: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]

EDOs: 11cdee, 13cdee, 24

Badness: 0.0827

13-limit

Commas: 66/65, 77/75, 147/143, 243/242

POTE generator: ~7/5 = 549.958

Map: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]

EDOs: 11cdeef, 13cdeef, 24

Badness: 0.0499

Superthird

Commas: 245/243, 78125/76832

POTE generator: ~9/7 = 439.076

Map: [<1 13 15 25|, <0 -18 -20 -35|]

Wedgie: <<18 20 35 -10 5 25||

EDOs: 41, 317bc, 358bc, 399bc

Badness: 0.1394

11-limit

Commas: 100/99, 245/243, 78125/76832

POTE generator: ~9/7 = 439.152

Map: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]

EDOs: 41, 153be, 194be, 235bce

Badness: 0.0709

13-limit

Commas: 100/99, 144/143, 196/195, 1375/1352

POTE generator: ~9/7 = 439.119

Map: [<1 13 15 25 6 24|, <0 -18 -20 -35 -4 -32|]

EDOs: 41

Badness: 0.0528

Magus

Commas: 50331648/48828125

POTE generator: ~5/4 = 391.225

Map: [<1 9 3|, <0 -11 -1|]

EDOs: 40, 43, 46, 181c, 227c, 273c, 319c

Badness: 0.3602

7-limit

Commas: 245/243, 28672/28125

POTE generator: ~5/4 = 391.465

Map: [<1 9 3 21|, <0 -11 -1 -27|]

Wedgie: <<11 1 27 -24 12 60||

EDOs: 46, 95, 141bc, 187bc, 328bc

Badness: 0.1084

11-limit

Commas: 176/175, 245/243, 1331/1323

POTE generator: ~5/4 = 391.503

Map: [<1 9 3 21 23|, <0 -11 -1 -27 -29|]

EDOs: 46, 95, 141bc

Badness: 0.0451

13-limit

Commas: 91/90, 176/175, 245/243, 1331/1323

POTE generator: ~5/4 = 391.366

Map: [<1 9 3 21 23 1|, <0 -11 -1 -27 -29 4|]

EDOs: 46, 233bcf, 279bcf

Badness: 0.0430

Leapweek

Commas: 245/243, 2097152/2066715

POTE generator: ~3/2 = 704.536

Map: [<1 1 17 -6|, <0 1 -25 15|]

EDOs: 17, 46, 109, 155, 264b, 419b

Badness: 0.14058

11-limit

Commas: 245/243, 385/384, 1331/1323

POTE generator: ~3/2 = 704.554

Map: [<1 1 17 -6 -3|, <0 1 -25 15 11|]

EDOs: 17, 46, 109, 264b, 373b, 637be

Badness: 0.0507

13-limit

Commas: 169/168, 245/243, 352/351, 364/363

POTE generator: ~3/2 = 704.571

Map: [<1 1 17 -6 -3 -1|, <0 1 -25 15 11 8|]

EDOs: 17, 46, 63, 109, 218f, 373bf

Badness: 0.0327