Fractional-octave temperaments

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All temperaments on this page have a fractional-octave period, such as 1\26, 1\31, or 1\41.

Temperaments discussed elsewhere include:

37th-octave temperaments

37EDO is accurate for harmonics 5, 7, 11, and 13, so various 37th-octave temperaments actually make sense.

Rubidium

The name of rubidium temperament comes from Rubidium, the 37th element.

Subgroup: 2.3.5.7

Comma list: 3136/3125, 4194304/4117715

Mapping: [37 0 86 104], 0 1 0 0]]

POTE generator: ~3/2 = 703.3903

Vals37, 74, 111

Badness: 0.312105

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1375/1372, 65536/65219

Mapping: [37 0 86 104 128], 0 1 0 0 0]]

POTE generator: ~3/2 = 703.0355

Vals: 37, 74, 111

Badness: 0.101001

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 640/637, 847/845, 1375/1372

Mapping: [37 0 86 104 128 137], 0 1 0 0 0 0]]

POTE generator: ~3/2 = 703.0520

Vals: 37, 74, 111

Badness: 0.048732

Triacontaheptoid

Subgroup: 2.3.5.7

Comma list: 244140625/242121642, 283115520/282475249

Mapping: [37 23 74 92], 0 3 1 1]]

POTE generator: ~5/4 = 385.3041

Vals37, 259b, 296, 629, 925c

Badness: 0.784746

11-limit

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4000/3993, 226492416/226474325

Mapping: [37 23 74 92 128], 0 3 1 1 0]]

POTE generator: ~5/4 = 385.3281

Vals: 37, 259b, 296, 629

Badness: 0.167327

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1375/1372, 4000/3993, 15379/15360

Mapping: [37 23 74 92 128 125], 0 3 1 1 0 1]]

POTE generator: ~5/4 = 385.3067

Vals: 37, 259b, 296, 629f, 925cf

Badness: 0.076183

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 625/624, 715/714, 1225/1224, 4000/3993, 11271/11264

Mapping: [37 23 74 92 128 125 175], 0 3 1 1 0 1 -2]]

POTE generator: ~5/4 = 385.3427

Vals: 37, 259b, 296, 629f

Badness: 0.052475

65th-octave temperaments

65EDO is accurate for harmonics 3, 5, and 11, so various 65th-octave temperaments actually make sense.

Terbium

The name of terbium temperament comes from Terbium, the 65th element.

Subgroup: 2.3.5.7

Comma list: 32805/32768, 78732/78125

Mapping: [65 103 151 0], 0 0 0 1]]

POTE generator: ~8/7 = 230.8641

Vals65, 130

Badness: 0.169778

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 4000/3993, 5632/5625

Mapping: [65 103 151 0 225], 0 0 0 1 0]]

POTE generator: ~8/7 = 230.4285

Vals: 65d, 130

Badness: 0.059966

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 2080/2079, 3584/3575

Mapping: [65 103 151 0 225 58], 0 0 0 1 0 1]]

POTE generator: ~8/7 = 230.0388

Vals: 65d, 130

Badness: 0.036267

118th-octave temperaments

118EDO is accurate for harmonics 3 and 5, so various 118th-octave temperaments actually make sense.

Parakleischis

118EDO and its multiples are members of both parakleismic and schismic, and from this it derives its name.

Subgroup: 2.3.5.7

Comma list: 32805/32768, 1224440064/1220703125

Mapping: [118 187 274 0], 0 0 0 1]]

POTE generator: ~8/7 = 231.2765

Vals118, 236, 354, 472, 2242, 2714b, 3186b, 3658b

Badness: 0.145166

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 32805/32768, 137781/137500

Mapping: [118 187 274 0 77], 0 0 0 1 1]]

POTE generator: ~8/7 = 231.4883

Vals: 118, 354, 472

Badness: 0.049316