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 includes:

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

Template:Val list

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: Template:Val list

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

Template:Val list

Badness: 0.048732

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

Template:Val list

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: Template:Val list

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: Template:Val list

Badness: 0.036267