Fractional-octave temperaments

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

Temperaments discussed elsewhere include:

• Cloudy temperaments (1\5 period)
  • Blacksmith
  • Cloudtone
  • Coblack
  • Pental
  • Sengasec
  • Quinkee
• Hexe, Sextile, Stearnscape (1\6 period)
• Akjaysmic temperaments (1\7 period)
  • Brahmagupta
  • Septant
  • Whitewood
  • Sevond
  • Neutron
• Octoid, Octant (1\8 period)
• Tritrizo temperaments (1\9 period)
  • Ennealimmal
  • Niner
  • Enneaportent
  • Novemkleismic
• Linus temperaments (1\10 period)
  • Decoid
  • Deca
  • Decic
  • Decistearn
  • Decal
  • Decavish
  • Decimetra
• Hendecatonic, Undeka (1\11 period)
• Compton, Atomic (1\12 period)
• Triskaidekic (1\13 period)
• Pentadecal, Quindecic (1\15 period)
• Hexadecoid (1\16 period)
• Chlorine (1\17 period)
• Hemiennealimmal (1\18 period)
• Enneadecal, Meanmag (1\19 period)
• Degrees (1\20 period)
• Icosidillic (1\22 period)
• Icositritonic (1\23 period)
• Hours (1\24 period)
• Bosonic (1\26 period)
• Trinealimmal (1\27 period)
• Oquatonic (1\28 period)
• Mystery (1\29 period)
• Birds (1\31 period)
• Decades (1\36 period)
• Hemienneadecal (1\38 period)
• Counterpyth (1\41 period)
• Meridic (1\43 period)
• Palladium (1\46 period)
• Mercator (1\53 period)
• Omicronbeta (1\72 period)
• Octogintic (1\80 period)
• Garistearn (1\94 period)
• Undecentic (1\99 period)
• Schisennealimmal (1\171 period)
• Lunennealimmal (1\441 period)

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

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

Vals: Template:Val list

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

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: Template:Val list

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: Template:Val list

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: Template:Val list

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

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

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

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: Template:Val list

Badness: 0.049316