Fractional-octave temperaments: Difference between revisions

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** [[Qintosec family #Sengasec|Sengasec]]
** [[Qintosec family #Sengasec|Sengasec]]
** [[Cloudy clan #Quinkee|Quinkee]]
** [[Cloudy clan #Quinkee|Quinkee]]
* [[Landscape microtemperaments #Sextile|Sextile]], [[Stearnsmic clan #Stearnscape|Stearnscape]] (1\6 period)
* [[Augmented family #Hexe|Hexe]], [[Landscape microtemperaments #Sextile|Sextile]], [[Stearnsmic clan #Stearnscape|Stearnscape]] (1\6 period)
* [[Akjaysma|Akjaysmic temperaments]] (1\7 period)
* [[Akjaysma|Akjaysmic temperaments]] (1\7 period)
** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]
** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]
Line 65: Line 65:
=== Rubidium ===
=== Rubidium ===
The name of rubidium temperament comes from Rubidium, the 37th element.
The name of rubidium temperament comes from Rubidium, the 37th element.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 104: Line 103:


Badness: 0.048732
Badness: 0.048732
=== Triacontaheptoid ===
Subgroup: 2.3.5.7
[[Comma list]]: 244140625/242121642, 283115520/282475249
[[Mapping]]: [{{val|37 23 74 92}}, {{val|0 3 1 1}}]
[[POTE generator]]: ~5/4 = 385.3041
{{Val list|legend=1| 37, 259b, 296, 629, 925c }}
[[Badness]]: 0.784746
==== 11-limit ====
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4000/3993, 226492416/226474325
Mapping: [{{val|37 23 74 92 128}}, {{val|0 3 1 1 0}}]
POTE generator: ~5/4 = 385.3281
Vals: {{Val list| 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: [{{val|37 23 74 92 128 125}}, {{val|0 3 1 1 0 1}}]
POTE generator: ~5/4 = 385.3067
Vals: {{Val list| 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: [{{val|37 23 74 92 128 125 175}}, {{val|0 3 1 1 0 1 -2}}]
POTE generator: ~5/4 = 385.3427
Vals: {{Val list| 37, 259b, 296, 629f }}
Badness: 0.052475


== 65th-octave temperaments ==
== 65th-octave temperaments ==
Line 110: Line 161:
=== Terbium ===
=== Terbium ===
The name of terbium temperament comes from Terbium, the 65th element.
The name of terbium temperament comes from Terbium, the 65th element.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 155: Line 205:
=== Parakleischis ===
=== Parakleischis ===
118EDO and its multiples are members of both [[parakleismic]] and [[Schismatic family|schismic]], and from this it derives its name.
118EDO and its multiples are members of both [[parakleismic]] and [[Schismatic family|schismic]], and from this it derives its name.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7

Revision as of 22:34, 12 October 2021

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

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

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

Template:Val list

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

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

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

Template:Val list

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

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