Fractional-octave temperaments: Difference between revisions

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Temperaments discussed elsewhere include:
Temperaments discussed elsewhere include:


* [[Akjaysmic microtemperaments|Akjaysmic temperaments]] (1\7 period)
** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]]
** [[Schismatic family #Septant|Septant]]
** [[Apotome family #Whitewood|Whitewood]]
** [[Keemic temperaments #Sevond|Sevond]]
** [[Mistismic temperaments #Neutron|Neutron]]
* [[Ragismic microtemperaments #Octoid|Octoid]] (1\8 period)
* [[Tritrizo clan|Tritrizo temperaments]] (1\9 period)
* [[Tritrizo clan|Tritrizo temperaments]] (1\9 period)
** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]]
** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]]
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* [[31st-octave temperaments|Birds]] (1\31 period)
* [[31st-octave temperaments|Birds]] (1\31 period)
* [[Compton family #Decades|Decades]] (1\36 period)
* [[Compton family #Decades|Decades]] (1\36 period)
* [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]] (1\38 period)
* [[Counterpyth family|Counterpyth]] (1\41 period)
* [[Counterpyth family|Counterpyth]] (1\41 period)
* [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period)
* [[Mitonismic temperaments #Meridic|Meridic]] (1\43 period)
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=== 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 89: Line 98:


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


=== 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 131: Line 141:


Badness: 0.036267
Badness: 0.036267
== 118th-octave temperaments ==
[[118edo|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 [[Schismatic family|schismic]], and from this it derives its name.
Subgroup: 2.3.5.7
[[Comma list]]: 32805/32768, 1224440064/1220703125
[[Mapping]]: [{{val|118 187 274 0}}, {{val|0 0 0 1}}]
[[POTE generator]]: ~8/7 = 231.2765
{{Val list|legend=1| 118, 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: [{{val|118 187 274 0 77}}, {{val|0 0 0 1 1}}]
POTE generator: ~8/7 = 231.4883
Vals: {{Val list| 118, 354, 472 }}
Badness: 0.049316


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Temperament collection]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 12:09, 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

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

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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