11th-octave temperaments: Difference between revisions
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{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }} | {{Optimal ET sequence|legend=1| 22, 55, 77, 99 }} | ||
[[Badness]]: | [[Badness]] (Sintel): 10.652 | ||
=== Undekapent === | === Undekapent === | ||
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{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }} | {{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 17.067 | ||
=== Elven === | |||
{{see also| Sensibeta temperaments #Elven }} | |||
This temperament has a period of 1/11 octave, which represents [[3125/2916]] in the 5-limit. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo|-23 -66 55}} | |||
{{Mapping|legend=1| 11 2 7 | 0 5 6 }} | |||
: Mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }} | |||
[[Optimal tuning]] ([[POTE]]): ~648/625 = 109.091, ~6/5 = 317.681 | |||
{{Optimal ET sequence|legend=1| 121, 253, 374 }} | |||
[[Badness]] (Sintel): 429.4 | |||
== Hendeca == | == Hendeca == | ||
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{{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }} | {{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }} | ||
[[Badness]]: | [[Badness]] (Sintel): 4.371 | ||
=== 11-limit === | === 11-limit === | ||
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{{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }} | {{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }} | ||
Badness: | Badness (Sintel): 2.464 | ||
== Undeka == | == Undeka == | ||
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{{Optimal ET sequence|legend=1| 11c, 22 }} | {{Optimal ET sequence|legend=1| 11c, 22 }} | ||
[[Badness]]: | [[Badness]] (Sintel): 3.588 | ||
=== 11-limit === | === 11-limit === | ||
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{{Optimal ET sequence|legend=0| 11c, 22 }} | {{Optimal ET sequence|legend=0| 11c, 22 }} | ||
Badness: | Badness (Sintel): 2.270 | ||
=== 13-limit === | === 13-limit === | ||
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{{Optimal ET sequence|legend=0| 11cf, 22 }} | {{Optimal ET sequence|legend=0| 11cf, 22 }} | ||
Badness: | Badness (Sintel): 2.336 | ||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||
Revision as of 02:22, 11 February 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
An 11th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 11. Although 11edo itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are.
5-limit temperaments
Hendecapent
This temperament has a period of 1/11 octave, which represents 16/15 in the 5-limit. There are some 7-limit extensions include hendecatonic (22 & 77) and hendeca (22 & 33).
Subgroup: 2.3.5
Comma list: 8796093022208/8649755859375
Mapping: [⟨11 0 43], ⟨0 1 -1]]
- Mapping generators: ~16/15, ~3
Optimal tuning (POTE): ~16/15 = 109.091, ~3/2 = 702.947
Optimal ET sequence: 22, 55, 77, 99
Badness (Sintel): 10.652
Undekapent
This temperament has a period of 1/11 octave, three of them represent 6/5 in the 5-limit.
Subgroup: 2.3.5
Comma list: 48828125/45349632
Mapping: [⟨11 0 8], ⟨0 1 1]]
- Mapping generators: ~648/625, ~3
Optimal tuning (POTE): ~648/625 = 109.091, ~3/2 = 703.829
Optimal ET sequence: 22, 77c, 99c, 121c
Badness (Sintel): 17.067
Elven
This temperament has a period of 1/11 octave, which represents 3125/2916 in the 5-limit.
Subgroup: 2.3.5
Comma list: [-23 -66 55⟩
Mapping: [⟨11 2 7], ⟨0 5 6]]
- Mapping generators: ~3125/2916, ~[10 29 -24⟩
Optimal tuning (POTE): ~648/625 = 109.091, ~6/5 = 317.681
Optimal ET sequence: 121, 253, 374
Badness (Sintel): 429.4
Hendeca
- Not to be confused with Hendec.
This temperament has a period of 1/11 octave, nine of them represent 7/4 in the 7-limit, as well as undeka.
Subgroup: 2.3.5.7
Comma list: 225/224, 122880/117649
Mapping: [⟨11 0 43 31], ⟨0 1 -1 0]]
- Mapping generators: ~16/15, ~3
Optimal tuning (POTE): ~16/15 = 109.091, ~3/2 = 703.313
Optimal ET sequence: 11, 22, 55d, 77d, 99dd
Badness (Sintel): 4.371
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 352/343
Mapping: [⟨11 0 43 31 38], ⟨0 1 -1 0 0]]
Optimal tuning (POTE): ~16/15 = 109.091, ~3/2 = 703.090
Optimal ET sequence: 11, 22, 55d, 77d, 99dd
Badness (Sintel): 2.464
Undeka
Subgroup: 2.3.5.7
Comma list: 875/864, 3200/3087
Mapping: [⟨11 0 8 31], ⟨0 1 1 0]]
- Mapping generators: ~21/20, ~3
Optimal tuning (POTE): ~21/20 = 109.091, ~3/2 = 708.792
Badness (Sintel): 3.588
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 352/343, 385/384
Mapping: [⟨11 0 8 31 38], ⟨0 1 1 0 0]]
Optimal tuning (POTE): ~21/20 = 109.091, ~3/2 = 706.768
Badness (Sintel): 2.270
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/63, 100/99, 169/165, 352/343
Mapping: [⟨11 0 8 31 38 23], ⟨0 1 1 0 0 1]]
Optimal tuning (POTE): ~13/12 = 109.091, ~3/2 = 707.764
Badness (Sintel): 2.336