11th-octave temperaments: Difference between revisions
- hendeca, - undeka (moved to appropriate temp collection pages) |
Canonicalize hendecatonic and undeka. Undeka is weaker but it hardly matters |
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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. | 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. | ||
== | == Hendecatonic == | ||
This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit | : ''For extensions, see [[Porwell temperaments #Hendecatonic]] and [[Marvel temperaments #Hendeca]].'' | ||
This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
| Line 23: | Line 25: | ||
[[Badness]] (Sintel): 10.7 | [[Badness]] (Sintel): 10.7 | ||
== | == Undeka == | ||
: ''For extensions, see [[Keemic temperaments #Undeka]].'' | |||
This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit. | This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit. | ||
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== Elven == | == Elven == | ||
: ''For extensions, see [[Sensibeta temperaments #Elven]].'' | |||
This temperament has a period of 1/11 octave, which represents [[3125/2916]] in the 5-limit. | This temperament has a period of 1/11 octave, which represents [[3125/2916]] in the 5-limit. | ||
Revision as of 10:47, 5 July 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.
Hendecatonic
- For extensions, see Porwell temperaments #Hendecatonic and Marvel temperaments #Hendeca.
This temperament has a period of 1/11 octave, which represents 16/15 in the 5-limit.
Subgroup: 2.3.5
Comma list: 8796093022208/8649755859375
Mapping: [⟨11 0 43], ⟨0 1 -1]]
- Mapping generators: ~16/15, ~3
- WE: ~16/15 = 109.0904 ¢, ~3/2 = 702.6861 ¢
- error map: ⟨-0.445 +0.286 +0.613]
- CWE: ~16/15 = 109.0909 ¢, ~3/2 = 702.9082 ¢
- error map: ⟨0.000 +0.953 +1.687]
Optimal ET sequence: 22, 55, 77, 99, 869bcc, 968bcc, 1067bccc, 1166bccc
Badness (Sintel): 10.7
Undeka
- For extensions, see Keemic temperaments #Undeka.
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
- WE: ~648/625 = 109.1809 ¢, ~3/2 = 704.4091 ¢
- error map: ⟨+0.990 +3.444 -7.468]
- CWE: ~648/625 = 109.0909 ¢, ~3/2 = 704.6983 ¢
- error map: ⟨0.000 +2.743 -8.888]
Optimal ET sequence: 22, 77c, 99c
Badness (Sintel): 17.1
Elven
- For extensions, see 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: [-23 -66 55⟩
Mapping: [⟨11 2 7], ⟨0 5 6]]
- mapping generators: ~3125/2916, ~[10 29 -24⟩
- WE: ~3125/2916 = 109.0998 ¢, ~[10 29 -24⟩ = 336.8921 ¢
- error map: ⟨+0.097 +0.705 -1.263]
- CWE: ~3125/2916 = 109.0909 ¢, ~[10 29 -24⟩ = 336.8814 ¢
- error map: ⟨0.000 +0.634 -1.389]
Optimal ET sequence: 121, 253, 374, 627c
Badness (Sintel): 429