Sensibeta temperaments: Difference between revisions
Created page with "{{Technical data page}} This is a collection of rank-2 temperaments tempering out the sensibeta comma, 1071875/1062882 = {{monzo| -1 -12 5 3 }}. Temperament considered below is elven. Discussed elsewhere are: * ''Sensi'' (+126/125 or +245/243) → Sensipent family * ''Betic'' (+225/224) → Sycamore family == Elven == Subgroup: 2.3.5.7 Comma list: 1071875..." Tags: Mobile edit Mobile web edit |
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* ''[[Sensi]]'' (+126/125 or +245/243) → [[Sensipent family #Septimal sensi|Sensipent family]] | * ''[[Sensi]]'' (+126/125 or +245/243) → [[Sensipent family #Septimal sensi|Sensipent family]] | ||
* ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic|Sycamore family]] | * ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic|Sycamore family]] | ||
* ''[[Slithy]]'' (+4000/3969 or +420175/419904) → [[Octagar temperaments #Slithy|Octagar temperaments]] | |||
* ''[[Ketchup]]'' (+5120/5103) → [[Hemifamity temperaments #Ketchup|Hemifamity temperaments]] | |||
* ''[[Polypyth]]'' (+6144/6125) → [[Porwell temperaments #Polypyth|Porwell temperaments]] | |||
* ''[[Marfifths]]'' (+10976/10935 or +15625/15552) → [[Kleismic family #Marfifths|Kleismic family]] | |||
== Elven == | == Elven == | ||
{{see also|11th-octave temperaments}} | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
Latest revision as of 02:03, 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.
This is a collection of rank-2 temperaments tempering out the sensibeta comma, 1071875/1062882 = [-1 -12 5 3⟩.
Temperament considered below is elven. Discussed elsewhere are:
- Sensi (+126/125 or +245/243) → Sensipent family
- Betic (+225/224) → Sycamore family
- Slithy (+4000/3969 or +420175/419904) → Octagar temperaments
- Ketchup (+5120/5103) → Hemifamity temperaments
- Polypyth (+6144/6125) → Porwell temperaments
- Marfifths (+10976/10935 or +15625/15552) → Kleismic family
Elven
Subgroup: 2.3.5.7
Comma list: 1071875/1062882, 9765625/9680832
Mapping: [⟨11 2 7 0], ⟨0 5 6 10]]
- Mapping generators: ~729/686, ~756/625
Optimal ET sequence: 121, 253, 374
Badness (Sintel): 11.372
11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 4375/4356, 59290/59049
Mapping: [⟨11 2 7 0 1], ⟨0 5 6 10 12]]
Optimal tunings:
- WE: ~729/686 = 109.101¢, ~297/245 = 336.877¢
- CWE: ~729/686 = 109.091¢, ~297/245 = 336.863¢
Optimal ET sequence: 121, 253, 374
Badness (Sintel): 3.675
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 1375/1372, 1575/1573, 2200/2197
Mapping: [⟨11 2 7 0 1 16], ⟨0 5 6 10 12 8]]
Optimal tunings:
- WE: ~125/117 = 109.100¢, ~91/75 = 336.876¢
- CWE: ~125/117 = 109.091¢, ~91/75 = 336.863¢
Optimal ET sequence: 121, 253, 374
Badness (Sintel): 2.019
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 375/374, 595/594, 1275/1274, 2200/2197
Mapping: [⟨11 2 7 0 1 16 11], ⟨0 5 6 10 12 8 11]]
Optimal tunings:
- WE: ~125/117 = 109.099¢, ~17/14 = 336.867¢
- CWE: ~125/117 = 109.091¢, ~17/14 = 336.856¢
Optimal ET sequence: 121, 253, 374
Badness (Sintel): 1.495