Catfish: Difference between revisions
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{{Todo|inline=1|merge articles|comment= [[Catfish]] → [[Subgroup temperaments]] }} | |||
[[File:Salmon7.wav|thumb|Catfish[7] scale and 11:13:17 chord on A in 20ed11/5 tuning]] | [[File:Salmon7.wav|thumb|Catfish[7] scale and 11:13:17 chord on A in 20ed11/5 tuning]] | ||
'''Catfish''' is a [[11/5]]-repeating no-twos-or-threes [[rank-2 temperament]] which tempers out the commas 2093663/2088025 and 54925/54043 in the 11/5.11.13.17 fractional subgroup (equatable to 5.11.13.17). This implies a generator approximating [[17/11]] or its inverse 121/85. It can be viewed as the no-twos-or-threes analog to [[meantone]] with 11:13:17 being the substitute for 4:5:6. It possesses MOS scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>. | '''Catfish''' is a [[11/5]]-repeating no-twos-or-threes [[rank-2 temperament]] which tempers out the commas 2093663/2088025 and 54925/54043 in the 11/5.11.13.17 fractional subgroup (equatable to 5.11.13.17). This implies a generator approximating [[17/11]] or its inverse 121/85. It can be viewed as the no-twos-or-threes analog to [[meantone]] with 11:13:17 being the substitute for 4:5:6. It possesses MOS scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>. | ||
Revision as of 14:05, 16 October 2026
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Todo: merge articles |
Catfish is a 11/5-repeating no-twos-or-threes rank-2 temperament which tempers out the commas 2093663/2088025 and 54925/54043 in the 11/5.11.13.17 fractional subgroup (equatable to 5.11.13.17). This implies a generator approximating 17/11 or its inverse 121/85. It can be viewed as the no-twos-or-threes analog to meantone with 11:13:17 being the substitute for 4:5:6. It possesses MOS scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
20ed11/5 is one of the best tunings for this temperament, although it does noticeably flatten the 13/11 in the 11:13:17 chord.
Interval chain (CTE tuning)
| Generators up | Cents |
|---|---|
| 0 | 0.0 |
| 1 | 613.3 |
| 2 | 1226.6 |
| 3 | 474.9 |
| 4 | 1088.2 |
| 5 | 336.5 |
| 6 | 949.8 |
| 7 | 198.1 |
Ed11/5 tunings
- 9ed11/5 using 4\9ed11/5
- 11ed11/5 using 5\11ed11/5
- 20ed11/5 using 9\20ed11/5
- 29ed11/5 using 13\29ed11/5
Scales
Temperament data
Subgroup: 11/5.11.13.17
Comma list: 2093663/2088025, 54925/54043
Mapping: [⟨1 -1 1 4], ⟨0 9 5 -1]]
CTE generator: ~121/85 = 613.305