|
|
| Line 1: |
Line 1: |
| {{Todo|inline=1|merge articles|comment= [[Catfish]] → [[Subgroup temperaments]] }}
| | #redirect [[No-twos subgroup temperaments #Catfish]] |
| [[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>.
| |
|
| |
|
| [[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) ==
| |
| {|class="wikitable"
| |
| |-
| |
| ! 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 ==
| |
| * [[Catfish7]]
| |
| * [[Catfish9]]
| |
|
| |
| == Temperament data ==
| |
| [[Subgroup]]: 11/5.11.13.17
| |
|
| |
| [[Comma list]]: 2093663/2088025, 54925/54043
| |
|
| |
| [[Mapping]]: [⟨1 -1 1 4], ⟨0 9 5 -1]]
| |
|
| |
| [[Constrained tuning|CTE generator]]: ~121/85 = 613.305
| |
|
| |
| [[Category:Catfish| ]] <!-- main article -->
| |
| [[Category:Rank-2 temperaments]] | | [[Category:Rank-2 temperaments]] |
| [[Category:Non-octave temperaments]] | | [[Category:Non-octave temperaments]] |