Catfish: Difference between revisions
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[[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. | [[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) == | == Interval chain (CTE tuning) == | ||
{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
!Generators up | ! Generators up | ||
!Cents | ! Cents | ||
|- | |- | ||
|0 | | 0 | ||
|0.0 | | 0.0 | ||
|- | |- | ||
|1 | | 1 | ||
|613.3 | | 613.3 | ||
|- | |- | ||
|2 | | 2 | ||
|1226.6 | | 1226.6 | ||
|- | |- | ||
|3 | | 3 | ||
|474.9 | | 474.9 | ||
|- | |- | ||
|4 | | 4 | ||
|1088.2 | | 1088.2 | ||
|- | |- | ||
|5 | | 5 | ||
|336.5 | | 336.5 | ||
|- | |- | ||
|6 | | 6 | ||
|949.8 | | 949.8 | ||
|- | |- | ||
|7 | | 7 | ||
|198.1 | | 198.1 | ||
|} | |} | ||
== | == Ed11/5 tunings == | ||
*[[9ed11/5]] using 4\9ed11/5 | *[[9ed11/5]] using 4\9ed11/5 | ||
*[[11ed11/5]] using 5\11ed11/5 | *[[11ed11/5]] using 5\11ed11/5 | ||
*[[20ed11/5]] using 9\20ed11/5 | *[[20ed11/5]] using 9\20ed11/5 | ||
*[[29ed11/5]] using 13\29ed11/5 | *[[29ed11/5]] using 13\29ed11/5 | ||
==Scales== | |||
*[[Catfish7]] | == Scales == | ||
*[[Catfish9]] | * [[Catfish7]] | ||
==Temperament data== | * [[Catfish9]] | ||
== Temperament data == | |||
[[Subgroup]]: 11/5.11.13.17 | [[Subgroup]]: 11/5.11.13.17 | ||
| Line 50: | Line 53: | ||
[[Constrained tuning|CTE generator]]: ~121/85 = 613.305 | [[Constrained tuning|CTE generator]]: ~121/85 = 613.305 | ||
[[Category: | [[Category:Catfish| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category: | [[Category:Non-octave temperaments]] | ||
Latest revision as of 09:22, 29 April 2025
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