Catfish: Difference between revisions

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[[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 5.11.13.17 subgroup. 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>.


[[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.
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*[[Catfish7]]
*[[Catfish7]]
*[[Catfish9]]
*[[Catfish9]]
==Temperament data==
Subgroup: 11/5.11.13.17
[[Comma list]]: 2093663/2088025, 54925/54043
Mapping: [⟨1 -1 1 4], ⟨0 9 5 -1]]
[[Category:Temperaments]]
[[Category:Temperaments]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]

Revision as of 07:35, 17 March 2023

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)

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

Scales

Temperament data

Subgroup: 11/5.11.13.17

Comma list: 2093663/2088025, 54925/54043

Mapping: [⟨1 -1 1 4], ⟨0 9 5 -1]]