Cataharry temperaments: Difference between revisions

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[[#Swetneus|Swetneus]]
{{Technical data page}}
This is a collection of rank-2 temperaments tempering out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:
* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
* ''[[Unicorn]]'' (+126/125) → [[Unicorn family #Septimal unicorn|Unicorn family]]
* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* ''[[Buzzard]]'' (+1728/1715) → [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
* [[Harry]] (+2401/2400) → [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
* [[Hamity]] (+2430/2401) → [[Amity family #Hamity|Amity family]]
* ''[[Subpental]]'' (+3136/3125) → [[Hemimean clan #Subpental|Hemimean clan]]
* ''[[Hemischis]]'' (+6144/6125) → [[Porwell temperaments #Hemischis|Porwell temperaments]]
* ''[[Mirkat]]'' (+16875/16807) → [[Mirkwai clan #Mirkat|Mirkwai clan]]
* ''[[Hours]]'' (+33075/32768) → [[Compton family #Hours|Compton family]]
* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]


Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2> = 19683/19600.
== Swetneus ==
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 19683/19600, 50421/50000
 
{{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}
 
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 144.956
 
{{Optimal ET sequence|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}
 
[[Badness]]: 0.133168
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 3388/3375, 19683/19600
 
Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941
 
{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}
 
Badness: 0.055163
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=Swetneus=
Comma list: 351/350, 441/440, 676/675, 847/845
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
 
Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939
 
{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}
 
Badness: 0.028876
 
== Majvamoid ==
The ''majvamoid'' temperament (149 & 183) is an extension of the [[Subgroup temperaments #No-sevens subgroup|majvam]] temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 19683/19600, 29360128/29296875
 
{{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}
 
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 459.031
 
{{Optimal ET sequence|legend=1| 34d, 115d, 149, 183, 332, 515, 847, 1362bc }}
 
[[Badness]]: 0.207280
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 5632/5625, 19683/19600
 
Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}


Commas: 19683/19600, 50421/50000
Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027


POTE generator: ~49/45 = 144.956
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}


Map: [|1 4 8 8>, |0 -20 -47 -43>]
Badness: 0.065874


Wedgie: <<20 47 43 28 12 -32||
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 58, 91, 149, 505d, 654bd, 803bd
Comma list: 351/350, 676/675, 1573/1568, 4225/4224


Badness: 0.1332
Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}


==11-limit==
Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028
Commas: 441/440, 3388/3375, 19683/19600


POTE generator: ~49/45 = 144.941
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef }}


Map: [|1 4 8 8 13>, |0 -20 -47 -43 -79>]
Badness: 0.034696


EDOs: 58, 149, 207, 356e, 563cde, 919bcde
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0552
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224


==13-limit==
Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}
Commas: 351/350, 441/440, 676/675, 847/845


POTE generator: ~49/45 = 144.939
Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027


Map: [|1 4 8 8 13 13>, |0 -20 -47 -43 -79 -77>]
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}


EDOs: 58, 149, 207, 356e, 563cde, 919bcdef
Badness: 0.023302


Badness: 0.0289
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Cataharry| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:40, 24 June 2025

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 cataharry comma, [-4 9 -2 -2⟩ = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:

Swetneus

The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 50421/50000

Mapping: [⟨1 4 8 8], ⟨0 -20 -47 -43]]


Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.956

Optimal ET sequence: 58, 91, 149, 505d, 654bd, 803bd

Badness: 0.133168

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3388/3375, 19683/19600

Mapping: [⟨1 4 8 8 13], ⟨0 -20 -47 -43 -79]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941

Optimal ET sequence: 58, 149, 207, 356e, 563cde, 919bcde

Badness: 0.055163

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 676/675, 847/845

Mapping: [⟨1 4 8 8 13 13], ⟨0 -20 -47 -43 -79 -77]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939

Optimal ET sequence: 58, 149, 207, 356e, 563cde, 919bcdef

Badness: 0.028876

Majvamoid

The majvamoid temperament (149 & 183) is an extension of the majvam temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 29360128/29296875

Mapping: [⟨1 10 5 38], ⟨0 -22 -7 -92]]


Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.031

Optimal ET sequence: 34d, 115d, 149, 183, 332, 515, 847, 1362bc

Badness: 0.207280

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 19683/19600

Mapping: [⟨1 10 5 38 31], ⟨0 -22 -7 -92 -72]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027

Optimal ET sequence: 34d, 149, 183, 332e, 515e, 698e

Badness: 0.065874

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 676/675, 1573/1568, 4225/4224

Mapping: [⟨1 10 5 38 31 19], ⟨0 -22 -7 -92 -72 -40]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028

Optimal ET sequence: 34d, 149, 183, 332ef, 515ef

Badness: 0.034696

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224

Mapping: [⟨1 10 5 38 31 19 6], ⟨0 -22 -7 -92 -72 -40 -5]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027

Optimal ET sequence: 34d, 149, 183, 332ef, 515ef, 698ef

Badness: 0.023302

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