Cataharry temperaments: Difference between revisions

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{{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:  
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, 81/80} → [[Meantone family #Godzilla]]
* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
* ''[[immunized]]'', {64/63, 8748/8575} → [[Immunity family #Immunized]]
* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
* ''[[unicorn]]'', {126/125, 10976/10935} → [[Unicorn family #Septimal unicorn]]
* ''[[Unicorn]]'' (+126/125) → [[Unicorn family #Septimal unicorn|Unicorn family]]
* [[catakleismic]], {225/224, 4375/4374} → [[Kleismic family #Catakleismic]]
* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[hemiseven]]'', {1029/1024, 19683/19600} → [[Gamelismic clan #Hemiseven]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* ''[[buzzard]]'', {1728/1715, 5120/5103} → [[Hemifamity temperaments #Buzzard]]
* ''[[Buzzard]]'' (+1728/1715) → [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
* [[harry]], {2401/2400, 19683/19600} → [[Breedsmic temperaments #Harry]]
* [[Harry]] (+2401/2400) → [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
* [[hamity]], {2430/2401, 4000/3969} → [[Amity family #Hamity]]
* [[Hamity]] (+2430/2401) → [[Amity family #Hamity|Amity family]]
* ''[[subpental]]'', {3136/3125, 19683/19600} → [[Hemimean clan #Subpental]]
* ''[[Subpental]]'' (+3136/3125) → [[Hemimean clan #Subpental|Hemimean clan]]
* ''[[hemischis]]'', {6144/6125, 19683/19600} → [[Porwell temperaments #Hemischis]]
* ''[[Hemischis]]'' (+6144/6125) → [[Porwell temperaments #Hemischis|Porwell temperaments]]
* ''[[mirkat]]'', {16875/16807, 19683/19600} → [[Mirkwai clan #Mirkat]]
* ''[[Mirkat]]'' (+16875/16807) → [[Mirkwai clan #Mirkat|Mirkwai clan]]
* ''[[hours]]'', {19683/19600, 33075/32768} → [[Compton family #Hours]]
* ''[[Hours]]'' (+33075/32768) → [[Compton family #Hours|Compton family]]
* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]


== Swetneus ==
== Swetneus ==
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 19683/19600, 50421/50000
[[Comma list]]: 19683/19600, 50421/50000


[[Mapping]]: [{{val| 1 4 8 8 }}, {{val| 0 -20 -47 -43 }}]
{{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}


{{Multival|legend=1| 20 47 43 28 12 -32 }}


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


{{Val list|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}
{{Optimal ET sequence|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}


[[Badness]]: 0.133168
[[Badness]]: 0.133168
Line 35: Line 37:
Comma list: 441/440, 3388/3375, 19683/19600
Comma list: 441/440, 3388/3375, 19683/19600


Mapping: [{{val| 1 4 8 8 13 }}, {{val| 0 -20 -47 -43 -79 }}]
Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}


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


Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcde }}
{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}


Badness: 0.055163
Badness: 0.055163
Line 48: Line 50:
Comma list: 351/350, 441/440, 676/675, 847/845
Comma list: 351/350, 441/440, 676/675, 847/845


Mapping: [{{val| 1 4 8 8 13 13 }}, {{val| 0 -20 -47 -43 -79 -77 }}]
Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}


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


Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcdef }}
{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}


Badness: 0.028876
Badness: 0.028876


== Majvamoid ==
== 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.
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 19683/19600, 29360128/29296875
[[Comma list]]: 19683/19600, 29360128/29296875


[[Mapping]]: [{{val|1 10 5 38}}, {{val|0 -22 -7 -92}}]
{{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}


{{Multival|legend=1|22 7 92 -40 84 94}}


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


{{Val list|legend=1| 34d, 115d, 149, 183, 332, 515, 847, 1362bc }}
{{Optimal ET sequence|legend=1| 34d, 115d, 149, 183, 332, 515, 847, 1362bc }}


[[Badness]]: 0.207280
[[Badness]]: 0.207280
Line 78: Line 79:
Comma list: 3025/3024, 5632/5625, 19683/19600
Comma list: 3025/3024, 5632/5625, 19683/19600


Mapping: [{{val|1 10 5 38 31}}, {{val|0 -22 -7 -92 -72}}]
Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}


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


Vals: {{Val list| 34d, 149, 183, 332e, 515e, 698e }}
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}


Badness: 0.065874
Badness: 0.065874
Line 91: Line 92:
Comma list: 351/350, 676/675, 1573/1568, 4225/4224
Comma list: 351/350, 676/675, 1573/1568, 4225/4224


Mapping: [{{val|1 10 5 38 31 19}}, {{val|0 -22 -7 -92 -72 -40}}]
Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}


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


Vals: {{Val list| 34d, 149, 183, 332ef, 515ef }}
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef }}


Badness: 0.034696
Badness: 0.034696
Line 104: Line 105:
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224


Mapping: [{{val|1 10 5 38 31 19 6}}, {{val|0 -22 -7 -92 -72 -40 -5}}]
Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}


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


Vals: {{Val list| 34d, 149, 183, 332ef, 515ef, 698ef }}
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}


Badness: 0.023302
Badness: 0.023302


[[Category:Regular temperament theory]]
[[Category:Temperament collections]]
[[Category:Temperament collection]]
[[Category:Pages with mostly numerical content]]
[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Cataharry| ]] <!-- key article -->
[[Category:Rank 2]]
[[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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