Cataharry temperaments: Difference between revisions

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{{Technical data page}}
{{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 temperament|rank-2]] '''cataharry temperaments''', which [[tempering out|temper out]] the [[cataharry comma]] ({{monzo|legend=1| -4 9 -2 -2 }}, [[ratio]]: 19683/19600). For the family of [[rank-3 temperament]]s, see [[Cataharry family]].
 
Discussed elsewhere are:  
* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
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* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]
* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]
Considered below is swetneus and majvamoid, in the order of increasing [[badness]].


== Swetneus ==
== Swetneus ==
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{{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}
{{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}


 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 144.956{{c}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 144.956


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


[[Badness]]: 0.133168
[[Badness]] (Smith): 0.133168


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}
Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}


Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/45 = 144.941{{c}}


{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}
{{Optimal ET sequence|legend=0| 58, 149, 207, 356e, 563cde, 919bcde }}


Badness: 0.055163
Badness (Smith): 0.055163


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}
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 tuning (POTE): ~2 = 1200.000{{c}}, ~49/45 = 144.939{{c}}


{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}
{{Optimal ET sequence|legend=0| 58, 149, 207, 356e, 563cde, 919bcdef }}


Badness: 0.028876
Badness (Smith): 0.028876


== Majvamoid ==
== Majvamoid ==
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{{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}
{{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}


 
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~125/96 = 459.031{{c}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 459.031


{{Optimal ET sequence|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]] (Smith): 0.207280


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}
Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}


Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.027{{c}}


{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}
{{Optimal ET sequence|legend=0| 34d, 149, 183, 332e, 515e, 698e }}


Badness: 0.065874
Badness (Smith): 0.065874


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}
Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}


Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.028{{c}}


{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef }}
{{Optimal ET sequence|legend=0| 34d, 149, 183, 332ef, 515ef }}


Badness: 0.034696
Badness (Smith): 0.034696


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.000{{c}}, ~125/96 = 459.027{{c}}


{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}
{{Optimal ET sequence|legend=0| 34d, 149, 183, 332ef, 515ef, 698ef }}


Badness: 0.023302
Badness (Smith): 0.023302


[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Cataharry| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 09:14, 20 July 2026

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 cataharry temperaments, which temper out the cataharry comma (monzo: [-4 9 -2 -2⟩, ratio: 19683/19600). For the family of rank-3 temperaments, see Cataharry family.

Discussed elsewhere are:

Considered below is swetneus and majvamoid, in the order of increasing badness.

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 = 1200.000 ¢, ~49/45 = 144.956 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~49/45 = 144.941 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~49/45 = 144.939 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~125/96 = 459.031 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~125/96 = 459.027 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~125/96 = 459.028 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~125/96 = 459.027 ¢

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

Badness (Smith): 0.023302

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