Quintosec family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}.
The '''quintosec family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[quintosec comma]] ({{monzo|legend=1| 47 -15 -10 }}, [[ratio]]: 140 737 488 355 328 / 140 126 044 921 875).


== Quintosec ==
== Quintosec ==
Quintosec is naturally a 2.3.5.11-subgroup temperament. It was documented as ''qintosec'' on the temperament finder, which was probably due to a typo<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. The original, intended spelling is now restored, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.  
Quintosec is naturally a [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament. It was documented as ''qintosec'' on the [https://x31eq.com/temper/ Temperament Finder], which was probably due to a typo<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. The original, intended spelling is restored here, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 10: Line 10:


{{Mapping|legend=1| 5 1 22 | 0 2 -3 }}
{{Mapping|legend=1| 5 1 22 | 0 2 -3 }}
: Mapping generators: ~524288/455625, ~16384/10125
: Mapping generators: ~524288/455625, ~16384/10125


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~524288/455625 = 1＼5, ~16384/10125 = 831.1061 (~16/15 = 111.1061)
* [[CTE]]: ~524288/455625 = 240.0000{{c}}, ~16384/10125 = 831.1061{{c}} (~16/15 = 111.1061{{c}})
* [[POTE]]: ~524288/455625 = 1＼5, ~16384/10125 = 831.1051 (~16/15 = 111.1051)
* [[POTE]]: ~524288/455625 = 240.0000{{c}}, ~16384/10125 = 831.1051{{c}} (~16/15 = 111.1051{{c}})


{{Optimal ET sequence|legend=1| 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
{{Optimal ET sequence|legend=1| 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}


[[Badness]]: 0.139191
[[Badness]] (Smith): 0.139191


=== 2.3.5.11 subgroup ===
=== 2.3.5.11 subgroup ===
Line 29: Line 28:


Optimal tunings:  
Optimal tunings:  
* CTE: ~1024/891 = 1＼5, ~160/99 = 831.0932 (~16/15 = 111.0932)
* CTE: ~1024/891 = 240.0000{{c}}, ~160/99 = 831.0932{{c}} (~16/15 = 111.0932{{c}})
* CWE: ~1024/891 = 1＼5, ~160/99 = 831.0743 (~16/15 = 111.0743)
* CWE: ~1024/891 = 240.0000{{c}}, ~160/99 = 831.0743{{c}} (~16/15 = 111.0743{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c }}
{{Optimal ET sequence|legend=0| 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c }}


Badness: 0.0195
Badness (Smith): 0.0195


== Qintosec ==
== Qintosec ==
Qintosec can be described as the 10 &amp; 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.  
Qintosec can be described as the 10 & 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 45: Line 44:
{{Mapping|legend=1| 5 1 22 21 | 0 2 -3 -2 }}
{{Mapping|legend=1| 5 1 22 21 | 0 2 -3 -2 }}


Optimal tunings:  
[[Optimal tuning]]s:  
* CTE: ~400/343 = 1＼5, ~80/49 = 831.7095 (~15/14 = 111.7095)
* [[CTE]]: ~400/343 = 240.0000{{c}}, ~80/49 = 831.7095{{c}} (~15/14 = 111.7095{{c}})
* POTE: ~400/343 = 1＼5, ~80/49 = 831.5525 (~15/14 = 111.5525)
* [[POTE]]: ~400/343 = 240.0000{{c}}, ~80/49 = 831.5525{{c}} (~15/14 = 111.5525{{c}})


{{Optimal ET sequence|legend=1| 10, …, 55d, 65d, 75, 140d }}
{{Optimal ET sequence|legend=1| 10, …, 55d, 65d, 75, 140d }}


[[Badness]]: 0.156764
[[Badness]] (Smith): 0.156764


=== 11-limit ===
=== 11-limit ===
Line 61: Line 60:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/48 = 1＼5, ~80/49 = 831.1939 (~15/14 = 111.1939)
* CTE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.1939{{c}} (~15/14 = 111.1939{{c}})
* POTE: ~55/48 = 1＼5, ~80/49 = 831.3110 (~15/14 = 111.3110)
* POTE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.3110{{c}} (~15/14 = 111.3110{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10, 55d, 65d, 140de }}
{{Optimal ET sequence|legend=0| 10, 55d, 65d, 140de }}


Badness: 0.077907
Badness (Smith): 0.077907


=== Qinto ===
=== Qinto ===
Line 76: Line 75:


Optimal tunings:  
Optimal tunings:  
* CTE: ~220/189 = 1＼5, ~44/27 = 832.4051 (~15/14 = 112.4051)
* CTE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4051{{c}} (~15/14 = 112.4051{{c}})
* POTE: ~220/189 = 1＼5, ~44/27 = 832.4480 (~15/14 = 112.4480)
* POTE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4480{{c}} (~15/14 = 112.4480{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10, 75 }}
{{Optimal ET sequence|legend=0| 10, 75 }}


Badness: 0.127732
Badness (Smith): 0.127732


== Sengasec ==
== Sengasec ==
Sengasec can be described as the 10 &amp; 55 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.
Sengasec can be described as the 10 & 55 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 93: Line 92:


[[Optimal tuning]]:  
[[Optimal tuning]]:  
* [[CTE]]: ~8/7 = 1＼5, ~45/28 = 831.1061 (~16/15 = 111.1061)
* [[CTE]]: ~8/7 = 240.0000{{c}}, ~45/28 = 831.1061{{c}} (~16/15 = 111.1061{{c}})
* [[POTE]]: ~8/7 = 1＼5, ~45/28 = 831.1126 (~16/15 = 111.1126)
* [[POTE]]: ~8/7 = 240.0000{{c}}, ~45/28 = 831.1126{{c}} (~16/15 = 111.1126{{c}})


{{Optimal ET sequence|legend=1| 10, …, 55, 65, 140dd }}
{{Optimal ET sequence|legend=1| 10, …, 55, 65, 140dd }}


[[Badness]]: 0.156259
[[Badness]] (Smith): 0.156259


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~8/7 = 1＼5, ~45/28 = 830.7772 (~16/15 = 110.7772)
* CTE: ~8/7 = 240.0000{{c}}, ~45/28 = 830.7772{{c}} (~16/15 = 110.7772{{c}})
* POTE: ~8/7 = 1＼5, ~45/28 = 830.6592 (~16/15 = 110.6592)
* POTE: ~8/7 = 240.0000{{c}}, ~45/28 = 830.6592{{c}} (~16/15 = 110.6592{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10, 55, 65 }}
{{Optimal ET sequence|legend=0| 10, 55, 65 }}


Badness: 0.081607
Badness (Smith): 0.081607


=== 13-limit ===
=== 13-limit ===
Line 123: Line 122:


Optimal tunings:  
Optimal tunings:  
* CTE: ~8/7 = 1＼5, ~45/28 = 830.8942 (~16/15 = 110.8942)
* CTE: ~8/7 = 240.0000{{c}}, ~45/28 = 830.8942{{c}} (~16/15 = 110.8942{{c}})
* POTE: ~8/7 = 1＼5, ~45/28 = 830.9099 (~16/15 = 110.9099)
* POTE: ~8/7 = 240.0000{{c}}, ~45/28 = 830.9099{{c}} (~16/15 = 110.9099{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10, 55, 65 }}
{{Optimal ET sequence|legend=0| 10, 55, 65 }}


Badness: 0.056390
Badness (Smith): 0.056390


== Decoid ==
== Decoid ==
{{See also| Breedsmic temperaments #Decoid }}
{{See also| Breedsmic temperaments #Decoid }}


Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used as its generator. It may be described as the 130 &amp; 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice.  
Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used as its generator. It may be described as the 130 & 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}
{{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}
: Mapping generators: ~15/14, ~8192/4725
: Mapping generators: ~15/14, ~8192/4725


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 1＼10, ~8192/4725 = 951.1086 (~16/15 = 111.1086, or ~225/224 = 8.8914)
* [[CTE]]: ~15/14 = 120.0000{{c}}, ~8192/4725 = 951.1086{{c}} (~16/15 = 111.1086{{c}}, or ~225/224 = 8.8914{{c}})
* [[POTE]]: ~15/14 = 1＼10, ~8192/4725 = 951.0987 (~16/15 = 111.0987, or ~225/224 = 8.9013)
* [[POTE]]: ~15/14 = 120.0000{{c}}, ~8192/4725 = 951.0987{{c}} (~16/15 = 111.0987{{c}}, or ~225/224 = 8.9013{{c}})


{{Optimal ET sequence|legend=1| 10, …, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
{{Optimal ET sequence|legend=1| 10, …, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}


[[Badness]]: 0.033902
[[Badness]] (Smith): 0.033902


=== 11-limit ===
=== 11-limit ===
Line 159: Line 157:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 1＼10, ~400/231 = 951.0943 (~16/15 = 111.0943, or ~225/224 = 8.9057)
* CTE: ~15/14 = 120.0000{{c}}, ~400/231 = 951.0943{{c}} (~16/15 = 111.0943{{c}}, or ~225/224 = 8.9057{{c}})
* POTE: ~15/14 = 1＼10, ~400/231 = 951.0700 (~16/15 = 111.0700, or ~225/224 = 8.9300)
* POTE: ~15/14 = 120.0000{{c}}, ~400/231 = 951.0700{{c}} (~16/15 = 111.0700{{c}}, or ~225/224 = 8.9300{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10e, …, 130, 270, 670, 940, 1210, 2150c }}
{{Optimal ET sequence|legend=0| 10e, …, 130, 270, 670, 940, 1210, 2150c }}


Badness: 0.018735
Badness (Smith): 0.018735


==== 13-limit ====
==== 13-limit ====
Line 174: Line 172:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 1＼10, ~26/15 = 951.0943 (~16/15 = 111.0943, or ~196/195 = 8.9057)
* CTE: ~15/14 = 120.0000{{c}}, ~26/15 = 951.0943{{c}} (~16/15 = 111.0943{{c}}, or ~196/195 = 8.9057{{c}})
* POTE: ~15/14 = 1＼10, ~26/15 = 951.0832 (~16/15 = 111.0832, or ~196/195 = 8.9168)
* POTE: ~15/14 = 120.0000{{c}}, ~26/15 = 951.0832{{c}} (~16/15 = 111.0832{{c}}, or ~196/195 = 8.9168{{c}})


Optimal ET sequence: {{Optimal ET sequence| 10e, …, 130, 270, 940, 1210f, 1480cf }}
{{Optimal ET sequence|legend=0| 10e, …, 130, 270, 940, 1210f, 1480cf }}


Badness: 0.013475
Badness (Smith): 0.013475


=== Triacontoid ===
=== Triacontoid ===
Line 187: Line 185:


Mapping: {{mapping| 30 0 141 108 80 | 0 2 -3 -1 1 }}
Mapping: {{mapping| 30 0 141 108 80 | 0 2 -3 -1 1 }}
: Mapping generators: ~45/44, ~8192/4725
: Mapping generators: ~45/44, ~8192/4725


Optimal tunings:  
Optimal tunings:  
* CTE: ~45/44 = 1＼30, ~8192/4725 = 951.1137 (~225/224 = 8.8863)
* CTE: ~45/44 = 40.0000{{c}}, ~8192/4725 = 951.1137{{c}} (~225/224 = 8.8863{{c}})
* POTE: ~45/44 = 1＼30, ~8192/4725 = 951.1121 (~225/224 = 8.8879)
* POTE: ~45/44 = 40.0000{{c}}, ~8192/4725 = 951.1121{{c}} (~225/224 = 8.8879{{c}})


Optimal ET sequence: {{Optimal ET sequence| 120, 150, 270 }}
{{Optimal ET sequence|legend=0| 120, 150, 270 }}


Badness: 0.075991
Badness (Smith): 0.075991


==== 13-limit ====
==== 13-limit ====
Line 206: Line 203:


Optimal tunings:  
Optimal tunings:  
* CTE: ~45/44 = 1＼30, ~26/15 = 951.1137 (~196/195 = 8.8863)
* CTE: ~45/44 = 40.0000{{c}}, ~26/15 = 951.1137{{c}} (~196/195 = 8.8863{{c}})
* POTE: ~45/44 = 1＼30, ~26/15 = 951.1130 (~196/195 = 8.8870)
* POTE: ~45/44 = 40.0000{{c}}, ~26/15 = 951.1130{{c}} (~196/195 = 8.8870{{c}})


Optimal ET sequence: {{Optimal ET sequence| 120, 150, 270 }}
{{Optimal ET sequence|legend=0| 120, 150, 270 }}


Badness: 0.040873
Badness (Smith): 0.040873


== References ==
== References ==

Revision as of 06:50, 4 September 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.

The quintosec family of temperaments tempers out the quintosec comma (monzo: [47 -15 -10⟩, ratio: 140 737 488 355 328 / 140 126 044 921 875).

Quintosec

Quintosec is naturally a 2.3.5.11-subgroup temperament. It was documented as qintosec on the Temperament Finder, which was probably due to a typo[1]. The original, intended spelling is restored here, and the distinctive no-u form is relegated to the lower-accuracy 7-limit extension considered below.

Subgroup: 2.3.5

Comma list: [47 -15 -10⟩

Mapping: [⟨5 1 22], ⟨0 2 -3]]

Mapping generators: ~524288/455625, ~16384/10125

Optimal tunings:

  • CTE: ~524288/455625 = 240.0000 ¢, ~16384/10125 = 831.1061 ¢ (~16/15 = 111.1061 ¢)
  • POTE: ~524288/455625 = 240.0000 ¢, ~16384/10125 = 831.1051 ¢ (~16/15 = 111.1051 ¢)

Optimal ET sequence: 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc

Badness (Smith): 0.139191

2.3.5.11 subgroup

Subgroup: 2.3.5.11

Comma list: 5632/5625, 26214400/26198073

Mapping: [⟨5 1 22 45], ⟨0 2 -3 -8]]

Optimal tunings:

  • CTE: ~1024/891 = 240.0000 ¢, ~160/99 = 831.0932 ¢ (~16/15 = 111.0932 ¢)
  • CWE: ~1024/891 = 240.0000 ¢, ~160/99 = 831.0743 ¢ (~16/15 = 111.0743 ¢)

Optimal ET sequence: 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c

Badness (Smith): 0.0195

Qintosec

Qintosec can be described as the 10 & 65d temperament, tempering out the marvel comma, 225/224 in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 225/224, 2560000/2470629

Mapping: [⟨5 1 22 21], ⟨0 2 -3 -2]]

Optimal tunings:

  • CTE: ~400/343 = 240.0000 ¢, ~80/49 = 831.7095 ¢ (~15/14 = 111.7095 ¢)
  • POTE: ~400/343 = 240.0000 ¢, ~80/49 = 831.5525 ¢ (~15/14 = 111.5525 ¢)

Optimal ET sequence: 10, …, 55d, 65d, 75, 140d

Badness (Smith): 0.156764

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 3840/3773

Mapping: [⟨5 1 22 21 0], ⟨0 2 -3 -2 5]]

Optimal tunings:

  • CTE: ~55/48 = 240.0000 ¢, ~80/49 = 831.1939 ¢ (~15/14 = 111.1939 ¢)
  • POTE: ~55/48 = 240.0000 ¢, ~80/49 = 831.3110 ¢ (~15/14 = 111.3110 ¢)

Optimal ET sequence: 10, 55d, 65d, 140de

Badness (Smith): 0.077907

Qinto

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 332750/321489

Mapping: [⟨5 1 22 21 -7], ⟨0 2 -3 -2 7]]

Optimal tunings:

  • CTE: ~220/189 = 240.0000 ¢, ~44/27 = 832.4051 ¢ (~15/14 = 112.4051 ¢)
  • POTE: ~220/189 = 240.0000 ¢, ~44/27 = 832.4480 ¢ (~15/14 = 112.4480 ¢)

Optimal ET sequence: 10, 75

Badness (Smith): 0.127732

Sengasec

Sengasec can be described as the 10 & 55 temperament, tempering out the cloudy comma, 16807/16384 and the sengic comma, 686/675 in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 686/675, 16807/16384

Mapping: [⟨5 1 22 14], ⟨0 2 -3 0]]

Optimal tuning:

  • CTE: ~8/7 = 240.0000 ¢, ~45/28 = 831.1061 ¢ (~16/15 = 111.1061 ¢)
  • POTE: ~8/7 = 240.0000 ¢, ~45/28 = 831.1126 ¢ (~16/15 = 111.1126 ¢)

Optimal ET sequence: 10, …, 55, 65, 140dd

Badness (Smith): 0.156259

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 686/675

Mapping: [⟨5 1 22 14 0], ⟨0 2 -3 0 5]]

Optimal tunings:

  • CTE: ~8/7 = 240.0000 ¢, ~45/28 = 830.7772 ¢ (~16/15 = 110.7772 ¢)
  • POTE: ~8/7 = 240.0000 ¢, ~45/28 = 830.6592 ¢ (~16/15 = 110.6592 ¢)

Optimal ET sequence: 10, 55, 65

Badness (Smith): 0.081607

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 243/242, 686/675

Mapping: [⟨5 1 22 14 0 22], ⟨0 2 -3 0 5 -1]]

Optimal tunings:

  • CTE: ~8/7 = 240.0000 ¢, ~45/28 = 830.8942 ¢ (~16/15 = 110.8942 ¢)
  • POTE: ~8/7 = 240.0000 ¢, ~45/28 = 830.9099 ¢ (~16/15 = 110.9099 ¢)

Optimal ET sequence: 10, 55, 65

Badness (Smith): 0.056390

Decoid

See also: Breedsmic temperaments § Decoid

Decoid tempers out 2401/2400 and 67108864/66976875, as well as the linus comma, [11 -10 -10 10⟩. Either 8/7 or 16/15 can be used as its generator. It may be described as the 130 & 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 67108864/66976875

Mapping: [⟨10 0 47 36], ⟨0 2 -3 -1]]

Mapping generators: ~15/14, ~8192/4725

Optimal tunings:

  • CTE: ~15/14 = 120.0000 ¢, ~8192/4725 = 951.1086 ¢ (~16/15 = 111.1086 ¢, or ~225/224 = 8.8914 ¢)
  • POTE: ~15/14 = 120.0000 ¢, ~8192/4725 = 951.0987 ¢ (~16/15 = 111.0987 ¢, or ~225/224 = 8.9013 ¢)

Optimal ET sequence: 10, …, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc

Badness (Smith): 0.033902

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 5632/5625, 9801/9800

Mapping: [⟨10 0 47 36 98], ⟨0 2 -3 -1 -8]]

Optimal tunings:

  • CTE: ~15/14 = 120.0000 ¢, ~400/231 = 951.0943 ¢ (~16/15 = 111.0943 ¢, or ~225/224 = 8.9057 ¢)
  • POTE: ~15/14 = 120.0000 ¢, ~400/231 = 951.0700 ¢ (~16/15 = 111.0700 ¢, or ~225/224 = 8.9300 ¢)

Optimal ET sequence: 10e, …, 130, 270, 670, 940, 1210, 2150c

Badness (Smith): 0.018735

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095

Mapping: [⟨10 0 47 36 98 37], ⟨0 2 -3 -1 -8 0]]

Optimal tunings:

  • CTE: ~15/14 = 120.0000 ¢, ~26/15 = 951.0943 ¢ (~16/15 = 111.0943 ¢, or ~196/195 = 8.9057 ¢)
  • POTE: ~15/14 = 120.0000 ¢, ~26/15 = 951.0832 ¢ (~16/15 = 111.0832 ¢, or ~196/195 = 8.9168 ¢)

Optimal ET sequence: 10e, …, 130, 270, 940, 1210f, 1480cf

Badness (Smith): 0.013475

Triacontoid

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 42592/42525, 1771561/1769472

Mapping: [⟨30 0 141 108 80], ⟨0 2 -3 -1 1]]

Mapping generators: ~45/44, ~8192/4725

Optimal tunings:

  • CTE: ~45/44 = 40.0000 ¢, ~8192/4725 = 951.1137 ¢ (~225/224 = 8.8863 ¢)
  • POTE: ~45/44 = 40.0000 ¢, ~8192/4725 = 951.1121 ¢ (~225/224 = 8.8879 ¢)

Optimal ET sequence: 120, 150, 270

Badness (Smith): 0.075991

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 2401/2400, 4096/4095, 6656/6655

Mapping: [⟨30 0 141 108 80 111], ⟨0 2 -3 -1 1 0]]

Optimal tunings:

  • CTE: ~45/44 = 40.0000 ¢, ~26/15 = 951.1137 ¢ (~196/195 = 8.8863 ¢)
  • POTE: ~45/44 = 40.0000 ¢, ~26/15 = 951.1130 ¢ (~196/195 = 8.8870 ¢)

Optimal ET sequence: 120, 150, 270

Badness (Smith): 0.040873

References

  1. ↑ Yahoo Tuning Group | 2D temperament names, part I -- reclassified temperaments from message #101780
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