Stearnsmic clan: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo| 1 10 0 -6 }} = 118098/117649.
The '''stearnsmic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[stearnsma]] ({{monzo|legend=1| 1 10 0 -6 }}, [[ratio]]: 118098/117649), a no-5's comma of about 6.59 [[cent]]s.  


== No-five stearnsmic ==
== No-5 stearnsmic ==
[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7


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{{Mapping|legend=2| 2 1 2 | 0 3 5 }}
{{Mapping|legend=2| 2 1 2 | 0 3 5 }}


{{Mapping|legend=3| 2 1 0 2 | 0 3 0 5 }}
: mapping generators: ~343/243, ~9/7
: mapping generators: ~343/243, ~9/7
{{Mapping|legend=3| 2 1 0 2 | 0 3 0 5 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~343/243 = 599.994¢, ~9/7 = 433.884¢
* [[WE]]: ~343/243 = 599.994{{c}}, ~9/7 = 433.884{{c}}
* [[CWE]]: ~343/243 = 600.000¢, ~9/7 = 433.885¢
* [[CWE]]: ~343/243 = 600.000{{c}}, ~9/7 = 433.885{{c}}


{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 130, 224, 354, 484, 838 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~343/243 = 599.986¢, ~9/7 = 433.890¢
* [[WE]]: ~343/243 = 599.986{{c}}, ~9/7 = 433.890{{c}}
* [[CWE]]: ~343/243 = 600.000¢, ~9/7 = 433.901¢
* [[CWE]]: ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}


{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~343/243 = 599.806¢, ~9/7 = 434.078¢
* [[WE]]: ~343/243 = 599.806{{c}}, ~9/7 = 434.078{{c}}
* [[CWE]]: ~343/243 = 600.000¢, ~9/7 = 434.203¢
* [[CWE]]: ~343/243 = 600.000{{c}}, ~9/7 = 434.203{{c}}


{{Optimal ET sequence|legend=1| 58, 94, 152 }}
{{Optimal ET sequence|legend=1| 58, 94, 152 }}
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Mapping: {{mapping| 2 1 -12 2 -9 | 0 3 23 5 22 }}
Mapping: {{mapping| 2 1 -12 2 -9 | 0 3 23 5 22 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.217
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 434.217{{c}}


{{Optimal ET sequence|legend=0| 58, 94, 152 }}
{{Optimal ET sequence|legend=0| 58, 94, 152 }}
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Mapping: {{mapping| 2 1 -12 2 -9 -2 | 0 3 23 5 22 13 }}
Mapping: {{mapping| 2 1 -12 2 -9 -2 | 0 3 23 5 22 13 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 434.221
Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 434.221{{c}}


{{Optimal ET sequence|legend=0| 58, 94, 152f }}
{{Optimal ET sequence|legend=0| 58, 94, 152f }}
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Mapping: {{mapping| 2 1 -12 2 -9 -2 6 | 0 3 23 5 22 13 3 }}
Mapping: {{mapping| 2 1 -12 2 -9 -2 6 | 0 3 23 5 22 13 3 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.181
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~9/7 = 434.181{{c}}


{{Optimal ET sequence|legend=0| 58, 94, 152f }}
{{Optimal ET sequence|legend=0| 58, 94, 152f }}
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{{Mapping|legend=1| 6 3 2 6 | 0 6 11 10 }}
{{Mapping|legend=1| 6 3 2 6 | 0 6 11 10 }}
: mapping generators: ~2450/2187, ~567/500
: mapping generators: ~2450/2187, ~567/500


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2450/2187 = 199.998¢, ~567/500 = 216.940¢
* [[WE]]: ~2450/2187 = 199.998{{c}}, ~567/500 = 216.940{{c}}
* [[CWE]]: ~2450/2187 = 200.000¢, ~567/500 = 216.941¢
* [[CWE]]: ~2450/2187 = 200.000{{c}}, ~567/500 = 216.941{{c}}


{{Optimal ET sequence|legend=1| 72, 210, 282, 354 }}
{{Optimal ET sequence|legend=1| 72, 210, 282, 354 }}
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Mapping: {{mapping| 6 3 2 6 11 | 0 6 11 10 9 }}
Mapping: {{mapping| 6 3 2 6 11 | 0 6 11 10 9 }}


Optimal tuning (CTE): ~55/49 = 1\6, ~567/500 = 216.9242 (~100/99 = 16.9242)
Optimal tuning (CTE): ~55/49 = 200.0000{{c}}, ~567/500 = 216.9242{{c}} (~100/99 = 16.9242{{c}})


{{Optimal ET sequence|legend=0| 72, 210e, 282, 354 }}
{{Optimal ET sequence|legend=0| 72, 210e, 282, 354 }}
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Mapping: {{mapping| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}
Mapping: {{mapping| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}


Optimal tuning (CTE): ~55/49 = 1\6, ~312/275 = 216.9332 (~105/104 = 16.9332)
Optimal tuning (CTE): ~55/49 = 200.0000{{c}}, ~312/275 = 216.9332{{c}} (~105/104 = 16.9332{{c}})


{{Optimal ET sequence|legend=0| 72, 210ef, 282, 354 }}
{{Optimal ET sequence|legend=0| 72, 210ef, 282, 354 }}
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Mapping: {{mapping| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}
Mapping: {{mapping| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}


Optimal tuning (CTE): ~55/49 = 1\6, ~17/15 = 216.9345 (~105/104 = 16.9345)
Optimal tuning (CTE): ~55/49 = 200.0000{{c}}, ~17/15 = 216.9345{{c}} (~105/104 = 16.9345{{c}})


{{Optimal ET sequence|legend=0| 72, 210efg, 282, 354 }}
{{Optimal ET sequence|legend=0| 72, 210efg, 282, 354 }}
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== Garistearn ==
== Garistearn ==
The garistearn temperament (94 & 282) has a period of 1/94-octave and tempers out 118098/117649 and the [[garischisma]], 33554432/33480783.
The garistearn temperament (94 & 282) has a period of 1/94-octave and tempers out 118098/117649 and the [[garischisma]], 33554432/33480783.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}
{{Mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}
: mapping generators: ~1029/1024, ~5
: mapping generators: ~1029/1024, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.3137¢
* [[CTE]]: ~1029/1024 = 12.7660{{c}}, ~5/4 = 386.3137{{c}}
* [[CWE]]: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.6637¢
* [[CWE]]: ~1029/1024 = 12.7660{{c}}, ~5/4 = 386.6637{{c}}


{{Optimal ET sequence|legend=1| 94, 282, 658d, 940dd }}
{{Optimal ET sequence|legend=1| 94, 282, 658d, 940dd }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.0177¢
* CTE: ~1029/1024 = 12.7660{{c}}, ~5/4 = 386.0177{{c}}
* CWE: ~1029/1024 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.4545¢
* CWE: ~1029/1024 = 12.7660{{c}}, ~5/4 = 386.4545{{c}}


{{Optimal ET sequence|legend=0| 94, 282, 376, 658de }}
{{Optimal ET sequence|legend=0| 94, 282, 376, 658de }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.0177¢
* CTE: ~169/168 = 12.7660{{c}}, ~5/4 = 386.0177{{c}}
* CWE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.6570¢
* CWE: ~169/168 = 12.7660{{c}}, ~5/4 = 386.6570{{c}}


{{Optimal ET sequence|legend=0| 94, 282 }}
{{Optimal ET sequence|legend=0| 94, 282 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 385.9792¢
* CTE: ~169/168 = 12.7660{{c}}, ~5/4 = 385.9792{{c}}
* CWE: ~169/168 = 12.7660¢ (1 ⧵ 94), ~5/4 = 386.6751¢
* CWE: ~169/168 = 12.7660{{c}}, ~5/4 = 386.6751{{c}}


{{Optimal ET sequence|legend=0| 94, 282 }}
{{Optimal ET sequence|legend=0| 94, 282 }}
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{{See also| Trisedodge family }}
{{See also| Trisedodge family }}


The decistearn temperament (80 & 130) has a period of 1/10-octave and tempers out the [[hemimean comma]], 3136/3125 as well as the [[linus comma]].
The decistearn temperament (80 & 130) has a period of 1/10-octave and tempers out the [[hemimean comma]], 3136/3125 as well as the [[linus comma]].


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 10 2 14 5 | 0 3 2 5 }}
{{Mapping|legend=1| 10 2 14 5 | 0 3 2 5 }}
: mapping generators: ~15/14, ~135/98
: mapping generators: ~15/14, ~135/98


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~15/14 = 119.975¢, ~135/98 = 553.845¢
* [[WE]]: ~15/14 = 119.975{{c}}, ~135/98 = 553.845{{c}}
* [[CWE]]: ~15/14 = 120.000¢, ~135/98 = 553.893¢
* [[CWE]]: ~15/14 = 120.000{{c}}, ~135/98 = 553.893{{c}}


{{Optimal ET sequence|legend=1| 50, 80, 130, 470cd, 600cd, 730cd, 860ccd }}
{{Optimal ET sequence|legend=1| 50, 80, 130, 470cd, 600cd, 730cd, 860ccd }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~15/14 = 119.953¢, ~11/8 = 553.864¢
* WE: ~15/14 = 119.953{{c}}, ~11/8 = 553.864{{c}}
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.978¢
* CWE: ~15/14 = 120.000{{c}}, ~11/8 = 553.978{{c}}


{{Optimal ET sequence|legend=0| 50, 80, 130, 210e, 340ce }}
{{Optimal ET sequence|legend=0| 50, 80, 130, 210e, 340ce }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~15/14 = 119.974¢, ~11/8 = 553.827¢
* WE: ~15/14 = 119.974{{c}}, ~11/8 = 553.827{{c}}
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.905¢
* CWE: ~15/14 = 120.000{{c}}, ~11/8 = 553.905{{c}}


{{Optimal ET sequence|legend=0| 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 50, 80, 130 }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~15/14 = 119.990¢, ~11/8 = 553.884¢
* WE: ~15/14 = 119.990{{c}}, ~11/8 = 553.884{{c}}
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.914¢
* CWE: ~15/14 = 120.000{{c}}, ~11/8 = 553.914{{c}}


{{Optimal ET sequence|legend=0| 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 50, 80, 130 }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~15/14 = 119.995¢, ~11/8 = 553.925¢
* WE: ~15/14 = 119.995{{c}}, ~11/8 = 553.925{{c}}
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.940¢
* CWE: ~15/14 = 120.000{{c}}, ~11/8 = 553.940{{c}}


{{Optimal ET sequence|legend=0| 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 50, 80, 130 }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~15/14 = 119.997¢, ~11/8 = 553.925¢
* WE: ~15/14 = 119.997{{c}}, ~11/8 = 553.925{{c}}
* CWE: ~15/14 = 120.000¢, ~11/8 = 553.933¢
* CWE: ~15/14 = 120.000{{c}}, ~11/8 = 553.933{{c}}


{{Optimal ET sequence|legend=0| 30dh, 50, 80, 130 }}
{{Optimal ET sequence|legend=0| 30dh, 50, 80, 130 }}

Latest revision as of 09:01, 14 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 stearnsmic clan of temperaments tempers out the stearnsma (monzo[1 10 0 -6, ratio: 118098/117649), a no-5's comma of about 6.59 cents.

No-5 stearnsmic

Subgroup: 2.3.7

Comma list: 118098/117649

Subgroup-val mapping[2 1 2], 0 3 5]]

Gencom mapping[2 1 0 2], 0 3 0 5]]

mapping generators: ~343/243, ~9/7

Optimal tunings:

  • WE: ~343/243 = 599.994 ¢, ~9/7 = 433.884 ¢
  • CWE: ~343/243 = 600.000 ¢, ~9/7 = 433.885 ¢

Optimal ET sequence14, 22, 36, 94, 130, 224, 354, 484, 838

Badness (Sintel): 0.382

Overview to extensions

The second comma in the comma list determines how we extend it to include the harmonic 5. Pogo adds 32805/32768, supers 5120/5103, echidna 1728/1715, and hedgehog 50/49. Those are strong extensions. The others are weak. Wizard adds 225/224. Harry adds 2401/2400. Those split the generator in two. Septisuperfourth adds 6144/6125 and splits the generator in three. Stearnscape adds 250047/250000 and splits the period in three. Octoid adds 4375/4374 and splits the period in four. Decistearn adds 3136/3125 splits the period in five. They all have neat extensions to the 11-limit via tempering out both 540/539 and 4000/3993, as well as 9801/9800, so that 11/10 and 9/7 add up to the semioctave.

Stearnsmic temperaments not listed include:

Considered below are pogo, supers, stearnscape, garistearn and decistearn.

Pogo

The pogo temperament (94 & 130) tempers out the schisma, whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It is also the temperament that reconciles the difference between tertiaschis and countertertiaschis, using its semi-octave period.

Subgroup: 2.3.5.7

Comma list: 32805/32768, 118098/117649

Mapping[2 1 22 2], 0 3 -24 5]]

mapping generators: ~343/243, ~9/7

Optimal tunings:

  • WE: ~343/243 = 599.986 ¢, ~9/7 = 433.890 ¢
  • CWE: ~343/243 = 600.000 ¢, ~9/7 = 433.901 ¢

Optimal ET sequence36, 94, 130, 224, 354

Badness (Sintel): 2.015

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 32805/32768

Mapping: [2 1 22 2 25], 0 3 -24 5 -25]]

Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~9/7 = 433.911 ¢

Optimal ET sequence: 36, 94, 130, 224, 354, 578

Badness (Smith): 0.031857

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 4096/4095

Mapping: [2 1 22 2 25 -2], 0 3 -24 5 -25 13]]

Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~9/7 = 433.911 ¢

Optimal ET sequence: 36, 94, 130, 224, 354, 578

Badness (Smith): 0.017514

Supers

Subgroup: 2.3.5.7

Comma list: 5120/5103, 118098/117649

Mapping[2 1 -12 2], 0 3 23 5]]

Optimal tunings:

  • WE: ~343/243 = 599.806 ¢, ~9/7 = 434.078 ¢
  • CWE: ~343/243 = 600.000 ¢, ~9/7 = 434.203 ¢

Optimal ET sequence58, 94, 152

Badness (Sintel): 2.347

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 5120/5103

Mapping: [2 1 -12 2 -9], 0 3 23 5 22]]

Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~9/7 = 434.217 ¢

Optimal ET sequence: 58, 94, 152

Badness: 0.028240

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1575/1573

Mapping: [2 1 -12 2 -9 -2], 0 3 23 5 22 13]]

Optimal tuning (POTE): ~99/70 = 600.000 ¢, ~9/7 = 434.221 ¢

Optimal ET sequence: 58, 94, 152f

Badness: 0.021645

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 289/288, 352/351, 442/441, 561/560

Mapping: [2 1 -12 2 -9 -2 6], 0 3 23 5 22 13 3]]

Optimal tuning (POTE): ~17/12 = 600.000 ¢, ~9/7 = 434.181 ¢

Optimal ET sequence: 58, 94, 152f

Badness: 0.021316

Stearnscape

Subgroup: 2.3.5.7

Comma list: 118098/117649, 250047/250000

Mapping[6 3 2 6], 0 6 11 10]]

mapping generators: ~2450/2187, ~567/500

Optimal tunings:

  • WE: ~2450/2187 = 199.998 ¢, ~567/500 = 216.940 ¢
  • CWE: ~2450/2187 = 200.000 ¢, ~567/500 = 216.941 ¢

Optimal ET sequence72, 210, 282, 354

Badness (Sintel): 2.289

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 137781/137500

Mapping: [6 3 2 6 11], 0 6 11 10 9]]

Optimal tuning (CTE): ~55/49 = 200.0000 ¢, ~567/500 = 216.9242 ¢ (~100/99 = 16.9242 ¢)

Optimal ET sequence: 72, 210e, 282, 354

Badness: 0.032096

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 34398/34375

Mapping: [6 3 2 6 11 -6], 0 6 11 10 9 26]]

Optimal tuning (CTE): ~55/49 = 200.0000 ¢, ~312/275 = 216.9332 ¢ (~105/104 = 16.9332 ¢)

Optimal ET sequence: 72, 210ef, 282, 354

Badness: 0.0258

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 729/728, 936/935, 1156/1155, 1575/1573

Mapping: [6 3 2 6 11 -6 5], 0 6 11 10 9 26 18]]

Optimal tuning (CTE): ~55/49 = 200.0000 ¢, ~17/15 = 216.9345 ¢ (~105/104 = 16.9345 ¢)

Optimal ET sequence: 72, 210efg, 282, 354

Badness: 0.0154

Garistearn

The garistearn temperament (94 & 282) has a period of 1/94-octave and tempers out 118098/117649 and the garischisma, 33554432/33480783.

Subgroup: 2.3.5.7

Comma list: 118098/117649, 33554432/33480783

Mapping[94 149 0 264], 0 0 1 0]]

mapping generators: ~1029/1024, ~5

Optimal tunings:

  • CTE: ~1029/1024 = 12.7660 ¢, ~5/4 = 386.3137 ¢
  • CWE: ~1029/1024 = 12.7660 ¢, ~5/4 = 386.6637 ¢

Optimal ET sequence94, 282, 658d, 940dd

Badness (Sintel): 7.770

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 33554432/33480783

Mapping: [94 149 0 264 107], 0 0 1 0 1]]

Optimal tunings:

  • CTE: ~1029/1024 = 12.7660 ¢, ~5/4 = 386.0177 ¢
  • CWE: ~1029/1024 = 12.7660 ¢, ~5/4 = 386.4545 ¢

Optimal ET sequence: 94, 282, 376, 658de

Badness (Sintel): 2.719

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 28672/28561

Mapping: [94 149 0 264 107 348], 0 0 1 0 1 0]]

Optimal tunings:

  • CTE: ~169/168 = 12.7660 ¢, ~5/4 = 386.0177 ¢
  • CWE: ~169/168 = 12.7660 ¢, ~5/4 = 386.6570 ¢

Optimal ET sequence: 94, 282

Badness (Sintel): 1.898

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873

Mapping: [94 149 0 264 107 348 166], 0 0 1 0 1 0 1]]

Optimal tunings:

  • CTE: ~169/168 = 12.7660 ¢, ~5/4 = 385.9792 ¢
  • CWE: ~169/168 = 12.7660 ¢, ~5/4 = 386.6751 ¢

Optimal ET sequence: 94, 282

Badness (Sintel): 1.406

Decistearn

The decistearn temperament (80 & 130) has a period of 1/10-octave and tempers out the hemimean comma, 3136/3125 as well as the linus comma.

Subgroup: 2.3.5.7

Comma list: 3136/3125, 118098/117649

Mapping[10 2 14 5], 0 3 2 5]]

mapping generators: ~15/14, ~135/98

Optimal tunings:

  • WE: ~15/14 = 119.975 ¢, ~135/98 = 553.845 ¢
  • CWE: ~15/14 = 120.000 ¢, ~135/98 = 553.893 ¢

Optimal ET sequence50, 80, 130, 470cd, 600cd, 730cd, 860ccd

Badness (Sintel): 2.418

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 3136/3125, 4000/3993

Mapping: [10 2 14 5 30], 0 3 2 5 1]]

Optimal tunings:

  • WE: ~15/14 = 119.953 ¢, ~11/8 = 553.864 ¢
  • CWE: ~15/14 = 120.000 ¢, ~11/8 = 553.978 ¢

Optimal ET sequence: 50, 80, 130, 210e, 340ce

Badness (Sintel): 1.275

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 540/539, 3136/3125

Mapping: [10 2 14 5 30 37], 0 3 2 5 1 0]]

Optimal tunings:

  • WE: ~15/14 = 119.974 ¢, ~11/8 = 553.827 ¢
  • CWE: ~15/14 = 120.000 ¢, ~11/8 = 553.905 ¢

Optimal ET sequence: 50, 80, 130

Badness (Sintel): 1.111

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 289/288, 351/350, 540/539, 1632/1625

Mapping: [10 2 14 5 30 37 27], 0 3 2 5 1 0 3]]

Optimal tunings:

  • WE: ~15/14 = 119.990 ¢, ~11/8 = 553.884 ¢
  • CWE: ~15/14 = 120.000 ¢, ~11/8 = 553.914 ¢

Optimal ET sequence: 50, 80, 130

Badness (Sintel): 1.235

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475

Mapping: [10 2 14 5 30 37 27 24], 0 3 2 5 1 0 3 4]]

Optimal tunings:

  • WE: ~15/14 = 119.995 ¢, ~11/8 = 553.925 ¢
  • CWE: ~15/14 = 120.000 ¢, ~11/8 = 553.940 ¢

Optimal ET sequence: 50, 80, 130

Badness (Sintel): 1.109

23-limit

By equating 16/13 with 69/56 and 85/69 (enabling 56:69:85 chords), we find 23/16 at 2 generators underneath 6 periods (which is the 5edo fifth, 6\10).

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475, 897/896

Mapping: [10 2 14 5 30 37 27 24 36], 0 3 2 5 1 0 3 4 2]]

Optimal tunings:

  • WE: ~15/14 = 119.997 ¢, ~11/8 = 553.925 ¢
  • CWE: ~15/14 = 120.000 ¢, ~11/8 = 553.933 ¢

Optimal ET sequence: 30dh, 50, 80, 130

Badness (Sintel): 1.017