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The '''Compton family''' tempers out the [[Pythagorean comma]], 531441/524288 = {{monzo| -19 12 }}, and hence the fifths form a closed 12-note circle of fifths, identical to [[12edo]]. While the tuning of the fifth will be that of 12et, two cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.
{{Technical data page}}
The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth will be that of 12edo, two [[cent]]s flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.


== Compton ==
== Compton ==
{{Main| Compton }}


In terms of the normal list, compton adds 413343/409600 = {{monzo| -14 10 -2 1 }} to the Pythagorean comma; however it can also be characterized by saying it adds [[225/224]]. Compton, however, does not need to be used as a 7-limit temperament; in the 5-limit it becomes the rank two 5-limit temperament tempering out the Pythagorean comma. In terms of equal temperaments, it is the 12&72 temperament, and [[72edo]], [[84edo]] or [[240edo]] make for good tunings. Possible generators are 21/20, 10/9, the secor, 6/5, 5/4, 7/5 and most importantly, 81/80.  
5-limit compton is also known as ''aristoxenean''. It tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, it is the {{nowrap| 12 & 72 }} temperament, and [[72edo]], [[84edo]] or [[240edo]] make for good tunings.  


In either the 5 or 7-limit, [[240edo]] is an excellent tuning, with 81/80 coming in at 15 cents exactly. The major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.
[[Subgroup]]: 2.3.5


In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this [[72edo]] can be recommended as a tuning.
[[Comma list]]: 531441/524288


Comma list: 531441/524288
{{Mapping|legend=1| 12 19 0 | 0 0 1 }}


[[POTE generator]]: ~5/4 = 384.884 or ~81/80 = 15.116
: mapping generators: ~256/243, ~5


Mapping: [{{val| 12 19 0 }}, {{val| 0 0 1 }}
[[Optimal tuning]]s:  
* [[CTE]]: ~256/243 = 100.000, ~5/4 = 386.314 (~81/80 = 13.686)
: [[error map]]: {{val| 0.000 -1.955 0.000 }}
* [[POTE]]: ~256/243 = 100.000, ~5/4 = 384.884 (~81/80 = 15.116)
: error map: {{val| 0.000 -1.955 -1.431 }}


{{Val list|legend=1| 12, 72, 84, 156, 240, 396b }}
{{Optimal ET sequence|legend=1| 12, 48, 60, 72, 84, 156, 240, 396b, 636bbc }}


=== 7-limit (aka Waage) ===
[[Badness]] (Smith): 0.094494
Comma list: 225/224, 250047/250000


[[POTE generator]]: ~5/4 = 383.7752
== Septimal compton ==
{{Main| Compton }}


Mapping: [{{val| 12 19 0 -22 }}, {{val| 0 0 1 2 }}]
Septimal compton is also known as ''waage''. In terms of the normal list, compton adds 413343/409600 ({{monzo| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]].


{{Val list|legend=1| 12, 60, 72, 228, 300c, 372bc, 444bc }}
In either the 5- or 7-limit, 240edo is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.


Badness: 0.035686
In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this 72edo can be recommended as a tuning. In 11-limit compton, intervals of 5 are off by one generator, intervals of 7 are off by two generators, and intervals of 11 are off by 3 generators.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 250047/250000
 
{{Mapping|legend=1| 12 19 0 -22 | 0 0 1 2 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~200/189 = 100.000, ~5/4 = 384.922 (~126/125 = 15.078)
: [[error map]]: {{val| 0.000 -1.955 -1.392 -1.017 }}
* [[POTE]]: ~200/189 = 100.000, ~5/4 = 383.775 (~126/125 = 16.225)
: error map: {{val| 0.000 -1.955 -2.538 -1.275 }}
 
{{Optimal ET sequence|legend=1| 12, 48d, 60, 72, 228, 300c, 372bc, 444bc }}
 
[[Badness]] (Smith): 0.035686
 
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 225/224, 441/440, 4375/4356
Comma list: 225/224, 441/440, 4375/4356


[[POTE generator]]: ~5/4 = 383.2660
Mapping: {{mapping| 12 19 0 -22 -42 | 0 0 1 2 3 }}


Mapping: [{{val|12 19 0 -22 -42 }}, {{val| 0 0 1 2 3 }}]
Optimal tunings:  
* CTE: ~35/33 = 100.000, ~5/4 = 384.324 (~100/99 = 15.676)
* POTE: ~35/33 = 100.000, ~5/4 = 383.266 (~100/99 = 16.734)


{{Val list|legend=1| 12, 60e, 72 }}
{{Optimal ET sequence|legend=0| 12, 48dee, 60e, 72 }}


Badness: 0.022235
Badness (Smith): 0.022235
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==== 13-limit  ====
Comma list: 225/224, 351/350, 364/363, 441/440
Comma list: 225/224, 351/350, 364/363, 441/440


POTE generator: ~5/4 = 383.9628
Mapping: {{mapping| 12 19 0 -22 -42 -67 | 0 0 1 2 3 4 }}


Mapping: [{{val| 12 19 0 -22 -42 -67 }}, {{val| 0 0 1 2 3 4 }}]
Optimal tunings:  
* CTE: ~35/33 = 100.000, ~5/4 = 384.685 (~105/104 = 15.315)
* POTE: ~35/33 = 100.000, ~5/4 = 383.963 (~105/104 = 16.037)


{{Val list|legend=1| 12f, 72, 84, 156, 228f, 300cf }}
{{Optimal ET sequence|legend=0| 12f, 48deefff, 60eff, 72, 228f }}


Badness: 0.021852
Badness (Smith): 0.021852
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


===== 17-limit  =====
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440


POTE generator: ~5/4 = 383.7500
Mapping: {{mapping| 12 19 0 -22 -42 -67 49 | 0 0 1 2 3 4 0 }}
 
Optimal tunings:
* CTE: ~18/17 = 100.000, ~5/4 = 384.685 (~105/104 = 15.315)
* POTE: ~18/17 = 100.000, ~5/4 = 383.750 (~105/104 = 16.250)


Mapping: [{{val| 12 19 0 -22 -42 -67 49 }}, {{val| 0 0 1 2 3 4 0 }}]
{{Optimal ET sequence|legend=0| 12f, 60eff, 72 }}


{{Val list|legend=1| 12f, 72, 84, 156g, 228fg }}
Badness (Smith): 0.017131


Badness: 0.017131
==== Comptone ====
Subgroup: 2.3.5.7.11.13


==== Comptone  ====
Comma list: 225/224, 325/324, 441/440, 1001/1000
Comma list: 225/224, 325/324, 441/440, 1001/1000


POTE generator: ~5/4 = 382.6116
Mapping: {{mapping| 12 19 0 -22 -42 100 | 0 0 1 2 3 -2 }}
 
Optimal tunings:
* CTE: ~35/33 = 100.000, ~5/4 = 383.552 (~100/99 = 16.448)
* POTE: ~35/33 = 100.000, ~5/4 = 382.612 (~100/99 = 17.388)


Mapping: [{{val| 12 19 0 -22 -42 100 }}, {{val| 0 0 1 2 3 -2 }}]
{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdef, 276cdeff }}


{{Val list|legend=1| 12, 60e, 72, 204cdef, 276cdef }}
Badness (Smith): 0.025144


Badness: 0.025144
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


===== 17-limit  =====
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440


POTE generator: ~5/4 = 382.5968
Mapping: {{mapping| 12 19 0 -22 -42 100 49 | 0 0 1 2 3 -2 0 }}


Mapping: [{{val| 12 19 0 -22 -42 100 49 }}, {{val| 0 0 1 2 3 -2 0 }}]
Optimal tunings:  
* CTE: ~18/17 = 100.000, ~5/4 = 383.552 (~100/99 = 16.448)
* POTE: ~18/17 = 100.000, ~5/4 = 382.597 (~100/99 = 17.403)


{{Val list|legend=1| 12, 60e, 72, 132deg, 204cdefg }}
{{Optimal ET sequence|legend=0| 12, 60e, 72, 204cdefg, 276cdeffgg }}


Badness: 0.016361
Badness (Smith): 0.016361


== Catler ==
== Catler ==
In terms of the normal comma list, catler is characterized by the addition of the [[schisma]], 32805/32768, to the Pythagorean comma, though it can also be characterized as adding [[81/80]], [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of [[12edo]]. Catler can also be characterized as the 12&24 temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are 36/35, 21/20, 15/14, 8/7, 7/6, 6/5, 9/7, 7/5, and most importantly, 64/63.   
In terms of the normal comma list, catler is characterized by the addition of the [[schisma]], 32805/32768, to the Pythagorean comma, though it can also be characterized as adding 81/80, [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of 12edo. Catler can also be characterized as the {{nowrap| 12 & 24 }} temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are [[36/35]], [[21/20]], [[15/14]], [[8/7]], [[7/6]], [[9/7]], [[7/5]], and most importantly, [[64/63]].   


Comma list: 81/80, 128/125
[[Subgroup]]: 2.3.5.7


[[POTE generator]]: ~64/63 = 26.790
[[Comma list]]: 81/80, 128/125


Mapping: [{{val| 12 19 28 0 }}, {{val| 0 0 0 1 }}]
{{Mapping|legend=1| 12 19 28 0 | 0 0 0 1 }}


{{Val list|legend=1| 12, 36, 48, 132, 180 }}
: mapping generators: ~16/15, ~7
 
[[Optimal tuning]]s:
* [[CTE]]: ~16/15 = 100.000, ~7/4 = 968.826 (~64/63 = 31.174)
: [[error map]]: {{val| 0.000 -1.955 +13.686 0.000 }}
* [[POTE]]: ~16/15 = 100.000, ~7/4 = 973.210 (~64/63 = 26.790)
: error map: {{val| 0.000 -1.955 +13.686 +4.384 }}
 
{{Optimal ET sequence|legend=1| 12, 24, 36, 48c, 84c }}
 
[[Badness]] (Smith): 0.050297
 
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 81/80, 99/98, 128/125
Comma list: 81/80, 99/98, 128/125


POTE generator: ~64/63 = 22.723
Mapping: {{mapping| 12 19 28 0 -26 | 0 0 0 1 2 }}


Mapping: [{{val| 12 19 28 0 -26 }}, {{val| 0 0 0 1 2 }}]
Optimal tunings:  
* CTE: ~16/15 = 100.000, ~7/4 = 973.779 (~64/63 = 26.221)
* POTE: ~16/15 = 100.000, ~7/4 = 977.277 (~64/63 = 22.723)


{{Val list|legend=1| 12, 48c, 108cd }}
{{Optimal ET sequence|legend=0| 12, 36e, 48c }}


Badness: 0.0582
Badness (Smith): 0.058213
 
=== Catlat ===
Subgroup: 2.3.5.7.11


=== Catlat  ===
Comma list: 81/80, 128/125, 540/539
Comma list: 81/80, 128/125, 540/539


POTE generator: ~64/63 = 27.864
Mapping: {{mapping| 12 19 28 0 109 | 0 0 0 1 -2 }}
 
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 972.823 (~64/63 = 27.177)
* POTE: ~16/15 = 100.000, ~7/4 = 972.136 (~64/63 = 27.864)


Mapping: [{{val| 12 19 28 0 109 }}, {{val| 0 0 0 1 -2 }}]
{{Optimal ET sequence|legend=0| 12e, 36, 48c, 84c }}


{{Val list|legend=1| 36, 48c, 84c }}
Badness (Smith): 0.081909


Badness: 0.0819
=== Catnip ===
Subgroup: 2.3.5.7.11


=== Catcall  ===
Comma list: 56/55, 81/80, 128/125
Comma list: 56/55, 81/80, 128/125


POTE generator: ~36/35 = 32.776
Mapping: {{mapping| 12 19 28 0 8 | 0 0 0 1 1 }}
 
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 961.874 (~64/63 = 38.126)
* POTE: ~16/15 = 100.000, ~7/4 = 967.224 (~64/63 = 32.776)


Mapping: [{{val| 12 19 28 0 8 }}, {{val| 0 0 0 1 1 }}]
{{Optimal ET sequence|legend=0| 12, 24, 36, 72ce }}


{{Val list|legend=1| 12, 24, 36, 72ce }}
Badness (Smith): 0.034478


Badness: 0.0345
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==== 13-limit  ====
Comma list: 56/55, 66/65, 81/80, 105/104
Comma list: 56/55, 66/65, 81/80, 105/104


POTE generator: ~36/35 = 37.232
Mapping: {{mapping| 12 19 28 0 8 11 | 0 0 0 1 1 1 }}
 
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 956.375 (~40/39 = 43.625)
* POTE: ~16/15 = 100.000, ~7/4 = 962.778 (~40/39 = 37.232)
 
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
 
Badness (Smith): 0.028363
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 51/50, 56/55, 66/65, 81/80, 105/104
 
Mapping: {{mapping| 12 19 28 0 8 11 49 | 0 0 0 1 1 1 0 }}
 
Optimal tunings:
* CTE: ~18/17 = 100.000, ~7/4 = 956.375 (~40/39 = 43.625)
* POTE: ~18/17 = 100.000, ~7/4 = 960.223 (~40/39 = 39.777)


Mapping: [{{val| 12 19 28 0 8 11 }}, {{val| 0 0 0 1 1 1 }}]
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}


{{Val list|legend=1| 12f, 24, 36f, 60cf }}
Badness (Smith): 0.023246


Badness: 0.0284
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 51/50, 56/55, 66/65, 76/75, 81/80, 96/95
 
Mapping: {{mapping| 12 19 28 0 8 11 49 51 | 0 0 0 1 1 1 0 0 }}
 
Optimal tunings:
* CTE: ~18/17 = 100.000, ~7/4 = 956.375 (~40/39 = 43.625)
* POTE: ~18/17 = 100.000, ~7/4 = 959.835 (~40/39 = 40.165)
 
{{Optimal ET sequence|legend=0| 12f, 24, 36f }}
 
Badness (Smith): 0.018985
 
==== Duodecic ====
Subgroup: 2.3.5.7.11.13


==== Duodecic  ====
Comma list: 56/55, 81/80, 91/90, 128/125
Comma list: 56/55, 81/80, 91/90, 128/125


POTE generator: ~36/35 = 37.688
Mapping: {{mapping| 12 19 28 0 8 78 | 0 0 0 1 1 -1 }}
 
Optimal tunings:
* CTE: ~16/15 = 100.000, ~7/4 = 961.255 (~64/63 = 38.745)
* POTE: ~16/15 = 100.000, ~7/4 = 962.312 (~64/63 = 37.688)


Mapping: [{{val| 12 19 28 0 8 78 }}, {{val| 0 0 0 1 1 -1 }}]
{{Optimal ET sequence|legend=0| 12, 24, 36 }}


{{Val list|legend=1| 12, 24, 36, 60c }}
Badness (Smith): 0.038307


Badness: 0.0383
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17


===== 17-limit  =====
Comma list: 51/50, 56/55, 81/80, 91/90, 128/125
Comma list: 51/50, 56/55, 81/80, 91/90, 128/125


POTE generator: ~36/35 = 38.097
Mapping:{{mapping| 12 19 28 0 8 78 49 | 0 0 0 1 1 -1 0 }}


Mapping: [{{val| 12 19 28 0 8 78 49 }}, {{val| 0 0 0 1 1 -1 0 }}]
Optimal tunings:  
* CTE: ~18/17 = 100.000, ~7/4 = 961.255 (~64/63 = 38.745)
* POTE: ~18/17 = 100.000, ~7/4 = 961.903 (~64/63 = 38.097)


{{Val list|legend=1| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}


Badness: 0.0275
Badness (Smith): 0.027487
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19


===== 19-limit  =====
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95


POTE generator: ~36/35 = 38.080
Mapping: {{mapping| 12 19 28 0 8 78 49 51 | 0 0 0 1 1 -1 0 0 }}


Mapping: [{{val| 12 19 28 0 8 78 49 51 }}, {{val| 0 0 0 1 1 -1 0 0 }}]
Optimal tunings:  
* CTE: ~18/17 = 100.000, ~7/4 = 961.255 (~64/63 = 38.745)
* POTE: ~18/17 = 100.000, ~7/4 = 961.920 (~64/63 = 38.080)


{{Val list|legend=1| 12, 24, 36, 60c }}
{{Optimal ET sequence|legend=0| 12, 24, 36, 60c }}


Badness: 0.0209
Badness (Smith): 0.020939


== Duodecim ==
== Duodecim ==
Comma list: 36/35, 50/49, 64/63
[[Subgroup]]: 2.3.5.7.11


POTE generator: ~45/44 = 34.977
[[Comma list]]: 36/35, 50/49, 64/63


Mapping: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
{{Mapping|legend=1| 12 19 28 34 0 | 0 0 0 0 1 }}


{{Val list|legend=1| 12, 24d }}
: mapping genereators: ~16/15, ~11


== Omicronbeta  ==
[[Optimal tuning]]s:
Comma list: 225/224, 243/242, 441/440, 4375/4356
* [[CTE]]: ~16/15 = 1\12, ~11/8 = 551.318 (~33/32 = 48.682)
: [[error map]]: {{val| 0.000 -1.955 +13.686 +31.174 0.000 }}
* [[POTE]]: ~16/15 = 1\12, ~11/8 = 565.023 (~55/54 = 34.977)
: error map: {{val| 0.000 -1.955 +13.686 +31.174 +13.705 }}


POTE generator: ~13/8 = 837.814
{{Optimal ET sequence|legend=1| 12, 24d, 36d }}


Mapping: [{{val| 72 114 167 202 249 266 }}, {{val| 0 0 0 0 0 1 }}]
[[Badness]] (Smith): 0.030536


{{Val list|legend=1| 72, 144, 216c, 288cdf, 504bcdef }}
== Hours ==
The hours temperament has a period of 1/24 octave and tempers out the [[cataharry comma]] (19683/19600) and the mirwomo comma (33075/32768). The name ''hours'' was named for the reason that the period is 1/24 octave and there are 24 hours per day.


Badness: 0.0300
[[Subgroup]]: 2.3.5.7


== Hours  ==
[[Comma list]]: 19683/19600, 33075/32768
Comma list: 19683/19600, 33075/32768


POTE generator: ~225/224 = 2.100
{{Mapping|legend=1| 24 38 0 123 | 0 0 1 -1 }}


Mapping: [{{val| 24 38 0 123 83 }}, {{val| 0 0 1 -1 0 }}]
: mapping generators: ~36/35, ~5


{{Multival|legend=1| 0 24 -24 38 -38 -123 }}
[[Optimal tuning]]s:
* [[CTE]]: ~36/35 = 50.000, ~5/4 = 384.226 (~81/80 = 15.774)
: [[error map]]: {{val| 0.000 -1.955 -2.088 -3.052 }}
* [[POTE]]: ~36/35 = 50.000, ~5/4 = 384.033 (~81/80 = 15.967)
: error map: {{val| 0.000 -1.955 -2.280 -2.859 }}


{{Val list|legend=1| 24, 48, 72, 312bd, 384bcd, 456bcd, 528bcd, 600bcd }}
{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdd, 528bcdd, 600bccdd }}


Badness: 0.1161
[[Badness]] (Smith): 0.116091
 
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 243/242, 385/384, 9801/9800
Comma list: 243/242, 385/384, 9801/9800


POTE generator: ~225/224 = 2.161
Mapping: {{mapping| 24 38 0 123 83 | 0 0 1 -1 0 }}


Mapping: [{{val| 24 38 0 123 83 }}, {{val| 0 0 1 -1 0 }}]
Optimal tunings:  
* CTE: ~36/35 = 50.000, ~5/4 = 384.226 (~121/120 = 15.774)
* POTE: ~36/35 = 50.000, ~5/4 = 384.054 (~121/120 = 15.946)


{{Val list|legend=1| 24, 48, 72, 312bd, 384bcd, 456bcde, 528bcde }}
{{Optimal ET sequence|legend=1| 24, 48, 72, 312bd, 384bcdd, 456bcdde, 528bcdde }}


Badness: 0.0362
Badness (Smith): 0.036248
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 243/242, 351/350, 364/363, 385/384
Comma list: 243/242, 351/350, 364/363, 385/384


POTE generator: ~225/224 = 3.955
Mapping: {{mapping| 24 38 0 123 83 33 | 0 0 1 -1 0 1 }}
 
Optimal tunings:
* CTE: ~36/35 = 50.000, ~5/4 = 385.420 (~121/120 = 14.580)
* POTE: ~36/35 = 50.000, ~5/4 = 384.652 (~121/120 = 15.348)
 
{{Optimal ET sequence|legend=1| 24, 48f, 72, 168df, 240dff }}
 
Badness (Smith): 0.026931
 
== Gamelstearn ==
The gamelstearn temperament has a period of 1/36 octave and tempers out the [[gamelisma]] (1029/1024) and the [[stearnsma]] (118098/117649).
 
It used to be named "decades".
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 118098/117649
 
{{Mapping|legend=1| 36 57 0 101 | 0 0 1 0 }}
 
: mapping generators: ~49/48, ~5
 
[[Optimal tuning]]s:
* [[CTE]]: ~49/48 = 33.333, ~5/4 = 386.314 (~81/80 = 13.686)
: [[error map]]: {{val| 0.000 -1.955 0.000 -2.159 }}
* [[POTE]]: ~49/48 = 33.333, ~5/4 = 384.764 (~81/80 = 15.236)
: error map: {{val| 0.000 -1.955 -1.549 -2.159 }}
 
{{Optimal ET sequence|legend=1| 36, 72, 252, 324bd, 396bd }}
 
[[Badness]] (Smith): 0.108016
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1029/1024, 4000/3993
 
Mapping: {{mapping| 36 57 0 101 41 | 0 0 1 0 1 }}
 
Optimal tunings:
* CTE: ~49/48 = 33.333, ~5/4 = 385.797 (~81/80 = 14.203)
* POTE: ~49/48 = 33.333, ~5/4 = 385.150 (~81/80 = 14.850)
 
{{Optimal ET sequence|legend=1| 36, 72, 396bd, 468bcd, 540bcd, 612bccdd, 684bbccdd, 756bbccdd }}
 
Badness (Smith): 0.043088
 
== Omicronbeta ==
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 225/224, 243/242, 385/384, 4000/3993
 
{{Mapping|legend=1| 72 114 167 202 249 0 | 0 0 0 0 0 1 }}
 
: mapping generators: ~100/99, ~13


Mapping: [{{val| 24 38 0 123 83 33 }}, {{val| 0 0 1 -1 0 1 }}]
[[Optimal tuning]]s:  
* [[CTE]]: ~100/99 = 16.667, ~13/8 = 840.528 (~325/324 = 7.194)
: [[error map]]: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 0.000 }}
* [[POTE]]: ~100/99 = 16.667, ~13/8 = 837.814 (~364/363 = 4.481)
: error map: {{val| 0.000 -1.955 -2.980 -2.159 -1.318 -2.713 }}


{{Val list|legend=1| 24, 48f, 72, 168df, 240df }}
{{Optimal ET sequence|legend=1| 72, 144, 216c, 288cdf }}


Badness: 0.0269
[[Badness]] (Smith): 0.029956


[[Category:Theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Compton]]
[[Category:Compton family| ]] <!-- main article -->
[[Category:Compton| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
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