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Pentafrost tempers out the [[245/242|frostma]] in addition to 896/891 which also means that the [[schisma]] is tempered out, mapping prime 5 to 8 [[4/3|perfect fourths]] and -1 octaves.
Pentafrost tempers out the [[245/242|frostma]] in addition to 896/891 which also means that the [[schisma]] is tempered out, mapping prime 5 to 8 [[4/3|perfect fourths]] and -1 octaves.


Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


Comma list: [[245/242]], [[896/891]]
[[Comma list]]: [[245/242]], [[896/891]]


Mapping: {{mapping| 1 0 15 0 7 | 0 1 -8 0 -4 | 0 0 0 1 1 }}
{{Mapping|legend=1| 1 0 15 0 7 | 0 1 -8 0 -4 | 0 0 0 1 1 }}


: mapping generators: 2, ~3, ~7
: mapping generators: ~2, ~3, ~7


Optimal tunings:
[[Optimal tuning]]s:
* CTE: 2 = 1\1, ~3 = 1901.883, ~7 = 3364.864
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.883, ~7/4 = 964.864
* CWE: 2 = 1\1, ~3 = 1901.903, ~7 = 3364.614
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.903, ~7/4 = 964.614
* CE: 2 = 1\1, ~3 = 1902.006, ~7 = 3364.085
* [[CE]]: ~2 = 1\1, ~3/2 = 702.006, ~7/4 = 964.085
53edo may be an optimal ET.
 
{{Optimal ET sequence|legend=1| 12, 24, 29, 36, 41, 106d }}
 
[[Badness]]: 1.58 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: [[245/242]], [[105/104]], [[352/351]]
Comma list: [[105/104]], [[245/242]], [[352/351]]


Mapping: {{mapping| 1 0 15 0 7 12 | 0 1 -8 0 -4 -7 | 0 0 0 1 1 1 }}
Mapping: {{mapping| 1 0 15 0 7 12 | 0 1 -8 0 -4 -7 | 0 0 0 1 1 1 }}


: mapping generators: 2, ~3, ~7
: mapping generators: ~2, ~3, ~7


Optimal tunings:
Optimal tunings:
* CTE: 2 = 1\1, ~3 = 1902.106, ~7 = 3362.655
* CTE: ~2 = 1\1, ~3/2 = 702.106, ~7/4 = 962.655
* CWE: 2 = 1\1, ~3 = 1902.145, ~7 = 3362.175
* CWE: ~2 = 1\1, ~3/2 = 702.145, ~7/4 = 962.175
* CE: 2 = 1\1, ~3 = 1902.360, ~7 = 3362.210
* CE: ~2 = 1\1, ~3/2 = 702.360, ~7/4 = 962.210
<br>
 
41edo may be an optimal ET.
Optimal ET sequence: {{Optimal ET sequence| 12f, 24, 29, 41 }}
 
Badness: 1.59 × 10<sup>-3</sup>
 
=== Permafrost ===
=== Permafrost ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: [[245/242]], [[896/891]], [[144/143]]
Comma list: [[144/143]], [[245/242]], [[896/891]]


Mapping: {{mapping| 1 0 15 0 7 -3 | 0 1 -8 0 -4 6 | 0 0 0 1 1 -1 }}
Mapping: {{mapping| 1 0 15 0 7 -3 | 0 1 -8 0 -4 6 | 0 0 0 1 1 -1 }}


: mapping generators: 2, ~3, ~7
: mapping generators: ~2, ~3, ~7


Optimal tunings:
Optimal tunings:
* CTE: 2 = 1\1, ~3 = 1901.783, ~7 = 3366.113
* CTE: 2 = 1\1, ~3/2 = 701.783, ~7/4 = 966.113
* CWE: 2 = 1\1, ~3 = 1901.753, ~7 = 3366.445
* CWE: 2 = 1\1, ~3/2 = 701.753, ~7/4 = 966.445
* CE: 2 = 1\1, ~3 = 1901.770, ~7 = 3365.771
* CE: 2 = 1\1, ~3/2 = 701.770, ~7/4 = 965.771
53edo may be an optimal ET.
 
Optimal ET sequence: {{Optimal ET sequence| 12, 17, 24, 36, 41, 77e }}
 
Badness: 2.62 × 10<sup>-3</sup>
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