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== Temperaments ==
== Temperaments ==
Note: groundfault uses extensions that identify the ~20/17~13/11 with ~19/16 and tempering out 209/208; however, this leads to considerable damage to prime 19.
=== Pentagoth ===
=== Pentagoth ===
[[Subgroup]]: 2.5.7.17
[[Subgroup]]: 2.5.7.17
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[[Badness]] (Sintel): 0.509
[[Badness]] (Sintel): 0.509


==== 2.5.7.13/11.17.23 ====
[[Subgroup]]: 2.5.7.13/11.17.23
[[Comma list]]: 221/220, 161/160, 1309/1300
{{Mapping|legend=2|1 2 2 0 4 5|0 1 1 0 1 0|0 0 2 1 -1 -2}}
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~5/4 = 387.513, ~[[13/11]] = 288.786
[[Badness]] (Sintel): 0.191
===== No-3 no-19 23-limit =====
[[Subgroup]]: 2.5.7.11.13.17.23
[[Comma list]]: 176/175, 221/220, 161/160, 1309/1300
{{Mapping|legend=2|1 2 2 2 2 4 5|0 1 1 3 3 1 0|0 0 2 2 3 -1 -2}}
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~5/4 = 390.453, ~[[13/11]] = 288.844
[[Badness]] (Sintel): 0.497
=== Pentagoth clan ===
Rank-2 temperaments supporting pentagoth
==== Vengeance ====
==== Vengeance ====
{{Main| Vengeance }}
{{Main| Vengeance }}
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[[Badness]] (Sintel): 0.447
[[Badness]] (Sintel): 0.447


===== 2.5.7.13/11.17.19.23 =====
===== 2.5.7.13/11.17.23 =====
[[Subgroup]]: 2.5.7.13/11.17.19.23
[[Subgroup]]: 2.5.7.13/11.17.23
 
[[Comma list]]: 221/220, 161/160, 209/208, 1235/1232
 
{{Mapping|legend=2|1 2 2 0 4 4 5|0 1 1 0 1 0 0|0 0 2 1 -1 1 -2}}


[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~5/4 = 386.133, ~[[13/11]] = 289.374
[[Comma list]]: 221/220, 161/160, 1309/1300, 343/340


[[Badness]] (Sintel): 0.212
{{Mapping|legend=2|1 4 4 0 6 5|0 -7 -5 1 -8 -2}}


===== No-3 23-limit =====
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~[[13/11]] = 287.412
[[Subgroup]]: 2.5.7.11.13.17.19.23


[[Comma list]]: 176/175, 221/220, 161/160, 209/208, 1309/1300
[[Badness]] (Sintel): 0.256
===== No-3 no-19 23-limit =====
[[Subgroup]]: 2.5.7.11.13.17.23
[[Comma list]]: 176/175, 221/220, 161/160, 1309/1300, 343/340


{{Mapping|legend=2|1 2 2 2 2 4 4 5|0 1 1 3 3 1 0 0|0 0 2 2 3 -1 1 -2}}
{{Mapping|legend=2|1 4 4 8 8 6 5|0 -7 -5 -19 -18 -8 -2}}


[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~5/4 = 389.217, ~[[13/11]] = 289.608
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~[[13/11]] = 286.821


[[Badness]] (Sintel): 0.586
[[Badness]] (Sintel): 0.671


== Etymology ==
== Etymology ==
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[[Category:Pentagoth]]
[[Category:Pentagoth]]
[[Category:Rank 2]]
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