2023/2000: Difference between revisions
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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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[[Comma list]]: 2023/2000, 78608/78125 | [[Comma list]]: 2023/2000, 78608/78125 | ||
{{Mapping|legend=2|1 1 1|0 3 7}} | {{Mapping|legend=2|1 1 5 1|0 3 -5 7}} | ||
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~[[34/25]] = 527.718 | [[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~[[34/25]] = 527.718 | ||
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[[Badness]] (Sintel): 0.447 | [[Badness]] (Sintel): 0.447 | ||
===== 2.5.7.13/11.17.23 ===== | |||
[[Subgroup]]: 2.5.7.13/11.17.23 | |||
[[Comma list]]: 221/220, 161/160, 1309/1300, 343/340 | |||
{{Mapping|legend=2|1 4 4 0 6 5|0 -7 -5 1 -8 -2}} | |||
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~[[13/11]] = 287.412 | |||
[[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 4 4 8 8 6 5|0 -7 -5 -19 -18 -8 -2}} | |||
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~[[13/11]] = 286.821 | |||
[[Badness]] (Sintel): 0.671 | |||
== Etymology == | == Etymology == | ||
As of June 6, 2026, pentagoth is the name given to the rank-3 temperament 2.5.7.17[2023/2000] by [[groundfault]]. It originally referred to a temperament now called [[vengeance]], which as a 2.5.7.17 temperament tempers out this comma. | As of June 6, 2026, pentagoth is the name given to the rank-3 temperament 2.5.7.17[2023/2000] by [[groundfault]]. It originally referred to a rank-2 temperament now called [[vengeance]], which as a 2.5.7.17 temperament tempers out this comma. | ||
[[Category:Pentagoth]] | [[Category:Pentagoth]] | ||
[[Category:Rank 2]] | |||