19th-octave temperaments: Difference between revisions
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[[19edo]] has excellent 5-limit accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with harmonics 7, 11, and 13 mapped to an independent generator | {{Infobox fractional-octave|19}} | ||
[[19edo]] has excellent 5-limit accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with harmonics 7, 11, and 13 mapped to an independent generator. Undevigintone has the same 2.3.5.7.13 subgroup mapping as 19et with harmonic 11 mapped to an independent generator. | |||
See also [[enneadecal]] and [[superenneadecal]]. | See also [[enneadecal]] and [[superenneadecal]]. | ||
== Graywood == | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 1162261467/1073741824 | |||
{{Mapping|legend=1|19 30 38|0 0 1}} | |||
[[Optimal tuning]] ([[CTE]]): ~2187/2048 = 1\19, ~5/4 = 386.314 | |||
[[Support]]ing [[ET]]s: {{EDOs|19, 38c, 57c, 76c, 95bcc }} | |||
== Meanmag == | == Meanmag == | ||
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: mapping generators: ~25/24, ~7 | : mapping generators: ~25/24, ~7 | ||
[[Optimal tuning]] ([[POTE]]): ~25/24 = 1\19, ~8/7 = 238.396 | [[Optimal tuning]] ([[POTE]]): ~25/24 = 1\19, ~8/7 = 238.396 | ||
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Badness: 0.066829 | Badness: 0.066829 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.045844 | Badness: 0.045844 | ||
== (5-limit) enneadecal == | |||
''For the 7-limit temperament, see [[Ragismic microtemperaments#Enneadecal]].'' | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 19073486328125/19042491875328 | |||
{{Mapping|legend=1|19 19 33|0 1 1}} | |||
[[Optimal tuning]] ([[CTE]]): ~648/625 = 1\19, ~3/2 = 701.990 | |||
[[Support]]ing [[ET]]s: {{EDOs|171, 19, 152, 323, 494, 665, 190, 133, 836, 817, 475, 114, 361, 209 }} | |||
== Undevigintone == | == Undevigintone == | ||
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Badness: 0.022933 | Badness: 0.022933 | ||
{{Navbox fractional-octave}} | |||