19th-octave temperaments: Difference between revisions
Looks like many of these categories are redundant |
No edit summary |
||
| (10 intermediate revisions by 7 users not shown) | |||
| Line 1: | Line 1: | ||
{{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. | [[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 == | ||
| Line 11: | Line 23: | ||
: 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 | ||
| Line 33: | Line 43: | ||
Badness: 0.066829 | Badness: 0.066829 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 45: | Line 55: | ||
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 == | ||
| Line 74: | Line 97: | ||
Badness: 0.022933 | Badness: 0.022933 | ||
{{Navbox fractional-octave}} | |||