Syntonic–kleismic equivalence continuum: Difference between revisions
Move hogzilla, stump, and unsmate here |
Move graywood and 5-limit enneadecal here |
||
| Line 17: | Line 17: | ||
|- | |- | ||
| 0 | | 0 | ||
| | | [[Graywood]] | ||
| [[19-comma|1162261467/1073741824]] | | [[19-comma|1162261467/1073741824]] | ||
| {{Monzo| -30 19 }} | | {{Monzo| -30 19 }} | ||
| Line 102: | Line 102: | ||
| [[Mowgli]] || 15/2 = 7.5 || {{monzo| 0 22 -15 }} | | [[Mowgli]] || 15/2 = 7.5 || {{monzo| 0 22 -15 }} | ||
|} | |} | ||
== Graywood == | |||
Named by [[CompactStar]] in 2024, graywood tempers out the [[19-comma]], corresponding to {{nowrap| ''n'' {{=}} 0 }}. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 1162261467/1073741824 | |||
{{Mapping|legend=1| 19 30 0 | 0 0 1 }} | |||
: mapping generators: ~2187/2048, ~5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2187/2048 = 63.2773{{c}}, ~5/4 = 381.7568{{c}} | |||
: [[error map]]: {{val| +2.268 -3.637 -0.020 }} | |||
* [[CWE]]: ~2187/2048 = 63.1579{{c}}, ~5/4 = 382.7889{{c}} | |||
: error map: {{val| 0.000 -7.218 -3.525 }} | |||
{{Optimal ET sequence|legend=1| 19 }} | |||
[[Badness]] (Sintel): 32.4 | |||
== Hogzilla == | == Hogzilla == | ||
| Line 251: | Line 271: | ||
[[Badness]] (Sintel): 15.3 | [[Badness]] (Sintel): 15.3 | ||
== Enneadecal (5-limit) == | |||
: ''For extensions, see [[Ragismic microtemperaments #Enneadecal]].'' | |||
The 5-limit version of enneadecal tempers out the [[enneadeca]], which simply equates a stack of nineteen [[6/5]] minor thirds with five [[2/1|octaves]]. It corresponds to {{nowrap| ''n'' {{=}} 19/3 }}, with a 19th-octave period and a generator of a [[3/2|perfect fifth]]. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 19073486328125/19042491875328 | |||
{{Mapping|legend=1| 19 0 14 | 0 1 1 }} | |||
: mapping generators: ~648/625, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~648/625 = 63.1579{{c}}, ~3/2 = 701.9861{{c}} | |||
: [[error map]]: {{val| +0.013 +0.044 -0.095 }} | |||
* [[CWE]]: ~648/625 = 63.1579{{c}}, ~3/2 = 701.9900{{c}} | |||
: error map: {{val| 0.000 -0.035 -0.113 }} | |||
{{Optimal ET sequence|legend=1| 19, 95, 114, 133, 152, 171, 323, 494, 665, 1159, 1824, 2983, 7125c }} | |||
[[Badness]] (Sintel): 1.12 | |||
== Countermeantone == | == Countermeantone == | ||