19th-octave temperaments: Difference between revisions
Move graywood and 5-limit enneadecal to the equivalence continuum |
Hotcrystal0 (talk | contribs) Graywood notice |
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{{Infobox fractional-octave|19}} | {{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 | [[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 [[harmonic]]s [[7/1|7]], [[11/1|11]], and [[13/1|13]] mapped to an independent generator. Undevigintone has the same [[2.3.5.7.13 subgroup|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]]. | ||
For graywood, see [[Syntonic–kleismic equivalence continuum#Graywood]]. | |||
== Meanmag == | == Meanmag == | ||
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{{Mapping|legend=1| 19 30 44 0 | 0 0 0 1 }} | {{Mapping|legend=1| 19 30 44 0 | 0 0 0 1 }} | ||
: mapping generators: ~25/24, ~7 | : mapping generators: ~25/24, ~7 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~25/24 = 63.2931{{c}}, ~7/4 = 963.6625{{c}} | |||
: [[error map]]: {{val| +2.569 -3.162 -1.417 -0.026 }} | |||
* [[CWE]]: ~25/24 = 63.1579{{c}}, ~7/4 = 963.4030{{c}} | |||
: error map: {{val| 0.000 -7.218 -7.366 -5.423 }} | |||
{{Optimal ET sequence|legend=1| 19 | {{Optimal ET sequence|legend=1| 19, 57, 76, 171bbccdd }} | ||
[[Badness]]: | [[Badness]] (Sintel): 1.95 | ||
=== 11-limit === | === 11-limit === | ||
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Mapping: {{mapping| 19 30 44 0 119 | 0 0 0 1 -1 }} | Mapping: {{mapping| 19 30 44 0 119 | 0 0 0 1 -1 }} | ||
Optimal | Optimal tunings: | ||
* WE: ~25/24 = 63.2535{{c}}, ~7/4 = 967.9769{{c}} | |||
* CWE: ~25/24 = 63.1579{{c}}, ~7/4 = 966.6112{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 38, 57 }} | ||
Badness: | Badness (Sintel): 2.21 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
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Mapping: {{mapping| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }} | Mapping: {{mapping| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }} | ||
Optimal | Optimal tunings: | ||
* WE: ~25/24 = 63.2422{{c}}, ~7/4 = 966.3987{{c}} | |||
* CWE: ~25/24 = 63.1579{{c}}, ~7/4 = 965.3984{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 38, 57, 76 }} | ||
Badness: | Badness (Sintel): 1.89 | ||
== Undevigintone == | == Undevigintone == | ||
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{{Mapping|legend=1| 19 30 44 53 0 | 0 0 0 0 1 }} | {{Mapping|legend=1| 19 30 44 53 0 | 0 0 0 0 1 }} | ||
: mapping generators: ~28/27, ~11 | : mapping generators: ~28/27, ~11 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~28/27 = 63.3591{{c}}, ~11/8 = 539.7611{{c}} | |||
* [[CWE]]: ~28/27 = 63.1579{{c}}, ~11/8 = 540.6837{{c}} | |||
{{Optimal ET sequence|legend=1| 19, 38d }} | {{Optimal ET sequence|legend=1| 19, 38d }} | ||
[[Badness]]: | [[Badness]] (Sintel): 1.20 | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 19 30 44 53 0 70 | 0 0 0 0 1 0 }} | Mapping: {{mapping| 19 30 44 53 0 70 | 0 0 0 0 1 0 }} | ||
Optimal | Optimal tunings: | ||
* WE: ~28/27 = 63.3741{{c}}, ~11/8 = 538.8996{{c}} | |||
* CWE: ~28/27 = 63.1579{{c}}, ~11/8 = 539.4216{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 38df }} | ||
Badness: 0. | Badness (Sintel): 0.948 | ||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||