Landscape microtemperaments: Difference between revisions
m Fix |
Move septimal atomic here as it's less accurate than the 5-limit. This also facilitates documenting further extensions. |
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* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]] | * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]] | ||
Considered below are sextile, septichrome, pnict, avicenna, terture, slendscape, akjayland, magnesium, chromium, zinc, and poe. | Considered below are sextile, septichrome, pnict, atomic, avicenna, terture, slendscape, akjayland, magnesium, chromium, zinc, and poe. | ||
== Sextile == | == Sextile == | ||
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[[Badness]] (Sintel): 1.16 | [[Badness]] (Sintel): 1.16 | ||
== Atomic == | |||
: For the 5-limit version, see [[Very high accuracy temperaments #Atomic]].'' | |||
Atomic tempers out the [[atom]], {{monzo| 161 -84 -12 }}, and in the [[7-limit]] the [[nommisma]], {{monzo| -55 30 2 1 }}, so that a stack of two [[schisma]]s gives the [[garischisma]], from which intervals of [[7/1|7]] can be derived. It may be described as the {{nowrap| 12 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid monocot. | |||
Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments #Hafnium|hafnium]]. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 250047/250000, {{monzo| -55 30 2 1 }} | |||
{{Mapping| 12 0 161 338 | 0 1 -7 -16 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~30375/28672 = 99.999866{{c}}, ~3/2 = 701.948670{{c}} (~32805/32768 = 1.949605{{c}}) | |||
: [[error map]]: {{val| -0.0016 -0.0079 +0.0353 -0.0241 }} | |||
* [[CWE]]: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949698{{c}} (~32805/32768 = 1.949698{{c}}) | |||
: error map: {{val| 0.0000 -0.0053 +0.0384 -0.0211 }} | |||
{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }} | |||
[[Badness]] (Sintel): 1.16 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 9801/9800, 151263/151250, 184549376/184528125 | |||
Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }} | |||
Optimal tunings: | |||
* WE: ~30375/28672 = 99.999760{{c}}, ~3/2 = 701.946301{{c}} (~32805/32768 = 1.947983{{c}}) | |||
* CWE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.948121{{c}} (~32805/32768 = 1.948121{{c}}) | |||
{{Optimal ET sequence|legend=0| 12, …, 600e, 612, 1236, 1848 }} | |||
Badness (Sintel): 0.530 | |||
== Avicenna == | == Avicenna == | ||