Tags: Mobile edit Mobile web edit |
|
| Line 390: |
Line 390: |
|
| |
|
| == Atomic == | | == Atomic == |
| {{See also | Kirnberger's atom }}
| | : ''For extensions, see [[Landscape microtemperaments #Atomic]].'' |
|
| |
|
| Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate. | | Atomic tempers out [[Kirnberger's atom]], the microscopic interval separating eleven [[schisma]]s and a [[syntonic comma]], or twelfth schismas and a [[Pythagorean comma]]. It is a member of the [[schismic–commatic equivalence continuum]] with {{nowrap| ''n'' {{=}} 12 }}. In this extremely accurate temperament, the [[3/2|perfect fifth]] is one [[schisma]] sharp of its [[12edo]] value. |
| | |
| Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments #Hafnium|hafnium]].
| |
|
| |
|
| [[Subgroup]]: 2.3.5 | | [[Subgroup]]: 2.3.5 |
| Line 412: |
Line 410: |
|
| |
|
| [[Badness]] (Sintel): 0.0892 | | [[Badness]] (Sintel): 0.0892 |
|
| |
| === 7-limit ===
| |
| Subgroup: 2.3.5.7
| |
|
| |
| Comma list: 250047/250000, {{monzo| -55 30 2 1 }}
| |
|
| |
| Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}
| |
|
| |
| Optimal tunings:
| |
| * WE: ~30375/28672 = 99.999866{{c}}, ~3/2 = 701.948670{{c}} (~32805/32768 = 1.949605{{c}})
| |
| * CWE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949698{{c}} (~32805/32768 = 1.949698{{c}})
| |
|
| |
| {{Optimal ET sequence|legend=0| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
| |
|
| |
| Badness (Sintel): 1.160
| |
|
| |
| === 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
| |
|
| |
|
| == Revopentic == | | == Revopentic == |