Very high accuracy temperaments: Difference between revisions

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 == 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
@@ Line 412: / Line 410: @@
 [[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 ==
@@ Line 521: / Line 489: @@
 = Rank-3 temperaments =
+== Akjaysmic ==
+{{See also| Akjaysma }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: {{monzo| 47 -7 -7 -7 }}
+{{Mapping|legend=1| 7 0 0 47 | 0 1 0 -1 | 0 0 1 -1 }}
+: mapping generators: ~1157625/1048576, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~1157625/1048576 = 171.427811{{c}}, ~3/2 = 701.962313{{c}}, ~5/4 = 386.328628{{c}}
+: [[error map]]: {{val| -0.0053 +0.0020 +0.0043 +0.0062 }}
+* [[CWE]]: ~1157625/1048576 = 171.428571{{c}}, ~3/2 = 701.964859{{c}}, ~5/4 = 386.330310{{c}}
+: error map: {{val| 0.0000 +0.0099 +0.0166 +0.0218 }}
+{{Optimal ET sequence|legend=1| 140, 217, 224, 301, 441, 966, 1106, 1407, 1547, 1848, 2513, 2954, 6349, 9303, 11151, 14105, 17500, 20454 }}
+[[Badness]] (Sintel): 2.22
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 184549376/184528125, 199297406/199290375
+Mapping: {{mapping| 7 0 0 47 -168 | 0 1 0 -1 10 | 0 0 1 -1 5 }}
+: mapping generators: ~29160/26411, ~3, ~5
+Optimal tunings:
+* WE: ~29160/26411 = 171.427802{{c}}, ~3/2 = 701.964561{{c}}, ~5/4 = 386.329837{{c}}
+* CWE: ~29160/26411 = 171.428571{{c}}, ~3/2 = 701.967291{{c}}, ~5/4 = 386.331624{{c}}
+{{Optimal ET sequence|legend=0| 301, 441, 665e, 742, 1106, 1547, 1848, 3395, 4501, 5243, 6349, 17941, 24290, 30639, 45185cde, 63126bcde, 69475bccdde, 75824bccddee }}
+Badness (Sintel): 1.32
 == Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
 [[Subgroup]]: 2.3.5.7