Miscellaneous 7-limit temperaments: Difference between revisions

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 See also [[Miscellaneous 5-limit temperaments]].
+== Wizmic ==
+Wizmic tempers out the [[wizma]], the sum of the two smallest [[superparticular ratio]]s in the 7-limit. It splits the [[septimal comma]] into two equal parts, which can serve as the last generator of this temperament, besides the [[octave]] and the [[3/2|perfect fifth]]. Adding a perfect fifth to this gives a [[245/162|sensamagic fifth]], which is the generator shown in the data below. Two sensamagic fifths minus an octave give [[~]][[8/7]], and five minus two octaves give a sub-octave short of the octave by a [[syntonic comma]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 420175/419904
+{{Mapping|legend=1| 1 0 3 0 | 0 1 4 0 | 0 0 5 -2 }}
+: Mapping generators: ~2, ~3, ~245/162
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0161{{c}}, ~3/2 = 701.9929{{c}}, ~245/162 = 715.6723{{c}}
+: [[Error map]]: {{val| +0.016 +0.054 -0.029 -0.106 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9981{{c}}, ~245/162 = 715.6543{{c}}
+: Error map: {{val| 0.000 +0.043 -0.050 -0.134 }}
+{{Optimal ET sequence|legend=1| 22, 27, 45, 49, 50, 72, 99, 171, 441, 612, 2812, 3082, 3253, 3424, 3694, 3865, 4306, 4777d, 4918d, 5089d, 5701d }}
+[[Badness]] (Sintel): 0.381
 == Breeze ==
+Breeze tempers out the [[breeze comma]] in the 7-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 45: / Line 67: @@
 [[Badness]] (Sintel): 0.661
-== Canopic a.k.a. mirkwai ==
+== Scheme ==
+Scheme tempers out the [[scheme comma]] in the 7-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 14348907/14336000
+{{Mapping|legend=1| 1 0 0 -14 | 0 1 0 15 | 0 0 1 -3 }}
+: Mapping generators: ~2, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0267{{c}}, ~3/2 = 701.8565{{c}}, ~5/4 = 386.2912{{c}}
+: [[Error map]]: {{val| +0.027 -0.072 +0.031 +0.015 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8494{{c}}, ~5/4 = 386.3135{{c}}
+: Error map: {{val| 0.000 -0.106 -0.000 -0.025 }}
+{{Optimal ET sequence|legend=1| 53, 111, 118, 171, 742, 795, 913, 966, 1137, 1308, 2050, 2221, 2392, 3358, 3529, 7229b, 10758bbd }}
+[[Badness]] (Sintel): 1.47
+== Canopic ==
 : ''For extensions, see [[Swetismic temperaments #Indra]].''
-Canopic, a.k.a. mirkwai, tempers out the [[canopic comma]] in the 7-limit.
+Canopic (formerly ''mirkwai'') tempers out the [[canopic comma]] in the 7-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 167: / Line 209: @@
 [[Projection pair]]: <code>5 2401/486</code> to 2.3.7
-== Schismean ==
+== Aberdietic ==
-Schismean tempers out the [[3645/3584|schismean comma]] in the 7-limit. It equates [[7/5]] with a stack of three [[9/8]]'s.
+Aberdietic tempers out the [[3645/3584|aberdiesis]] in the 7-limit. It equates [[7/5]] with a stack of three [[9/8]]'s.
 [[Subgroup]]: 2.3.5.7
@@ Line 181: / Line 223: @@
 * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.459{{c}}, ~5/4 = 383.104{{c}}
-{{Optimal ET sequence|legend=1| 5c, 7d, 12, 19, 31, 81 }}
+{{Optimal ET sequence|legend=1| 5c, 7d, 12, 19, 31, 81, 98c, 117c, 129c, 148bc, 160bc, 179bcd }}
 [[Badness]] (Sintel): 2.96
@@ Line 270: / Line 312: @@
 [[Badness]] (Sintel): 3.40
+== Triwellismic ==
+Triwellismic tempers out the [[triwellisma]]. Besides the [[octave]] and [[3/2|perfect fifth]], it is generated by a [[15/14]] semitone,  with six of them making a retroptolemaic fifth, [[243/160]], and seven making a septimal augmented fifth, [[729/448]]. An alternative generator is the [[10/7]] tritone, with two minus an octave giving the [[jubilisma]] and three jubilismas being equated with [[16/15]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 235298/234375
+{{Mapping|legend=1| 1 0 1 1 | 0 1 5 6 | 0 0 -6 -7 }}
+: Mapping generators: ~2, ~3, ~15/14
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9876{{c}}, ~3/2 = 701.3045{{c}}, ~15/14 = 120.5354{{c}}
+: [[Error map]]: {{val| -0.012 +0.031 +0.466 -0.584 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9958{{c}}, ~15/14 = 120.5308{{c}}
+: Error map: {{val| 0.000 +0.041 +0.480 -0.567 }}
+{{Optimal ET sequence|legend=1| 29, 31, 60, 68, 91, 99, 229, 289, 388, 518, 906 }}
+[[Badness]] (Sintel): 3.55
 == Decovulture ==
 : ''For extensions, see [[Olympic clan #Baffin]].''
+Decovulture tempers out the [[decovulture comma]] and splits the [[3/1|3rd harmonic]] into two semitwelfths, separated from ~[[7/4]] and ~[[12/7]] each by a [[diaschisma]].
 [[Subgroup]]: 2.3.5.7