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 480: / Line 522: @@
 [[Badness]] (Sintel): 8.77
+== Aristoschismic ==
+Aristoschismic tempers out the [[aristoschisma]], which is the difference between the [[septischisma]] and the [[schisma]]. It sets the [[Pythagorean comma]] to the mean of the [[syntonic comma]] and the [[septimal comma]], so like [[orthoschismic]] and [[septischismic]], it functions as a [[detemperament]] of [[garibaldi]]. [[441edo]] shows an excellent example of an edo tuning (with the chain of fifths from [[147edo]]), but it can be tuned even more accurately than that.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: {{monzo| 40 -22 -1 -1 }}
+{{Mapping|legend=1| 1 0 0 40 | 0 1 0 -22 | 0 0 1 -1 }}
+: Mapping generators: ~2, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9738{{c}}, ~3/2 = 702.0173{{c}}, ~5/4 = 386.3696{{c}}
+: [[Error map]]: {{val| -0.026 +0.036 +0.004 +0.005 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0343{{c}}, ~5/4 = 386.3610{{c}}
+: Error map: {{val| 0.000 +0.079 +0.047 +0.058 }}
+{{Optimal ET sequence|legend=1| 41, 53, 94, …, 294, 306, 335, 347, 388, 400, 441, 935, 1376, 3193, 4087, 4528, 5463, 5904, 7280, 12743bcd, 13184bcd, 18647bbccdd }}
+[[Badness]] (Sintel): 11.2
 == Septimagic ==