4L 3s/Temperaments: Difference between revisions

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-== Myna (27&31) ==
+== Myna ==
+Subgroup: 2.3.5.7
+[[Comma list]]: 126/125, 1728/1715
+[[Mapping]]: [{{val| 1 9 9 8 }}, {{val| 0 -10 -9 -7 }}]
+Mapping generators: ~2, ~5/3
+{{Multival|legend=1| 10 9 7 -9 -17 -9 }}
+[[POTE generator]]: ~6/5 = 310.146
+[[Minimax tuning]]:
+* 7- and [[9-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}]
+: [[Eigenmonzo]]s: 2, 3
+{{Val list|legend=1| 27, 31, 58, 89 }}
+[[Badness]]: 0.0270
 == Kleismic ==
 Subgroup: 2.3.5
@@ Line 16: / Line 37: @@
 {{Val list|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
-== Orgone (15&11, 2.7.11) ==
+== Orgone ==
 {{main|Orgone}}
 Commas:65536/65219
@@ Line 28: / Line 49: @@
 EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc
-== Sixix (18&25) ==
+== Dual-3 Sixix ==
-[[Sixix]] can be viewed as a [[dual-fifth temperaments|dual-fifth temperament]], i.e. a temperament on the 2.3+.3-.5 "subgroup" (3+ = sharp 3, 3- = flat 3):
+Subgroup: 2.3⁻.9.5
-* It has both a sharp fifth and a flat fifth but no near-just 3/2.
-* Combining the sharp fifth and the flat fifth yields a good approximation of 9/8; two 9/8's make a 5/4, so it tempers out 81/80 in the underlying 2.9.5 subgroup.
+Comma list: 81/80, {{monzo| 2 -3 0 1 }}
-* The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in [[porcupine]] harmony. Tempering out this comma leads to [[7edo]].
+Mapping: [{{val| 1 2 4 4 }}, {{val| 0 -2 -3 -6 }}]
+.9.5 POTE generator: 335.8409
+{{Val list|legend=1| 18, 25, 43 }}
+== Sixix ==
+Subgroup: 2.3.5
+Comma list: 3125/2916
+Mapping: [{{val| 1 3 4 }}, {{val| 0 -5 -6 }}]
+POTE generator: ~6/5 = 338.365
+{{Val list|legend=1| 7, 25, 32 }}
+Badness: 0.1531
 [[Category:Smitonic|T]]
 [[Category:Temperament]]