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
+[[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 (unchanged-intervals): 2, 3
+{{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}
+[[Badness]]: 0.0270
 == Kleismic ==
 Subgroup: 2.3.5
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 [[Tuning ranges]]:
-* valid range: [300.000, 327.273] (4 to 11b)
+* [[diamond monotone]] range: [300.000, 327.273] (4 to 11b)
-* nice range: [315.641, 317.263]
+* [[diamond tradeoff]] range: [315.641, 317.263]
-* strict range: [315.641, 317.263]
+* diamond monotone and tradeoff range: [315.641, 317.263]
-{{Val list|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
+{{Optimal ET sequence|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
-== Orgone (15&11, 2.7.11) ==
+== Orgone ==
 {{main|Orgone}}
 Commas:65536/65219
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 POTE generator: ~77/64 = 323.372
-Sval map: [&lt;1 2 4|, &lt;0 3 -2|]
+Sval mapping: [&lt;1 2 4|, &lt;0 3 -2|]
+EDOs: {{EDOs|7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc}}
+== Dual-3 Sixix ==
+Subgroup: 2.3⁻.9.5
+Comma list: 81/80, {{monzo| 2 -3 0 1 }}
+Mapping: [{{val| 1 2 4 4 }}, {{val| 0 -2 -3 -6 }}]
+.9.5 POTE generator: 335.8409
+{{Optimal ET sequence|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
+{{Optimal ET sequence|legend=1| 7, 25, 32 }}
-EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc
+Badness: 0.1531
-== Sixix (18&25) ==
-[[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):
-* 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.
-* 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]].
 [[Category:Smitonic|T]]
-[[Category:Temperament]]
+[[Category:Lists of temperaments]]