159th-octave temperaments: Difference between revisions

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== Aemic (rank-3) ==

''Aemic'', a shortening of aemilic ~~(see below)~~ tempers out the [[frameshift comma]] and the [[nexus comma]]. ~~Aemic is alternately defined by setting~~ the 2.3.11 ~~mapping~~ to that of 159edo and the rest ~~being~~ independent generators. On the patent val it is ~~supported~~ by first 10 multiples of 159edo.

''Aemic'', a shortening of [[mercator family #Aemillic|aemilic]], tempers out the [[frameshift comma]] and the [[nexus comma]]. It sets the [[2.3.11 subgroup]] to that of 159edo and the rest are independent generators. On the [[patent val]] it is [[support]]ed by first 10 multiples of 159edo.

[[Subgroup]]: 2.3.5.7.11

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: mapping generators: ~243/242 ~~= 1\159~~, ~5, ~7

: mapping generators: ~243/242, ~5, ~7

[[~~Support~~]]~~ing~~ [[ET]]s: {{~~EDOs~~| 159, 318, 477, 636, 795, 954, ~~1113, 1272~~, ~~1431~~, ~~1590~~ }}

[[Optimal tuning]]s:

* [[WE]]: ~243/242 = 7.5475{{c}}, ~5/4 = 386.2128{{c}}, ~7/4 = 968.7250{{c}}

: [[error map]]: {{val| +0.050 +0.012 -0.000 -0.000 -0.200 }}

* [[CWE]]: ~243/242 = 7.5472{{c}}, ~5/4 = 386.2259{{c}}, ~7/4 = 968.7197{{c}}

: error map: {{val| 0.000 -0.068 -0.088 -0.106 -0.375 }}

{{Optimal ET sequence|legend=1| 159, 318, 477(c), 636, 795, 954, 1749e, 2703e, 3657ee }}

[[Badness]] (Sintel): 71.2

@@ Line 9: / Line 9: @@
 == Aemic (rank-3) ==
-''Aemic'', a shortening of aemilic (see below) tempers out the [[frameshift comma]] and the [[nexus comma]]. Aemic is alternately defined by setting the 2.3.11 mapping to that of 159edo and the rest being independent generators. On the patent val it is supported by first 10 multiples of 159edo.
+''Aemic'', a shortening of [[mercator family #Aemillic|aemilic]], tempers out the [[frameshift comma]] and the [[nexus comma]]. It sets the [[2.3.11 subgroup]] to that of 159edo and the rest are independent generators. On the [[patent val]] it is [[support]]ed by first 10 multiples of 159edo.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 16: / Line 16: @@
 {{Mapping|legend=1| 159 252 0 0 550 | 0 0 1 0 0 | 0 0 0 1 0 }}
-: mapping generators: ~243/242 = 1\159, ~5, ~7
+: mapping generators: ~243/242, ~5, ~7
-[[Support]]ing [[ET]]s: {{EDOs| 159, 318, 477, 636, 795, 954, 1113, 1272, 1431, 1590 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~243/242 = 7.5475{{c}}, ~5/4 = 386.2128{{c}}, ~7/4 = 968.7250{{c}}
+: [[error map]]: {{val| +0.050 +0.012 -0.000 -0.000 -0.200 }}
+* [[CWE]]: ~243/242 = 7.5472{{c}}, ~5/4 = 386.2259{{c}}, ~7/4 = 968.7197{{c}}
+: error map: {{val| 0.000 -0.068 -0.088 -0.106 -0.375 }}
+{{Optimal ET sequence|legend=1| 159, 318, 477(c), 636, 795, 954, 1749e, 2703e, 3657ee }}
+[[Badness]] (Sintel): 71.2
 {{Navbox fractional-octave}}