Wizmic microtemperaments: Difference between revisions

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== Gariwizmic ==

Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just.

Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just. Unlike schismic, it finds 5/4 at the ''trans''diminished fourth (+45 fifths) minus a half pythagorean comma, or equivalently, at the ''trans''diminished octave (+39 fifths) minus a semioctave.

[[Subgroup]]: 2.3.5.7

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* WE: ~46305/32768 = 599.996, ~3/2 = 702.177

* mapping generators: ~46305/32768, ~3

* CWE: ~~~46305/32768~~ = ~~1\2~~, ~3/2 = ~~702~~.~~217~~

[[Optimal tuning|Optimal tunings]]:

* [[WE]]: ~2 = 599.996{{c}}, ~3/2 = 702.177{{c}}

: [[error map]]: {{val|-0.069, 0.153, -0.021, -0.053}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6512{{c}}

: error map: {{val|0.000 0.261 0.114 0.149}}

{{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}

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[[Badness]]: 2.225 (Sintel)

=== Cassawizmic ===

==== Cassawizmic ====

Subgroup: 2.3.5.7.11

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* WE: ~99/70 = 599.979, ~3/2 = 702.194

* mapping generators: ~99/70, ~3

* CWE: ~99/70 = 1\2, ~3/2 = 702.218

* WE: ~99/70 = 599.979, ~3/2 = 702.194 [[error map]]: {{val|-0.042 0.197 0.106 -0.001 -0.440}}

* CWE: ~99/70 = 1\2, ~3/2 = 702.218 [[error map]]: {{val|0.000 0.263 0.185 0.123 -0.306}}

{{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}

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[[Badness]]: 1.008 (Sintel)

==== ~~Subgroup: 2.3.5.7.11.~~13 ====

==== 13-limit ====

Comma list: [[2080/2079]], [[1716/1715]], [[4096/4095]], [[35035/34992]]

* WE: ~99/70 = 599.996, ~3/2 = 702.210

* mapping generators: ~99/70, ~3

[[Optimal tuning|Optimal tunings]]:

* WE: ~99/70 = 599.996, ~3/2 = 702.210 [[error map]]: {{val|-0.008 0.246 0.035 0.146 -0.412 -0.353}}

* CWE: ~99/70 = 1\2, ~3/2 = 702.215

* [[error map]]: {{val|-0.000 0.260 0.054 0.170 -0.383 -0.321}}

{{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}

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* WE: ~99/70 = 599.996, ~3/2 = 702.210

* mapping generators: ~99/70, ~3

* CWE: ~99/70 = 1\2, ~3/2 = 702.215

[[Optimal tuning|Optimal tunings]]:

* WE: ~99/70 = 599.996, ~3/2 = 702.210 [[error map]]: {{val|-0.006 0.250 0.057 0.147 -0.394 -0.355 -0.079}}

* CWE: ~99/70 = 1\2, ~3/2 = 702.215 [[error map]]: {{val|-0.000 0.260 0.070 0.165 -0.374 -0.332 -0.055}}

{{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}

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[[Badness]]: 0.655 (Sintel)

==== Androwizmic ====

[[Category:Temperament collections]]

[[Category:Wizmic microtemperaments| ]]

@@ Line 235: / Line 235: @@
 == Gariwizmic ==
-Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just.
+Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just. Unlike schismic, it finds 5/4 at the ''trans''diminished fourth (+45 fifths) minus a half pythagorean comma, or equivalently, at the ''trans''diminished octave (+39 fifths) minus a semioctave.
 [[Subgroup]]: 2.3.5.7
@@ Line 243: / Line 243: @@
 {{Mapping|legend=1| 2 2 -41 22|0 1 39 -14}}
-* WE: ~46305/32768 = 599.996, ~3/2 = 702.177
+* mapping generators: ~46305/32768, ~3
-* CWE: ~46305/32768 = 1\2, ~3/2 = 702.217
+[[Optimal tuning|Optimal tunings]]:
+* [[WE]]: ~2 = 599.996{{c}}, ~3/2 = 702.177{{c}}
+: [[error map]]: {{val|-0.069, 0.153, -0.021, -0.053}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6512{{c}}
+: error map: {{val|0.000 0.261 0.114 0.149}}
 {{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}
@@ Line 250: / Line 258: @@
 [[Badness]]: 2.225 (Sintel)
-=== Cassawizmic ===
+==== Cassawizmic ====
 Subgroup: 2.3.5.7.11
@@ Line 257: / Line 265: @@
 {{Mapping|legend=1| 2 2 -41 22 -20|0 1 39 -14 23}}
-* WE: ~99/70 = 599.979, ~3/2 = 702.194
+* mapping generators: ~99/70, ~3
-* CWE: ~99/70 = 1\2, ~3/2 = 702.218
+* WE: ~99/70 = 599.979, ~3/2 = 702.194 [[error map]]: {{val|-0.042 0.197 0.106 -0.001 -0.440}}
+* CWE: ~99/70 = 1\2, ~3/2 = 702.218 [[error map]]: {{val|0.000 0.263 0.185 0.123 -0.306}}
 {{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}
@@ Line 264: / Line 274: @@
 [[Badness]]: 1.008 (Sintel)
-==== Subgroup: 2.3.5.7.11.13 ====
+==== 13-limit ====
 Comma list: [[2080/2079]], [[1716/1715]], [[4096/4095]], [[35035/34992]]
 {{Mapping|legend=1| 2 2 -41 22 -20 39|0 1 39 -14 23 -27}}
-* WE: ~99/70 = 599.996, ~3/2 = 702.210
+* mapping generators: ~99/70, ~3
+[[Optimal tuning|Optimal tunings]]:
+* WE: ~99/70 = 599.996, ~3/2 = 702.210 [[error map]]: {{val|-0.008 0.246 0.035 0.146 -0.412 -0.353}}
 * CWE: ~99/70 = 1\2, ~3/2 = 702.215
+* [[error map]]: {{val|-0.000 0.260 0.054 0.170 -0.383 -0.321}}
 {{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}
@@ Line 281: / Line 295: @@
 {{Mapping|legend=1| 2 2 -41 22 -20 39|0 1 39 -14 23 -27}}
-* WE: ~99/70 = 599.996, ~3/2 = 702.210
+* mapping generators: ~99/70, ~3
-* CWE: ~99/70 = 1\2, ~3/2 = 702.215
+[[Optimal tuning|Optimal tunings]]:
+* WE: ~99/70 = 599.996, ~3/2 = 702.210 [[error map]]: {{val|-0.006 0.250 0.057 0.147 -0.394 -0.355 -0.079}}
+* CWE: ~99/70 = 1\2, ~3/2 = 702.215 [[error map]]: {{val|-0.000 0.260 0.070 0.165 -0.374 -0.332 -0.055}}
 {{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}
@@ Line 288: / Line 305: @@
 [[Badness]]: 0.655 (Sintel)
+==== Androwizmic ====
 [[Category:Temperament collections]]
 [[Category:Wizmic microtemperaments| ]] <!-- main article -->