Mitonismic temperaments: Difference between revisions

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These are rank-2 ~~temperaments~~ that temper out the mitonisma, 5250987/5242880 = {{monzo| -20 7 -1 4 }}.

These are [[rank-2 temperament]]s that temper out the mitonisma, 5250987/5242880 = {{monzo| -20 7 -1 4 }}.

== Meridic ==

Subgroup: 2.3.5.7

[[Comma list]]: 5250987/5242880, 2202927104/2197265625

[[Mapping]]: [{{val|43 ~~68 100 121~~}}, {{val|0 1 -1 -2}}]

[[Mapping]]: [{{val| 43 0 168 257 }}, {{val| 0 1 -1 -2 }}]

~~[[POTE generator]]~~: ~~~703125~~/~~702464 = 4.1632~~

Mapping generators: ~64/63, ~3

~~{{Val list|legend~~=~~1| 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd }}~~

[[POTE generator]]: ~3/2 = 701.8376

[[Badness]]: 0.~~230038~~

{{Optimal ET sequence|legend=1| 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd }}

[[Badness]] (Sintel): 5.822

=== 11-limit ===

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Comma list: 41503/41472, 172032/171875, 1240029/1239040

Mapping: [{{val|43 ~~68 100 121 148~~}}, {{val|0 1 -1 -2 5}}]

Mapping: [{{val| 43 0 168 257 -192 }}, {{val| 0 1 -1 -2 5 }}]

POTE generator: ~~~540~~/~~539~~ = 4.~~1828~~

POTE generator: ~3/2 = 701.8572

~~Vals:~~ {{~~Val list~~| 258, 301, 559, 860 }}

Badness: 0.~~111149~~

Badness (Sintel): 3.675

=== 13-limit ===

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Comma list: 2200/2197, 4096/4095, 21168/21125, 39366/39325

Mapping: [{{val|43 ~~68 100 121 148 159~~}}, {{val|0 1 -1 -2 5 1}}]

Mapping: [{{val| 43 0 168 257 -192 91 }}, {{val| 0 1 -1 -2 5 1 }}]

POTE generator: ~~~540~~/~~539~~ = 4.~~1765~~

POTE generator: ~3/2 = 701.8510

~~Vals:~~ {{~~Val list~~| 258, 301, 559, 860f }}

Badness: 0.~~071435~~

Badness (Sintel): 2.952

=== 17-limit ===

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Comma list: 833/832, 1701/1700, 2200/2197, 4096/4095, 11016/11011

Mapping: [{{val|43 ~~68 100 121 148 159 175~~}}, {{val|0 1 -1 -2 5 1 5}}]

Mapping: [{{val| 43 0 168 257 -192 91 -165 }}, {{val| 0 1 -1 -2 5 1 5 }}]

POTE generator: ~~~540~~/~~539~~ = 4.~~1974~~

POTE generator: ~3/2 = 701.8718

~~Vals:~~ {{~~Val list~~| 258, 301, 559, 860f }}

Badness: 0.~~047292~~

Badness (Sintel): 2.409

[[Category:Temperament]]

[[Category:Mitonismic temperaments| ]]

[[Category:~~Rank~~ 2]]

[[Category:Temperament collections]]

[[Category:Catalogs of rank-2 temperaments]]

@@ Line 1: / Line 1: @@
-These are rank-2 temperaments that temper out the mitonisma, 5250987/5242880 = {{monzo| -20 7 -1 4 }}.
+{{Technical data page}}
+These are [[rank-2 temperament]]s that temper out the mitonisma, 5250987/5242880 = {{monzo| -20 7 -1 4 }}.
-Temperaments dicussed elsewhere include [[Father family #Mother|mother]], [[Starling temperaments #Amigo|amigo]], [[Marvel temperaments #Merman|merman]], [[Gamelismic clan #Rodan|rodan]], [[Schismatic family #Sesquiquartififths|sesquiquartififths]], [[Hemimean clan #Arch|arch]], [[Minortonic family #Mitonic|mitonic]], [[Sensipent family #Bison|bison]], [[Hemimage temperaments #Cotoneum|cotoneum]], [[Horwell temperaments #Mutt|mutt]], [[Wizmic microtemperaments #Tokko|tokko]], and [[Pental family #Hemipental|hemipental]].
+Temperaments dicussed elsewhere include [[Father family #Mother|mother]], [[Starling temperaments #Amigo|amigo]], [[Marvel temperaments #Merman|merman]], [[Gamelismic clan #Rodan|rodan]], [[Schismatic family #Sesquiquartififths|sesquiquartififths]], [[Hemimean clan #Arch|arch]], [[Minortonic family #Mitonic|mitonic]], [[Sensipent family #Bison|bison]], [[Garischismic clan #Cotoneum|cotoneum]], [[Horwell temperaments #Mutt|mutt]], [[Wizmic microtemperaments #Tokko|tokko]], and [[Quintile family #Hemiquintile|hemiquintile]].
 == Meridic ==
+{{See also|43rd-octave temperaments#Meridic}}
 Subgroup: 2.3.5.7
 [[Comma list]]: 5250987/5242880, 2202927104/2197265625
-[[Mapping]]: [{{val|43 68 100 121}}, {{val|0 1 -1 -2}}]
+[[Mapping]]: [{{val| 43 0 168 257 }}, {{val| 0 1 -1 -2 }}]
-[[POTE generator]]: ~703125/702464 = 4.1632
+Mapping generators: ~64/63, ~3
-{{Val list|legend=1| 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd }}
+[[POTE generator]]: ~3/2 = 701.8376
-[[Badness]]: 0.230038
+{{Optimal ET sequence|legend=1| 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd }}
+[[Badness]] (Sintel): 5.822
 === 11-limit ===
@@ Line 21: / Line 25: @@
 Comma list: 41503/41472, 172032/171875, 1240029/1239040
-Mapping: [{{val|43 68 100 121 148}}, {{val|0 1 -1 -2 5}}]
+Mapping: [{{val| 43 0 168 257 -192 }}, {{val| 0 1 -1 -2 5 }}]
-POTE generator: ~540/539 = 4.1828
+POTE generator: ~3/2 = 701.8572
-Vals: {{Val list| 258, 301, 559, 860 }}
+{{Optimal ET sequence|legend=0| 258, 301, 559, 860 }}
-Badness: 0.111149
+Badness (Sintel): 3.675
 === 13-limit ===
@@ Line 34: / Line 38: @@
 Comma list: 2200/2197, 4096/4095, 21168/21125, 39366/39325
-Mapping: [{{val|43 68 100 121 148 159}}, {{val|0 1 -1 -2 5 1}}]
+Mapping: [{{val| 43 0 168 257 -192 91 }}, {{val| 0 1 -1 -2 5 1 }}]
-POTE generator: ~540/539 = 4.1765
+POTE generator: ~3/2 = 701.8510
-Vals: {{Val list| 258, 301, 559, 860f }}
+{{Optimal ET sequence|legend=0| 258, 301, 559, 860f }}
-Badness: 0.071435
+Badness (Sintel): 2.952
 === 17-limit ===
@@ Line 47: / Line 51: @@
 Comma list: 833/832, 1701/1700, 2200/2197, 4096/4095, 11016/11011
-Mapping: [{{val|43 68 100 121 148 159 175}}, {{val|0 1 -1 -2 5 1 5}}]
+Mapping: [{{val| 43 0 168 257 -192 91 -165 }}, {{val| 0 1 -1 -2 5 1 5 }}]
-POTE generator: ~540/539 = 4.1974
+POTE generator: ~3/2 = 701.8718
-Vals: {{Val list| 258, 301, 559, 860f }}
+{{Optimal ET sequence|legend=0| 258, 301, 559, 860f }}
-Badness: 0.047292
+Badness (Sintel): 2.409
-[[Category:Temperament]]
+[[Category:Mitonismic temperaments| ]] <!-- main article -->
-[[Category:Rank 2]]
+[[Category:Temperament collections]]
+[[Category:Catalogs of rank-2 temperaments]]

Mitonismic temperaments: Difference between revisions

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