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 }}.
{{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 ==
== Meridic ==
{{See also|43rd-octave temperaments#Meridic}}
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 5250987/5242880, 2202927104/2197265625
[[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 ===
=== 11-limit ===
Line 21: Line 25:
Comma list: 41503/41472, 172032/171875, 1240029/1239040
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 ===
=== 13-limit ===
Line 34: Line 38:
Comma list: 2200/2197, 4096/4095, 21168/21125, 39366/39325
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 ===
=== 17-limit ===
Line 47: Line 51:
Comma list: 833/832, 1701/1700, 2200/2197, 4096/4095, 11016/11011
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:Temperament collections]]
[[Category:Mitonismic temperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 03:23, 5 February 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

These are rank-2 temperaments that temper out the mitonisma, 5250987/5242880 = [-20 7 -1 4⟩.

Temperaments dicussed elsewhere include mother, amigo, merman, rodan, sesquiquartififths, arch, mitonic, bison, cotoneum, mutt, tokko, and hemiquintile.

Meridic

See also: 43rd-octave temperaments § Meridic

Subgroup: 2.3.5.7

Comma list: 5250987/5242880, 2202927104/2197265625

Mapping: [⟨43 0 168 257], ⟨0 1 -1 -2]]

Mapping generators: ~64/63, ~3

POTE generator: ~3/2 = 701.8376

Optimal ET sequence: 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd

Badness (Sintel): 5.822

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨43 0 168 257 -192], ⟨0 1 -1 -2 5]]

POTE generator: ~3/2 = 701.8572

Optimal ET sequence: 258, 301, 559, 860

Badness (Sintel): 3.675

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨43 0 168 257 -192 91], ⟨0 1 -1 -2 5 1]]

POTE generator: ~3/2 = 701.8510

Optimal ET sequence: 258, 301, 559, 860f

Badness (Sintel): 2.952

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨43 0 168 257 -192 91 -165], ⟨0 1 -1 -2 5 1 5]]

POTE generator: ~3/2 = 701.8718

Optimal ET sequence: 258, 301, 559, 860f

Badness (Sintel): 2.409

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