Horwell temperaments: Difference between revisions
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Horwell temperaments temper out the horwell comma, |-16 1 5 1> = 65625/65536. | Horwell temperaments temper out the horwell comma, |-16 1 5 1> = 65625/65536. | ||
Discussed elsewhere are [[Kleismic family|countercata]], [[Mirkwai clan|eris]], [[Escapade family|escaped]], [[Hemimean clan|hemithirds]], [[Diaschismic family|keen]], [[Semicomma family|orwell]], [[Schismatic family|pontiac]], [[Breedsmic temperaments|tertiaseptal]], and [[Würschmidt family|worschmidt]]. | |||
= Mutt = | = Mutt = | ||
{{Main|Mutt | {{Main|Mutt temperament}} | ||
[[Comma list]]: {{monzo| -44 -3 21 }} (the [[mutt comma]]) | [[Comma list]]: {{monzo| -44 -3 21 }} (the [[mutt comma]]) | ||
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Comma list: 65625/65536, 250047/250000 | Comma list: 65625/65536, 250047/250000 | ||
POTE generator: ~5/4 = 385.964 | |||
Mapping: [<3 5 7 8|, <0 -7 -1 12|] | Mapping: [<3 5 7 8|, <0 -7 -1 12|] | ||
Wedgie: <<21 3 -36 -44 -116 -92|| | |||
Vals: {{Val list| 84, 87, 171 }} | Vals: {{Val list| 84, 87, 171 }} | ||
Badness: 0.028406 | Badness: 0.028406 | ||
== 11-limit == | |||
Comma list: 441/440, 4375/4356, 16384/16335 | |||
Mapping: [<3 5 7 8 10|, <0 -7 -1 12 11|] | |||
POTE generator: ~5/4 = 386.020 | |||
Vals: {{Val list| 84, 87, 171, 258, 429e }} | |||
Badness: 0.058344 | |||
== 13-limit == | |||
Comma list: 364/363, 441/440, 625/624, 2200/2197 | |||
Mapping: [<3 5 7 8 10 11|, <0 -7 -1 12 11 3|] | |||
POTE generator: ~5/4 = 386.022 | |||
Vals: {{Val list| 84, 87, 171, 258, 429ef }} | |||
Badness: 0.029089 | |||
= Fifthplus = | = Fifthplus = | ||
Revision as of 11:49, 8 April 2021
Horwell temperaments temper out the horwell comma, |-16 1 5 1> = 65625/65536.
Discussed elsewhere are countercata, eris, escaped, hemithirds, keen, orwell, pontiac, tertiaseptal, and worschmidt.
Mutt
Comma list: [-44 -3 21⟩ (the mutt comma)
Mapping: [<3 5 7|, <0 -7 -1|]
POTE generator: ~5/4 = 385.980
Badness: 0.162467
7-limit
Comma list: 65625/65536, 250047/250000
POTE generator: ~5/4 = 385.964
Mapping: [<3 5 7 8|, <0 -7 -1 12|]
Wedgie: <<21 3 -36 -44 -116 -92||
Vals: Template:Val list
Badness: 0.028406
11-limit
Comma list: 441/440, 4375/4356, 16384/16335
Mapping: [<3 5 7 8 10|, <0 -7 -1 12 11|]
POTE generator: ~5/4 = 386.020
Vals: Template:Val list
Badness: 0.058344
13-limit
Comma list: 364/363, 441/440, 625/624, 2200/2197
Mapping: [<3 5 7 8 10 11|, <0 -7 -1 12 11 3|]
POTE generator: ~5/4 = 386.022
Vals: Template:Val list
Badness: 0.029089
Fifthplus
Comma list: 65625/65536, 420175/419904
POTE generator: ~5488/3645 = 708.774
Mapping: [<1 11 -3 20|, <0 -23 13 -42|]
Wedgie: <<23 -13 42 -74 2 134||
Badness: 0.025840
Emkay
Comma list: 65625/65536, 244140625/243045684
POTE generator: ~3125/2268 = 551.7745
Mapping: [<1 14 6 -28|, <0 -27 -8 67|]
Wedgie: <<27 8 -67 -50 -182 -178||
Badness: 0.135696
11-limit
Comma list: 3025/3024, 4000/3993, 65625/65536
POTE generator: ~11/8 = 551.7746
Mapping: [<1 14 6 -28 3|, <0 -27 -8 67 1|]
Vals: Template:Val list
Badness: 0.035586
13-limit
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
POTE generator: ~11/8 = 551.7749
Mapping: [<1 14 6 -28 3 6|, <0 -27 -8 67 1 -5|]
Vals: Template:Val list
Badness: 0.017853
Oquatonic
Comma list: 65625/65536, 390625/388962
POTE generator: ~126/125 = 16.3994
Mapping: [<28 44 65 79|, <0 1 0 -1|]
Wedgie: <<28 0 -28 -65 -123 -65||
Badness: 0.088286