Horwell temperaments: Difference between revisions
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== Kastro == | |||
{{see also| Very high accuracy temperaments #Astro }} | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 117649/116640 | |||
[[Mapping]]: [{{val| 1 5 1 6 }}, {{val| 0 -31 12 -29 }}] | |||
[[POTE generator]]s: ~3375/3136 = 132.1845 | |||
{{Val list|legend=1| 109, 118, 345d }} | |||
[[Badness]]: 0.183 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 385/384, 3388/3375, 12005/11979 | |||
[[Mapping]]: [{{val| 1 5 1 6 5 }}, {{val| 0 -31 12 -29 -14 }}] | |||
[[POTE generator]]s: ~121/112 = 132.1864 | |||
{{Val list|legend=1| 109, 118, 345de, 463de, 581dde }} | |||
[[Badness]]: 0.0527 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 169/168, 364/363, 385/384, 3388/3375 | |||
[[Mapping]]: [{{val| 1 5 1 6 5 7 }}, {{val| 0 -31 12 -29 -14 -30 }}] | |||
[[POTE generator]]s: ~13/12 = 132.1789 | |||
{{Val list|legend=1| 109, 118f, 227f }} | |||
[[Badness]]: 0.0467 | |||
== Oquatonic == | == Oquatonic == | ||
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[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament collection]] | |||
[[Category:Horwell temperaments| ]] <!-- main article --> | [[Category:Horwell temperaments| ]] <!-- main article --> | ||
[[Category:Horwell]] | [[Category:Horwell]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 13:30, 25 August 2021
Horwell temperaments temper out the horwell comma, [-16 1 5 1⟩ = 65625/65536.
Discussed elsewhere are bisupermajor, countercata, eris, escaped, hemithirds, keen, orwell, paramity, pontiac, tertiaseptal, and worschmidt.
Mutt
Subgroup: 2.3.5
Comma list: [-44 -3 21⟩
Mapping: [⟨3 5 7], ⟨0 -7 -1]]
POTE generator: ~5/4 = 385.980
Badness: 0.162467
7-limit
Subgroup: 2.3.5.7
Comma list: 65625/65536, 250047/250000
Mapping: [⟨3 5 7 8], ⟨0 -7 -1 12]]
Wedgie: ⟨⟨ 21 3 -36 -44 -116 -92 ]]
POTE generator: ~5/4 = 385.964
Vals: Template:Val list
Badness: 0.028406
11-limit
Subgroup: 2.3.5.7.11
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
Subgroup: 2.3.5.7.11.13
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
Subgroup: 2.3.5.7
Comma list: 65625/65536, 420175/419904
Mapping: [⟨1 11 -3 20], ⟨0 -23 13 -42]]
Wedgie: ⟨⟨ 23 -13 42 -74 2 134 ]]
POTE generator: ~5488/3645 = 708.774
Badness: 0.025840
Emkay
Emkay (87&224) tempers out the same 5-limit comma as the emka temperament (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out.
Subgroup: 2.3.5.7
Comma list: 65625/65536, 244140625/243045684
Mapping: [⟨1 14 6 -28], ⟨0 -27 -8 67]]
Wedgie: ⟨⟨ 27 8 -67 -50 -182 -178 ]]
POTE generator: ~3125/2268 = 551.7745
Badness: 0.135696
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 65625/65536
Mapping: [⟨1 14 6 -28 3], ⟨0 -27 -8 67 1]]
POTE generator: ~11/8 = 551.7746
Vals: Template:Val list
Badness: 0.035586
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
Mapping: [⟨1 14 6 -28 3 6], ⟨0 -27 -8 67 1 -5]]
POTE generator: ~11/8 = 551.7749
Vals: Template:Val list
Badness: 0.017853
Kastro
Subgroup: 2.3.5.7
Comma list: 65625/65536, 117649/116640
Mapping: [⟨1 5 1 6], ⟨0 -31 12 -29]]
POTE generators: ~3375/3136 = 132.1845
Badness: 0.183
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 3388/3375, 12005/11979
Mapping: [⟨1 5 1 6 5], ⟨0 -31 12 -29 -14]]
POTE generators: ~121/112 = 132.1864
Badness: 0.0527
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 364/363, 385/384, 3388/3375
Mapping: [⟨1 5 1 6 5 7], ⟨0 -31 12 -29 -14 -30]]
POTE generators: ~13/12 = 132.1789
Badness: 0.0467
Oquatonic
The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the hemfiness (4096000/4084101, saquinru-atriyo). In this temperament, major third of 5/4 is mapped into 9\28.
Subgroup: 2.3.5.7
Comma list: 65625/65536, 390625/388962
Mapping: [⟨28 44 65 79], ⟨0 1 0 -1]]
Wedgie: ⟨⟨ 28 0 -28 -65 -123 -65 ]]
POTE generator: ~126/125 = 16.3994
Badness: 0.088286