Horwell temperaments: Difference between revisions

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__FORCETOC__
Horwell temperaments temper out the horwell comma, {{monzo|-16 1 5 1}} = 65625/65536.
Horwell temperaments temper out the horwell comma, |-16 1 5 1> = 65625/65536.


Discussed elsewhere are [[Hemimage temperaments|bisupermajor]], [[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]].
Discussed elsewhere are [[Hemimage temperaments|bisupermajor]], [[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]].
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[[Comma list]]: {{monzo| -44 -3 21 }}
[[Comma list]]: {{monzo| -44 -3 21 }}


[[Mapping]]: [<3 5 7|, <0 -7 -1|]
[[Mapping]]: [{{val|3 5 7}}, {{val|0 -7 -1}}]


[[POTE tuning|POTE generator]]: ~5/4 = 385.980
[[POTE generator]]: ~5/4 = 385.980


{{Val list|legend=1| 84, 87, 171, 771, 942, 1113, 1284, 1455 }}
{{Val list|legend=1| 3, 84, 87, 171, 771, 942, 1113, 1284, 1455 }}


[[Badness]]: 0.162467
[[Badness]]: 0.162467
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Comma list: 65625/65536, 250047/250000
Comma list: 65625/65536, 250047/250000


POTE generator: ~5/4 = 385.964
Mapping: [{{val|3 5 7 8}}, {{val|0 -7 -1 12}}]


Mapping: [<3 5 7 8|, <0 -7 -1 12|]
{{Multival|legend=1|21 3 -36 -44 -116 -92}}


Wedgie: <<21 3 -36 -44 -116 -92||
POTE generator: ~5/4 = 385.964


Vals: {{Val list| 84, 87, 171 }}
Vals: {{Val list| 3, 84, 87, 171 }}


Badness: 0.028406
Badness: 0.028406
Line 32: Line 31:
== 11-limit ==
== 11-limit ==
Comma list: 441/440, 4375/4356, 16384/16335
Comma list: 441/440, 4375/4356, 16384/16335
Mapping: [{{val|3 5 7 8 10}}, {{val|0 -7 -1 12 11}}]


POTE generator: ~5/4 = 386.020
POTE generator: ~5/4 = 386.020


Mapping: [<3 5 7 8 10|, <0 -7 -1 12 11|]
Vals: {{Val list| 3, 84, 87, 171, 258, 429e }}
 
Vals: {{Val list| 84, 87, 171, 258, 429e }}


Badness: 0.058344
Badness: 0.058344
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== 13-limit ==
== 13-limit ==
Comma list: 364/363, 441/440, 625/624, 2200/2197
Comma list: 364/363, 441/440, 625/624, 2200/2197
Mapping: [{{val|3 5 7 8 10 11}}, {{val|0 -7 -1 12 11 3}}]


POTE generator: ~5/4 = 386.022
POTE generator: ~5/4 = 386.022


Mapping: [<3 5 7 8 10 11|, <0 -7 -1 12 11 3|]
Vals: {{Val list| 3, 84, 87, 171, 258, 429ef }}
 
Vals: {{Val list| 84, 87, 171, 258, 429ef }}


Badness: 0.029089
Badness: 0.029089
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[[Comma list]]: 65625/65536, 420175/419904
[[Comma list]]: 65625/65536, 420175/419904


[[POTE tuning|POTE generator]]: ~5488/3645 = 708.774
[[Mapping]]: [{{val|1 11 -3 20}}, {{val|0 -23 13 -42}}]


[[Mapping]]: [<1 11 -3 20|, <0 -23 13 -42|]
{{Multival|legend=1|23 -13 42 -74 2 134}}


[[Wedgie]]: <<23 -13 42 -74 2 134||
[[POTE generator]]: ~5488/3645 = 708.774


{{Val list|legend=1| 22, 149, 171, 1903c, 2074c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd }}
{{Val list|legend=1| 22, 149, 171, 1903c, 2074c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd }}
Line 66: Line 65:


= Emkay =
= Emkay =
{{See also|Hemimean clan#Emka}}
Emkay (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|emka temperament]] (37&50), but with rather the horwell (65625/65536) than the hemimean (3136/3125) tempered out.


[[Comma list]]: 65625/65536, 244140625/243045684
[[Comma list]]: 65625/65536, 244140625/243045684


[[POTE tuning|POTE generator]]: ~3125/2268 = 551.7745
[[Mapping]]: [{{val|1 14 6 -28}}, {{val|0 -27 -8 67}}]


[[Mapping]]: [<1 14 6 -28|, <0 -27 -8 67|]
{{Multival|legend=1|27 8 -67 -50 -182 -178}}


[[Wedgie]]: <<27 8 -67 -50 -182 -178||
[[POTE generator]]: ~3125/2268 = 551.7745


{{Val list|legend=1| 87, 137, 224, 311, 535, 1381c, 1916c }}
{{Val list|legend=1| 87, 137, 224, 311, 535, 1381c, 1916c }}
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== 11-limit ==
== 11-limit ==
Comma list: 3025/3024, 4000/3993, 65625/65536
Comma list: 3025/3024, 4000/3993, 65625/65536
Mapping: [{{val|1 14 6 -28 3}}, {{val|0 -27 -8 67 1}}]


POTE generator: ~11/8 = 551.7746
POTE generator: ~11/8 = 551.7746
Mapping: [<1 14 6 -28 3|, <0 -27 -8 67 1|]


Vals: {{Val list| 87, 137, 224, 311, 535, 1381ce, 1916ce }}
Vals: {{Val list| 87, 137, 224, 311, 535, 1381ce, 1916ce }}
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== 13-limit ==
== 13-limit ==
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
Mapping: [{{val|1 14 6 -28 3 6}}, {{val|0 -27 -8 67 1 -5}}]


POTE generator: ~11/8 = 551.7749
POTE generator: ~11/8 = 551.7749
Mapping: [<1 14 6 -28 3 6|, <0 -27 -8 67 1 -5|]


Vals: {{Val list| 87, 137, 224, 311, 535, 1916cef, 2451cceff, 2986cceeff }}
Vals: {{Val list| 87, 137, 224, 311, 535, 1916cef, 2451cceff, 2986cceeff }}
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[[Comma list]]: 65625/65536, 390625/388962
[[Comma list]]: 65625/65536, 390625/388962


[[POTE tuning|POTE generator]]: ~126/125 = 16.3994
[[Mapping]]: [{{val|28 44 65 79}}, {{val|0 1 0 -1}}]


[[Mapping]]: [<28 44 65 79|, <0 1 0 -1|]
{{Multival|legend=1|28 0 -28 -65 -123 -65}}


[[Wedgie]]: <<28 0 -28 -65 -123 -65||
[[POTE generator]]: ~126/125 = 16.3994


{{Val list|legend=1| 28, 56, 84, 140, 224, 364, 588, 952 }}
{{Val list|legend=1| 28, 56, 84, 140, 224, 364, 588, 952 }}

Revision as of 10:17, 27 May 2021

Horwell temperaments temper out the horwell comma, [-16 1 5 1⟩ = 65625/65536.

Discussed elsewhere are bisupermajor, countercata, eris, escaped, hemithirds, keen, orwell, pontiac, tertiaseptal, and worschmidt.

Mutt

Main article: Mutt temperament

Comma list: [-44 -3 21⟩

Mapping: [⟨3 5 7], ⟨0 -7 -1]]

POTE generator: ~5/4 = 385.980

Template:Val list

Badness: 0.162467

7-limit

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

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

Mapping: [⟨1 11 -3 20], ⟨0 -23 13 -42]]

Wedgie: ⟨⟨ 23 -13 42 -74 2 134 ]]

POTE generator: ~5488/3645 = 708.774

Template:Val list

Badness: 0.025840

Emkay

Emkay (87&224) tempers out the same 5-limit comma as the emka temperament (37&50), but with rather the horwell (65625/65536) than the hemimean (3136/3125) tempered out.

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

Template:Val list

Badness: 0.135696

11-limit

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

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

Oquatonic

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

Template:Val list

Badness: 0.088286

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