Horwell temperaments: Difference between revisions
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Discussed elsewhere are [[Hemimage temperaments|bisupermajor]], [[Kleismic family|countercata]], [[Mirkwai clan|eris]], [[Escapade family|escaped]], [[Hemimean clan|hemithirds]], [[Diaschismic family|keen]], [[Semicomma family|orwell]], [[Amity family|paramity]], [[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]], [[Amity family|paramity]], [[Schismatic family|pontiac]], [[Breedsmic temperaments|tertiaseptal]], and [[Würschmidt family|worschmidt]]. | ||
= Mutt = | == Mutt == | ||
{{Main|Mutt temperament}} | {{Main|Mutt temperament}} | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: {{monzo| -44 -3 21 }} | [[Comma list]]: {{monzo| -44 -3 21 }} | ||
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[[Badness]]: 0.162467 | [[Badness]]: 0.162467 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | |||
Comma list: 65625/65536, 250047/250000 | Comma list: 65625/65536, 250047/250000 | ||
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Badness: 0.028406 | Badness: 0.028406 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 4375/4356, 16384/16335 | Comma list: 441/440, 4375/4356, 16384/16335 | ||
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Badness: 0.058344 | Badness: 0.058344 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 441/440, 625/624, 2200/2197 | Comma list: 364/363, 441/440, 625/624, 2200/2197 | ||
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Badness: 0.029089 | Badness: 0.029089 | ||
= Fifthplus = | == Fifthplus == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 420175/419904 | [[Comma list]]: 65625/65536, 420175/419904 | ||
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[[Badness]]: 0.025840 | [[Badness]]: 0.025840 | ||
= Emkay = | == Emkay == | ||
Emkay (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|emka temperament]] (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out. | Emkay (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|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 | [[Comma list]]: 65625/65536, 244140625/243045684 | ||
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[[Badness]]: 0.135696 | [[Badness]]: 0.135696 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 4000/3993, 65625/65536 | Comma list: 3025/3024, 4000/3993, 65625/65536 | ||
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Badness: 0.035586 | Badness: 0.035586 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197 | Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197 | ||
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Badness: 0.017853 | Badness: 0.017853 | ||
= Oquatonic = | == 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 temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28. | 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 temperaments|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 | [[Comma list]]: 65625/65536, 390625/388962 | ||