Horwell temperaments: Difference between revisions
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Temperaments discussed elsewhere are | Temperaments discussed elsewhere are | ||
* ''[[ | * [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac|Schismatic family]] | ||
* ''[[Keen]]'' (+875/864) → [[Diaschismic family #Keen|Diaschismic family]] | |||
* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #Paramity|Amity family]] | |||
* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata|Kleismic family]] | |||
* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]] | |||
* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt|Würschmidt family]] | * ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt|Würschmidt family]] | ||
* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped|Escapade family]] | * ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped|Escapade family]] | ||
* ''[[ | * ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila|Mabila family]] | ||
* ''[[ | * ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana|Vishnu family]] | ||
* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds|Hemimean clan]] | * [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds|Hemimean clan]] | ||
* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor|Hemimage temperaments]] | * ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor|Hemimage temperaments]] | ||
* ''[[ | * ''[[Maquiloid]]'' (+686/675) → [[Maquila family #Maquiloid|Maquila family]] | ||
* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom|Vavoom family]] | * ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom|Vavoom family]] | ||
* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal|Breedsmic temperaments]] | |||
* ''[[Eris]]'' (+16875/16807) → [[Canopic clan #Eris|Canopic clan]] | |||
* ''[[Soviet ferris wheel]]'' (+{{monzo| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel|20th-octave temperaments]] | * ''[[Soviet ferris wheel]]'' (+{{monzo| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel|20th-octave temperaments]] | ||
Considered below are fifthplus, mutt, oquatonic, emkay, kastro, and bezique, in the order of increasing [[badness]]. | |||
== Fifthplus == | |||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sesesix]].'' | |||
Fifthplus tempers out the [[wizma]] in addition to the horwell comma, and may be described as the {{nowrap| 22 & 171 }}. The name ''fifthplus'' means using a sharp fifth interval (such as a [[superpyth]] fifth) as a generator. It is a restriction of [[24576/24565 #2.3.5.7.17 subgroup (prime archagall)|prime archagall]]. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 420175/419904 | |||
{{Mapping|legend=1| 1 -12 10 -22 | 0 23 -13 42 }} | |||
: mapping generators: ~2, ~5488/3645 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.0934{{c}}, ~5488/3645 = 708.8291{{c}} | |||
: [[error map]]: {{val| +0.093 -0.007 -0.158 -0.059 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5488/3645 = 708.7752{{c}} | |||
: error map: {{val| 0.000 -0.126 -0.391 -0.268 }} | |||
{{Optimal ET sequence|legend=1| 22, 149, 171, 1903c, 2074c, …, 3613ccd }} | |||
[[Badness]] (Sintel): 0.654 | |||
== Mutt == | == Mutt == | ||
{{Main| Mutt }} | {{Main| Mutt }} | ||
: ''For the 5-limit version, see [[Father–3 equivalence continuum #Mutt (5-limit)]].'' | |||
Mutt tempers out the [[landscape comma]] in addition to the horwell comma, and may be described as the {{nowrap| 84 & 87 }} temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Badness (Sintel): 1.20 | Badness (Sintel): 1.20 | ||
== | == Oquatonic == | ||
: ''For the 5-limit version, see [[ | : ''For the 5-limit version, see [[28th-octave temperaments #Oquatonic (5-limit)]].'' | ||
Oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the [[dimcomp comma]] (390625/388962). In this temperament, the [[5/4]] major third is mapped to 9\28. | |||
The name ''oquatonic'' was given by [[Petr Pařízek]] in 2011 as an abbreviation of the Italian [[wiktionary: ottantaquatro|''ottantaquatro'' ("eighty-four")]]<ref name="petr's long post"/>. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 65625/65536, | [[Comma list]]: 65625/65536, 390625/388962 | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 28 0 65 123 | 0 1 0 -1 }} | ||
: mapping generators: ~ | : mapping generators: ~128/125, ~3 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~ | * [[WE]]: ~128/125 = 42.8570{{c}}, ~3/2 = 702.1112{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| -0.004 +0.152 -0.609 +0.477 }} | ||
* [[CWE]]: ~ | * [[CWE]]: ~128/125 = 42.8571{{c}}, ~3/2 = 702.1132{{c}} | ||
: error map: {{val| 0.000 -0. | : error map: {{val| 0.000 +0.158 -0.599 +0.489 }} | ||
{{Optimal ET sequence|legend=1| 28, 56, 84, 140, 224, 364, 588, 952 }} | |||
[[Badness]] (Sintel): 2.23 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 1375/1372, 6250/6237, 65625/65536 | |||
Mapping: {{mapping| 28 0 65 123 230 | 0 1 0 -1 -3 }} | |||
Optimal tunings: | |||
* WE: ~128/125 = 42.8577{{c}}, ~3/2 = 702.0275{{c}} | |||
* CWE: ~128/125 = 42.8571{{c}}, ~3/2 = 702.0174{{c}} | |||
{{Optimal ET sequence|legend=0| 84, 140, 224, 364, 588 }} | |||
Badness (Sintel): 1.58 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 625/624, 1375/1372, 2080/2079, 2200/2197 | |||
Mapping: {{mapping| 28 0 65 123 230 148 | 0 1 0 -1 -3 -1 }} | |||
Optimal tunings: | |||
* WE: ~40/39 = 42.8571{{c}}, ~3/2 = 702.0289{{c}} | |||
* CWE: ~40/39 = 42.8571{{c}}, ~3/2 = 702.0288{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 84, 140, 224, 364, 588 }} | ||
Badness (Sintel): 0.908 | |||
== Emkay == | == Emkay == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Emka]].'' | |||
[[File:Scale Tree Graph For Emkay.png|thumb|Scale tree graph for emkay.]] | [[File:Scale Tree Graph For Emkay.png|thumb|Scale tree graph for emkay.]] | ||
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== Kastro == | == Kastro == | ||
: ''For the 5-limit version, see [[Very high accuracy temperaments #Astro]].'' | : ''For the 5-limit version, see [[Very high accuracy temperaments #Astro]].'' | ||
Kastro may be described as the {{nowrap| 109 & 118 }} temperament, named by [[Petr Pařízek]] in 2011 as a variation of ''astro''<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Badness (Sintel): 1.93 | Badness (Sintel): 1.93 | ||
== Bezique == | == Bezique == | ||
Bezique splits the octave into 32 equal parts and reaches 3/2, 8/5 and 11/8 in just one generator with the 64-tone mos. | Bezique splits the octave into 32 equal parts and reaches 3/2, 8/5 and 11/8 in just one generator with the 64-tone mos. A notable edo tuning overshadowed by [[224edo]] is [[320edo]]. Bezique was named by [[Eliora]] in 2023 for the fact that the card game of bezique is played with two packs of 32 cards. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||