Hewuermera temperaments: Difference between revisions
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'''Hewuermera''' rank | {{Technical data page}} | ||
'''Hewuermera''' [[rank two temperament]]s temper out the ''hewuermera'' comma, [[589824/588245]] = {{monzo|16 2 -1 -6}} (satribiru-agu), the amount by which a stack of six [[8/7]]s exceed 20/9 (minor whole tone [[10/9]] plus an octave). | |||
Full 7-limit temperaments discussed elsewhere are: | |||
* [[Meantone family # | * [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]] | ||
* [[ | * ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]] | ||
* [[ | * ''[[Slender]]'' (+225/224) → [[Marvel temperaments #Slender|Marvel temperaments]] | ||
* [[ | * ''[[Lemongrass]]'' (+245/243) → [[Buzzardsmic clan #Lemongrass|Buzzardsmic clan]] | ||
* [[ | * ''[[Hemiwürschmidt]]'' (+2401/2400) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]] | ||
* [[ | * ''[[Gamera]]'' (+4375/4374) → [[Ragismic microtemperaments #Gamera|Ragismic microtemperaments]] | ||
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]] | |||
* [[Hemifamity temperaments #Septiquarter| | * ''[[Eris]]'' (+16875/16807) → [[Mirkwai clan #Eris|Mirkwai clan]] | ||
* [[Mirkwai clan #Eris| | * ''[[Hemiquintile]]'' (+19683/19600) → [[Quintile family #Hemiquintile|Quintile family]] | ||
* [[26th-octave temperaments #Bosonic| | * ''[[Pogo]]'' (+32805/32768) → [[Schismatic family #Pogo|Schismatic family]] | ||
* ''[[Bosonic]]'' (+321489/320000) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]] | |||
== Hemidimfi == | == Hemidimfi == | ||
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[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Latest revision as of 00:43, 17 August 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
Hewuermera rank two temperaments temper out the hewuermera comma, 589824/588245 = [16 2 -1 -6⟩ (satribiru-agu), the amount by which a stack of six 8/7s exceed 20/9 (minor whole tone 10/9 plus an octave).
Full 7-limit temperaments discussed elsewhere are:
- Mothra (+81/80) → Meantone family
- Casablanca (+126/125) → Starling temperaments
- Slender (+225/224) → Marvel temperaments
- Lemongrass (+245/243) → Buzzardsmic clan
- Hemiwürschmidt (+2401/2400) → Hemimean clan
- Gamera (+4375/4374) → Ragismic microtemperaments
- Septiquarter (+5120/5103) → Hemifamity temperaments
- Eris (+16875/16807) → Mirkwai clan
- Hemiquintile (+19683/19600) → Quintile family
- Pogo (+32805/32768) → Schismatic family
- Bosonic (+321489/320000) → 26th-octave temperaments
Hemidimfi
The hemidimfi (130&193) has a generator of 304.6 cents (about a half of 64/45 tritone) and tempers out the hewuermera (589824/588245) and the breeze comma (2460375/2458624).
Subgroup: 2.3.5.7
Comma list: 589824/588245, 2460375/2458624
Mapping: [⟨1 -4 14 -1], ⟨0 22 -46 15]]
POTE generator: ~343/288 = 304.639
Optimal ET sequence: 63, 130, 323, 453, 776
Badness: 0.083491
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979, 16384/16335
Mapping: [⟨1 -4 14 -1 6], ⟨0 22 -46 15 -10]]
POTE generator: ~105/88 = 304.641
Optimal ET sequence: 63, 130, 193, 323e
Badness: 0.052236
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675, 4096/4095
Mapping: [⟨1 -4 14 -1 6 7], ⟨0 22 -46 15 -10 -13]]
POTE generator: ~105/88 = 304.639
Optimal ET sequence: 63, 130, 193, 323e, 453e, 776eef
Badness: 0.030433