Hewuermera temperaments: Difference between revisions

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These are rank-two temperaments that temper out the ''hewuermera'' comma (named by [[User:Xenllium|Xenllium]]), 589824/588245 = {{monzo|16 2 -1 -6}}, the amount by which a stack of six [[8/7]]s exceed 20/9 (minor whole tone [[10/9]] plus an octave).
{{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).


Temperaments dicussed elsewhere include:  
Full 7-limit temperaments discussed elsewhere are:
* [[Meantone family #Cynder|Cynder]]
* [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]]
* [[Würschmidt family #Hemiwürschmidt|Hemiwürschmidt]]
* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
* [[Starling temperaments #Casablanca|Casablanca]]
* ''[[Slender]]'' (+225/224) → [[Marvel temperaments #Slender|Marvel temperaments]]
* [[Marvel temperaments #Slender|Slender]]
* ''[[Lemongrass]]'' (+245/243) → [[Buzzardsmic clan #Lemongrass|Buzzardsmic clan]]
* [[Ragismic microtemperaments #Gamera|Gamera]]
* ''[[Hemiwürschmidt]]'' (+2401/2400) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
* [[Hemifamity temperaments #Septiquarter|Septiquarter]]
* ''[[Gamera]]'' (+4375/4374) → [[Ragismic microtemperaments #Gamera|Ragismic microtemperaments]]
* [[Mirkwai clan #Eris|Eris]]
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* ''[[Eris]]'' (+16875/16807) → [[Mirkwai clan #Eris|Mirkwai clan]]
* ''[[Hemiquintile]]'' (+19683/19600) → [[Quintile family #Hemiquintile|Quintile family]]
* ''[[Pogo]]'' (+32805/32768) → [[Schismatic family #Pogo|Schismatic family]]
* ''[[Bosonic]]'' (+321489/320000) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]


[[Category:Temperament]]
== 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]]: [{{val|1 -4 14 -1}}, {{val|0 22 -46 15}}]
 
[[POTE generator]]: ~343/288 = 304.639
 
{{Optimal ET sequence|legend=1| 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: [{{val|1 -4 14 -1 6}}, {{val|0 22 -46 15 -10}}]
 
POTE generator: ~105/88 = 304.641
 
{{Optimal ET sequence|legend=1| 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: [{{val|1 -4 14 -1 6 7}}, {{val|0 22 -46 15 -10 -13}}]
 
POTE generator: ~105/88 = 304.639
 
{{Optimal ET sequence|legend=1| 63, 130, 193, 323e, 453e, 776eef }}
 
Badness: 0.030433
 
[[Category:Temperament collections]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 12:31, 27 November 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:

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

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