Hewuermera temperaments: Difference between revisions

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'''Hewuermera''' rank-two temperaments temper out the ''hewuermera'' comma (satribiru-agu, 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]]
* [[Schismatic family #Pogo|Pogo]]
* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
* [[Würschmidt family #Hemiwürschmidt|Hemiwürschmidt]]
* ''[[Slender]]'' (+225/224) → [[Marvel temperaments #Slender|Marvel temperaments]]
* [[Pental family #Hemipental|Hemipental]]
* ''[[Lemongrass]]'' (+245/243) → [[Buzzardsmic clan #Lemongrass|Buzzardsmic clan]]
* [[Starling temperaments #Casablanca|Casablanca]]
* ''[[Hemiwürschmidt]]'' (+2401/2400) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
* [[Marvel temperaments #Slender|Slender]]
* ''[[Gamera]]'' (+4375/4374) → [[Ragismic microtemperaments #Gamera|Ragismic microtemperaments]]
* [[Ragismic microtemperaments #Gamera|Gamera]]
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* [[Hemifamity temperaments #Septiquarter|Septiquarter]]
* ''[[Eris]]'' (+16875/16807) → [[Mirkwai clan #Eris|Mirkwai clan]]
* [[Mirkwai clan #Eris|Eris]]
* ''[[Hemiquintile]]'' (+19683/19600) → [[Quintile family #Hemiquintile|Quintile family]]
* [[26th-octave temperaments #Bosonic|Bosonic]]
* ''[[Pogo]]'' (+32805/32768) → [[Schismatic family #Pogo|Schismatic family]]
* ''[[Bosonic]]'' (+321489/320000) → [[26th-octave temperaments #Bosonic|26th-octave temperaments]]


= Hemidimfi =
== Hemidimfi ==
The ''hemidimfi'' (130&193, named by [[User:Xenllium|Xenllium]]) has a generator of 304.6 cents (about a half of [[64/45]] tritone) and tempers out the hewuermera (589824/588245) and the sesquiquartisma (2460375/2458624).
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
Subgroup: 2.3.5.7
Line 24: Line 26:
[[POTE generator]]: ~343/288 = 304.639
[[POTE generator]]: ~343/288 = 304.639


{{Val list|legend=1| 63, 130, 323, 453, 776 }}
{{Optimal ET sequence|legend=1| 63, 130, 323, 453, 776 }}


[[Badness]]: 0.083491
[[Badness]]: 0.083491


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 37: Line 39:
POTE generator: ~105/88 = 304.641
POTE generator: ~105/88 = 304.641


Vals: {{Val list| 63, 130, 193, 323e }}
{{Optimal ET sequence|legend=1| 63, 130, 193, 323e }}


Badness: 0.052236
Badness: 0.052236


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 50: Line 52:
POTE generator: ~105/88 = 304.639
POTE generator: ~105/88 = 304.639


Vals: {{Val list| 63, 130, 193, 323e, 453e, 776eef }}
{{Optimal ET sequence|legend=1| 63, 130, 193, 323e, 453e, 776eef }}


Badness: 0.030433
Badness: 0.030433


[[Category:Temperament]]
[[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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