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).

'''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

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[[POTE generator]]: ~343/288 = 304.639

[[Badness]]: 0.083491

== 11-limit ==

=== 11-limit ===

Subgroup: 2.3.5.7.11

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POTE generator: ~105/88 = 304.641

~~Vals:~~ {{~~Val list~~| 63, 130, 193, 323e }}

Badness: 0.052236

== 13-limit ==

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

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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

[[Category:Temperament]]

[[Category:Temperament collections]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-'''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&amp;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&amp;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
@@ Line 24: / Line 26: @@
 [[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
-== 11-limit ==
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 37: / Line 39: @@
 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
-== 13-limit ==
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 50: / Line 52: @@
 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
-[[Category:Temperament]]
+[[Category:Temperament collections]]
 [[Category:Rank 2]]