Horwell temperaments: Difference between revisions

(9 intermediate revisions by 5 users not shown)

Line 1:

Horwell temperaments temper out the horwell comma, {{monzo|-16 1 5 1}} = 65625/65536.

Temperaments discussed elsewhere are

* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila|Mabila family]]

* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt|Würschmidt family]]

* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped|Escapade family]]

* ''[[Maquiloid]]'' (+686/675) → [[Maquila family #Maquiloid|Maquila family]]

* ''[[Keen]]'' (+875/864) → [[Diaschismic family #Keen|Diaschismic family]]

* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds|Hemimean clan]]

* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]

* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal|Breedsmic temperaments]]

* [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac|Schismatic family]]

* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata|Kleismic family]]

* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor|Hemimage temperaments]]

* ''[[Eris]]'' (+16875/16807) → [[Mirkwai clan #Eris|Mirkwai clan]]

* ''[[Narayana]]'' (+321489/320000) → [[Vishnuzmic family #Narayana|Vishnuzmic family]]

* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #Paramity|Amity family]]

* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom|Vavoom family]]

* ''[[Soviet ferris wheel]]'' (+{{monzo| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel|20th-octave temperaments]]

== Mutt ==

Line 26:

Line 43:

~~{{Multival|legend=1| 21 3 -36 -44 -116 -92 }}~~

[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~5/4 = 385.964 (~126/125 = 14.036)

Line 69:

Line 84:

~~{{Multival|legend=1| 23 -13 42 -74 2 134 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5488/3645 = 708.774

Line 86:

Line 99:

~~{{Multival|legend=1| 27 8 -67 -50 -182 -178 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3125/2268 = 551.7745

Line 120:

Line 131:

Badness: 0.017853

=== See also ===

* [[:File:Scale Tree Graph For Emkay.png]]

== Kastro ==

Line 163:

Line 177:

== Oquatonic ==

The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28.

: ''For the 5-limit version of this temperament, see [[28th-octave temperaments #Oquatonic (5-limit)]].''

The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28.

The name ''oquatonic'' was given by [[Petr Pařízek]] in 2011 as an abbreviation of the Italian [[wiktionary: ottantaquatro|''ottantaquatro'' ("eighty-four")]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.

[[Subgroup]]: 2.3.5.7

Line 172:

Line 190:

: mapping generators: ~128/125, ~3

~~{{Multival|legend=1| 28 0 -28 -65 -123 -65 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.1137

Line 249:

Line 265:

Badness: 0.0298

== Notes ==

[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Horwell temperaments| ]]

[[Category:Horwell| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
+{{Technical data page}}
 Horwell temperaments temper out the horwell comma, {{monzo|-16 1 5 1}} = 65625/65536.
-Discussed elsewhere are [[Hemimage temperaments|bisupermajor]], [[Kleismic family|countercata]], [[Mirkwai clan|eris]], [[Escapade family|escaped]], [[Hemimean clan|hemithirds]], [[Diaschismic family|keen]], [[Mabila family|mabila]], [[Maquila family|maquiloid]], [[Vishnuzmic family|narayana]], [[Semicomma family|orwell]], [[Amity family|paramity]], [[Schismatic family|pontiac]], [[Breedsmic temperaments|tertiaseptal]], [[Würschmidt family|worschmidt]], and [[soviet ferris wheel]].
+Temperaments discussed elsewhere are
+* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila|Mabila family]]
+* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt|Würschmidt family]]
+* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped|Escapade family]]
+* ''[[Maquiloid]]'' (+686/675) → [[Maquila family #Maquiloid|Maquila family]]
+* ''[[Keen]]'' (+875/864) → [[Diaschismic family #Keen|Diaschismic family]]
+* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds|Hemimean clan]]
+* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
+* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal|Breedsmic temperaments]]
+* [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac|Schismatic family]]
+* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata|Kleismic family]]
+* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor|Hemimage temperaments]]
+* ''[[Eris]]'' (+16875/16807) → [[Mirkwai clan #Eris|Mirkwai clan]]
+* ''[[Narayana]]'' (+321489/320000) → [[Vishnuzmic family #Narayana|Vishnuzmic family]]
+* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #Paramity|Amity family]]
+* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom|Vavoom family]]
+* ''[[Soviet ferris wheel]]'' (+{{monzo| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel|20th-octave temperaments]]
 == Mutt ==
@@ Line 26: / Line 43: @@
 {{Mapping|legend=1| 3 5 7 8 | 0 -7 -1 12 }}
-{{Multival|legend=1| 21 3 -36 -44 -116 -92 }}
 [[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~5/4 = 385.964 (~126/125 = 14.036)
@@ Line 69: / Line 84: @@
 {{Mapping|legend=1| 1 11 -3 20 | 0 -23 13 -42 }}
-{{Multival|legend=1| 23 -13 42 -74 2 134 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5488/3645 = 708.774
@@ Line 86: / Line 99: @@
 {{Mapping|legend=1| 1 14 6 -28 | 0 -27 -8 67 }}
-{{Multival|legend=1| 27 8 -67 -50 -182 -178 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3125/2268 = 551.7745
@@ Line 120: / Line 131: @@
 Badness: 0.017853
+=== See also ===
+* [[:File:Scale Tree Graph For Emkay.png]]
 == Kastro ==
@@ Line 163: / Line 177: @@
 == Oquatonic ==
-The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28.
+: ''For the 5-limit version of this temperament, see [[28th-octave temperaments #Oquatonic (5-limit)]].''
+The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28.
+The name ''oquatonic'' was given by [[Petr Pařízek]] in 2011 as an abbreviation of the Italian [[wiktionary: ottantaquatro|''ottantaquatro'' ("eighty-four")]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
 [[Subgroup]]: 2.3.5.7
@@ Line 172: / Line 190: @@
 : mapping generators: ~128/125, ~3
-{{Multival|legend=1| 28 0 -28 -65 -123 -65 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.1137
@@ Line 249: / Line 265: @@
 Badness: 0.0298
+== Notes ==
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Horwell temperaments| ]] <!-- main article -->
 [[Category:Horwell| ]] <!-- key article -->
 [[Category:Rank 2]]