Horwell temperaments: Difference between revisions

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

Temperaments discussed elsewhere are

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

* ''[[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]]

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

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

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

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

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

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

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Badness: 0.017853

=== See also ===

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

== Kastro ==

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== 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

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: mapping generators: ~128/125, ~3

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

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

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Badness: 0.0298

== Notes ==

[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Horwell temperaments| ]]

[[Category:Horwell| ]]

[[Category:Rank 2]]

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+{{Technical data page}}
 Horwell temperaments temper out the horwell comma, {{monzo|-16 1 5 1}} = 65625/65536.
 Temperaments discussed elsewhere are
-* ''[[Mabila]]'' (+49/48) → [[Mabila family #Septimal mabila|Mabila family]]
+* ''[[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]]
@@ Line 42: / 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 85: / 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 102: / 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 136: / Line 131: @@
 Badness: 0.017853
+=== See also ===
+* [[:File:Scale Tree Graph For Emkay.png]]
 == Kastro ==
@@ Line 179: / 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 188: / 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 265: / 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]]