Wizard: Difference between revisions

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'''Wizard''' is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a wide whole tone of about 217 cents which is the semi-octave complement of [[~]][[5/4]]. Six generators minus a semi-octave represents [[3/2]], and ten generators minus a full octave represents [[7/4]], [[tempering out]] the commas [[225/224]] and [[stearnsma|118098/117649]]. It is most naturally viewed as a temperament of the 2.3.5.7.11.17 [[subgroup]], where it tempers out 225/224, [[289/288]], [[385/384]], and [[561/560]].

'''Wizard''' is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a wide whole tone of about 217 cents which is the semi-octave complement of [[~]][[5/4]]. Six generators minus a semi-octave represents [[3/2]], and ten generators minus a full octave represents [[7/4]], [[tempering out]] the commas [[225/224]] and [[stearnsma|118098/117649]].

Three generator steps may be identified with [[16/11]], and the generator itself is close in size to [[17/15]], which if used, would imply the semi-octave represents [[17/12]]~[[24/17]] and that [[17/16]] is obtained by stacking six generators [[octave reduction|octave reduced]]. As such, it is most naturally viewed as a temperament of the 2.3.5.7.11.17 [[subgroup]], where it tempers out 225/224, [[289/288]], [[385/384]], and [[561/560]].

[[72edo]], [[94edo]], and especially [[166edo]] are among the good tuning options.

The name ''wizard'' appeared as early as 2003, presumably given by [[Gene Ward Smith]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5279.html Yahoo! Tuning Group | ''Poptimal generators'']</ref>.

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== Interval chain ==

In the following table, odd harmonics and ~~subharmonics 1–21~~ are in '''bold'''.

In the following table, odd harmonics 1–21 and their inverses are in '''bold'''.

{| class="wikitable center-1 right-2 right-4"

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| 7/5

|}

<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning

<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning, octave reduced

== Chords ==

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-'''Wizard''' is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a wide whole tone of about 217 cents which is the semi-octave complement of [[~]][[5/4]]. Six generators minus a semi-octave represents [[3/2]], and ten generators minus a full octave represents [[7/4]], [[tempering out]] the commas [[225/224]] and [[stearnsma|118098/117649]]. It is most naturally viewed as a temperament of the 2.3.5.7.11.17 [[subgroup]], where it tempers out 225/224, [[289/288]], [[385/384]], and [[561/560]].
+'''Wizard''' is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a wide whole tone of about 217 cents which is the semi-octave complement of [[~]][[5/4]]. Six generators minus a semi-octave represents [[3/2]], and ten generators minus a full octave represents [[7/4]], [[tempering out]] the commas [[225/224]] and [[stearnsma|118098/117649]].
+Three generator steps may be identified with [[16/11]], and the generator itself is close in size to [[17/15]], which if used, would imply the semi-octave represents [[17/12]]~[[24/17]] and that [[17/16]] is obtained by stacking six generators [[octave reduction|octave reduced]]. As such, it is most naturally viewed as a temperament of the 2.3.5.7.11.17 [[subgroup]], where it tempers out 225/224, [[289/288]], [[385/384]], and [[561/560]].
+[[72edo]], [[94edo]], and especially [[166edo]] are among the good tuning options.
 The name ''wizard'' appeared as early as 2003, presumably given by [[Gene Ward Smith]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5279.html Yahoo! Tuning Group | ''Poptimal generators'']</ref>.
@@ Line 6: / Line 10: @@
 == Interval chain ==
-In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
+In the following table, odd harmonics 1–21 and their inverses are in '''bold'''.
 {| class="wikitable center-1 right-2 right-4"
@@ Line 91: / Line 95: @@
 | 7/5
 |}
-<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning
+<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning, octave reduced
 == Chords ==