Wizard: Difference between revisions

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-'''Wizard''' is a half-octave [[marvel temperaments|marvel temperament]] that [[tempering out|tempers out]] the commas [[225/224]] and [[stearnsma|118098/117649]] in the [[7-limit]].
+'''Wizard''' is a half-octave [[regular temperament|temperament]] that [[tempering out|tempers out]] the commas [[225/224]] and [[stearnsma|118098/117649]] in the [[7-limit]]. 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]].
 See [[Marvel temperaments #Wizard]] for technical data.
+== Interval chain ==
+In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
+{| class="wikitable center-1 right-2 right-4"
+|-
+! rowspan="2" | #
+! colspan="2" | Period 0
+! colspan="2" | Period 1
+|-
+! Cents*
+! Approximate ratios
+! Cents*
+! Approximate ratios
+|-
+| 0
+| 0.00
+| '''1/1'''
+| 600.00
+| 17/12, 24/17
+|-
+| 1
+| 216.80
+| 17/15
+| 816.80
+| '''8/5'''
+|-
+| 2
+| 433.61
+| 9/7
+| 1033.61
+| 20/11
+|-
+| 3
+| 650.42
+| '''16/11'''
+| 50.42
+| 33/32, 36/35
+|-
+| 4
+| 867.22
+| 28/17, 33/20
+| 267.22
+| 7/6
+|-
+| 5
+| 1084.03
+| '''15/8''', 28/15
+| 484.03
+| 45/34
+|-
+| 6
+| 100.83
+| '''17/16''', 18/17
+| 700.83
+| '''3/2'''
+|-
+| 7
+| 317.64
+| 6/5
+| 917.64
+| 17/10
+|-
+| 8
+| 534.45
+| 34/25
+| 1134.45
+| 27/14, 48/25
+|-
+| 9
+| 751.25
+| 17/11
+| 151.25
+| 12/11
+|-
+| 10
+| 968.06
+| '''7/4'''
+| 368.06
+| 21/17
+|-
+| 11
+| 1184.86
+| 119/60, 135/68, 168/85, <br>175/88, 240/121
+| 584.86
+| 7/5
+|}
+<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning
 == Chords ==
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 |
 |}
-{{Stub}}
 [[Category:Wizard| ]] <!-- main article -->