Wizard - Revision history

FloraC: /* Chords and harmony */

2026-03-26T12:26:54Z

Chords and harmony

← Older revision		Revision as of 12:26, 26 March 2026
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	== Chords and harmony ==		== Chords and harmony ==
	{{~~Main~~\| Chords of wizard }}		{{See also\| Chords of wizard }}

	== Scales ==		== Scales ==

FloraC: + basic norm-based tunings

2026-03-26T12:26:09Z

+ basic norm-based tunings

@@ Line 108: / Line 108: @@
 <nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning, octave reduced
-== Chords ==
+== Chords and harmony ==
 {{Main| Chords of wizard }}
@@ Line 115: / Line 115: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"
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 <nowiki/>* Besides the octave
-== Notes ==
+== References ==
 [[Category:Wizard| ]] <!-- main article -->

FloraC: + infobox

2026-03-26T12:23:04Z

+ infobox

← Older revision		Revision as of 12:23, 26 March 2026
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			{{Infobox regtemp
			\| Title = Wizard
			\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.17
			\| Comma basis = [[225/224]], [[118098/117649]] (7-limit); <br>[[225/224]], [[385/384]], [[4000/3993]] (11-limit); <br>[[225/224]], [[289/288]], [[385/384]], [[561/560]]<br>(2.3.5.7.11.17)
			\| Edo join 1 = 22 \| Edo join 2 = 72
			\| Mapping = 2; 6 -1 10 -3 6
			\| Generators = 17/15 \| Generators tuning = 216.8 \| Optimization method = CWE
			\| MOS scales = [[6L 4s]], [[6L 10s]], [[6L 16s]], [[22L 6s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = 3.05 \| Complexity 1 = 28
			\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 3.05 \| Complexity 2 = 50
			}}
	'''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]].		'''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]].

Lériendil: Text replacement - "Eigenmonzo
(unchanged-interval)" to "Unchanged interval
(eigenmonzo)"

2025-06-21T06:55:56Z

Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"

← Older revision		Revision as of 06:55, 21 June 2025
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	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! [[Eigenmonzo\|~~Eigenmonzo~~<br>(~~unchanged-interval~~)]]*		! [[Eigenmonzo\|Unchanged interval<br>(eigenmonzo)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

FloraC: Expand a bit

2025-06-14T13:34:00Z

Expand a bit

← Older revision		Revision as of 13:34, 14 June 2025
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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>.		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 ==		== 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"		{\| class="wikitable center-1 right-2 right-4"
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	\| 7/5		\| 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 ==		== Chords ==

FloraC: + the earliest reference of this name that I can find

2025-06-14T13:20:11Z

+ the earliest reference of this name that I can find

← Older revision		Revision as of 13:20, 14 June 2025
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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]]. 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]].

			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>.

	See [[Marvel temperaments #Wizard]] for technical data.		See [[Marvel temperaments #Wizard]] for technical data.
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	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

			== Notes ==

	[[Category:Wizard\| ]] <!-- main article -->		[[Category:Wizard\| ]] <!-- main article -->

FloraC: - parent category

2025-04-28T14:50:16Z

- parent category

← Older revision		Revision as of 14:50, 28 April 2025
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	[[Category:Wizard\| ]] <!-- main article -->		[[Category:Wizard\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	~~[[Category:Temperaments]]~~
	[[Category:Marvel temperaments]]		[[Category:Marvel temperaments]]
	[[Category:Stearnsmic clan]]		[[Category:Stearnsmic clan]]

Lériendil at 00:08, 20 April 2025

2025-04-20T00:08:01Z

← Older revision		Revision as of 00:08, 20 April 2025
Line 264:		Line 264:

	[[Category:Wizard\| ]] <!-- main article -->		[[Category:Wizard\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Marvel temperaments]]		[[Category:Marvel temperaments]]
	[[Category:Stearnsmic clan]]		[[Category:Stearnsmic clan]]

FloraC: Expand

2025-02-01T09:04:31Z

Expand

← Older revision		Revision as of 09:04, 1 February 2025
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	'''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]].		'''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]].

	See [[Marvel temperaments #Wizard]] for technical data.		See [[Marvel temperaments #Wizard]] for technical data.

FloraC: /* Interval chain */ I missed a ratio

2025-01-27T12:28:54Z

Interval chain: I missed a ratio

← Older revision		Revision as of 12:28, 27 January 2025
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	\| 8		\| 8
	\| 534.45		\| 534.45
	\| 34/25		\| 15/11
	\| 1134.45		\| 1134.45
	\| 27/14, 48/25		\| 27/14, 48/25