Wizard: Difference between revisions
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'''Wizard''' is a half-octave [[ | '''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. | 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 == | == Chords == | ||
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| | | | ||
|} | |} | ||
[[Category:Wizard| ]] <!-- main article --> | [[Category:Wizard| ]] <!-- main article --> | ||
Revision as of 10:27, 27 January 2025
Wizard is a half-octave temperament that tempers out the commas 225/224 and 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.
| # | Period 0 | 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, 175/88, 240/121 |
584.86 | 7/5 |
* In 2.3.5.7.11.17-subgroup CWE tuning
Chords
Scales
Tunings
Tuning spectrum
| Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 9/7 | 382.458 | |
| 11/10 | 382.502 | |
| 3/2 | 383.007 | |
| 7/4 | 383.117 | |
| 11/9 | 383.161 | |
| 9/5 | 383.262 | 9- and 11-odd-limit minimax |
| 11/6 | 383.263 | |
| 11/7 | 383.269 | |
| 7/6 | 383.282 | |
| 7/5 | 383.408 | 7-odd-limit minimax |
| 5/3 | 383.480 | 5-odd-limit minimax |
| 11/8 | 383.773 | |
| 5/4 | 386.314 |