Wizard
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 |