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	15/11	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

Main article: Chords of wizard

Scales

• Wizard22

Tunings

Tuning spectrum

Edo generator	Eigenmonzo (unchanged-interval)*	Generator (¢)	Comments
	5/4	213.686
	17/14	215.968
9\50		216.000	Lower bound of 9- and 11-odd-limit, 11-limit 15-odd-limit, and 2.3.5.7.11.17-subgroup 17-odd-limit diamond monotone
	15/14	216.111
	11/8	216.227
22\122		216.393	122g val
	17/9	216.492
	5/3	216.520	5-odd-limit minimax
	21/17	216.583
	7/5	216.592	7-odd-limit minimax
13\72		216.667	Lower bound of 2.3.5.7.11.17-subgroup 21-odd-limit diamond monotone
	17/15	216.687
	7/6	216.718
	9/5	216.738	9- and 11-odd-limit minimax
	11/7	216.731
	21/20	216.733
	11/6	216.737
	11/9	216.839
30\166		216.867	166g val
	7/4	216.883
	21/16	216.924
	17/10	216.949
	3/2	216.993
17\94		217.021
	17/11	217.071
	15/11	217.119
	17/16	217.493
	11/10	217.498
	9/7	217.542
	15/8	217.654
4\22		218.182	Upper bound of 9- and 11-odd-limit, 11-limit 15-odd-limit, and 2.3.5.7.11.17-subgroup 17- and 21-odd-limit diamond monotone

* Besides the octave