# Chords of wizard

Below are listed the dyadic chords of 11-limit wizard temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.

The normal mapping for wizard is wiz = [<2 1 5 2 8|, <0 6 -1 10 -3|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a comma basis of 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.

Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

Wizard has MOS of size 6, 10, 16, 22, 28, 50 and 72. It may be seen that even ten notes supplies enough chords to be interesting, and that by the time we reach 22 we might feel we are pretty well supplied.

 Number Chord Transversal Type Complexity 1 0-101-200 1-8/5-9/7 marvel 4 2 0-101-300 1-8/5-16/11 utonal 6 3 0-201-300 1-20/11-16/11 otonal 6 4 0-101-399 1-8/5-7/6 keenanismic 8 5 0-200-399 1-9/7-7/6 swetismic 8 6 0-201-399 1-20/11-7/6 swetismic 8 7 0-300-399 1-16/11-7/6 keenanismic 8 8 0-200-599 1-9/7-3/2 utonal 12 9 0-399-599 1-7/6-3/2 otonal 12 10 0-101-698 1-8/5-6/5 otonal 14 11 0-599-698 1-3/2-6/5 utonal 14 12 0-201-897 1-20/11-12/11 otonal 18 13 0-300-897 1-16/11-12/11 otonal 18 14 0-599-897 1-3/2-12/11 utonal 18 15 0-698-897 1-6/5-12/11 utonal 18 16 0-101-998 1-8/5-7/4 keenanismic 20 17 0-300-998 1-16/11-7/4 keenanismic 20 18 0-399-998 1-7/6-7/4 utonal 20 19 0-599-998 1-3/2-7/4 otonal 20 20 0-698-998 1-6/5-7/4 keenanismic 20 21 0-897-998 1-12/11-7/4 keenanismic 20 22 0-101-1097 1-8/5-7/5 otonal 22 23 0-200-1097 1-9/7-7/5 swetismic 22 24 0-399-1097 1-7/6-7/5 utonal 22 25 0-698-1097 1-6/5-7/5 otonal 22 26 0-897-1097 1-12/11-7/5 swetismic 22 27 0-998-1097 1-7/4-7/5 utonal 22 28 0-101-1196 1-8/5-9/8 marvel 24 29 0-200-1196 1-9/7-9/8 utonal 24 30 0-599-1196 1-3/2-9/8 ambitonal 24 31 0-998-1196 1-7/4-9/8 otonal 24 32 0-1097-1196 1-7/5-9/8 marvel 24 33 0-201-1296 1-20/11-14/11 otonal 26 34 0-300-1296 1-16/11-14/11 otonal 26 35 0-399-1296 1-7/6-14/11 utonal 26 36 0-897-1296 1-12/11-14/11 otonal 26 37 0-998-1296 1-7/4-14/11 utonal 26 38 0-1097-1296 1-7/5-14/11 utonal 26 39 0-101-1297 1-8/5-9/5 otonal 26 40 0-200-1297 1-9/7-9/5 utonal 26 41 0-599-1297 1-3/2-9/5 utonal 26 42 0-698-1297 1-6/5-9/5 otonal 26 43 0-1097-1297 1-7/5-9/5 otonal 26 44 0-1196-1297 1-9/8-9/5 utonal 26 45 0-200-1496 1-9/7-18/11 utonal 30 46 0-201-1496 1-20/11-18/11 otonal 30 47 0-300-1496 1-16/11-18/11 otonal 30 48 0-399-1496 1-7/6-18/11 swetismic 30 49 0-599-1496 1-3/2-18/11 utonal 30 50 0-897-1496 1-12/11-18/11 otonal 30 51 0-1097-1496 1-7/5-18/11 swetismic 30 52 0-1196-1496 1-9/8-18/11 utonal 30 53 0-1296-1496 1-14/11-18/11 otonal 30 54 0-1297-1496 1-9/5-18/11 utonal 30