# Chords of harry

Below are listed the dyadic chords of 11-limit harry temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismicmic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.

The normal mapping for harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. 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.

Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for jove temperament rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below.

 Number Chord Transversal Type Complexity 1 0-201-401 1-9/7-7/6 swetismic 8 2 0-202-401 1-20/11-7/6 swetismic 8 3 0-202-501 1-20/11-10/9 utonal 10 4 0-301-501 1-11/9-10/9 otonal 10 5 0-201-502 1-9/7-11/7 otonal 10 6 0-301-502 1-11/9-11/7 utonal 10 7 0-201-602 1-9/7-3/2 utonal 12 8 0-301-602 1-11/9-3/2 rastmic 12 9 0-401-602 1-7/6-3/2 otonal 12 10 0-201-702 1-9/7-10/7 otonal 14 11 0-202-702 1-20/11-10/7 utonal 14 12 0-301-702 1-11/9-10/7 swetismic 14 13 0-401-702 1-7/6-10/7 swetismic 14 14 0-501-702 1-10/9-10/7 utonal 14 15 0-502-702 1-11/7-10/7 otonal 14 16 0-201-903 1-9/7-11/6 swetismic 18 17 0-301-903 1-11/9-11/6 utonal 18 18 0-401-903 1-7/6-11/6 otonal 18 19 0-502-903 1-11/7-11/6 utonal 18 20 0-602-903 1-3/2-11/6 otonal 18 21 0-702-903 1-10/7-11/6 swetismic 18 22 0-301-1003 1-11/9-7/4 werckismic 20 23 0-401-1003 1-7/6-7/4 utonal 20 24 0-501-1003 1-10/9-7/4 werckismic 20 25 0-502-1003 1-11/7-7/4 werckismic 20 26 0-602-1003 1-3/2-7/4 otonal 20 27 0-702-1003 1-10/7-7/4 werckismic 20 28 0-202-1103 1-20/11-5/3 utonal 22 29 0-401-1103 1-7/6-5/3 otonal 22 30 0-501-1103 1-10/9-5/3 utonal 22 31 0-602-1103 1-3/2-5/3 otonal 22 32 0-702-1103 1-10/7-5/3 utonal 22 33 0-903-1103 1-11/6-5/3 otonal 22 34 0-201-1202 1-9/7-9/8 utonal 24 35 0-301-1202 1-11/9-9/8 rastmic 24 36 0-502-1202 1-11/7-9/8 werckismic 24 37 0-602-1202 1-3/2-9/8 ambitonal 24 38 0-702-1202 1-10/7-9/8 werckismic 24 39 0-903-1202 1-11/6-9/8 rastmic 24 40 0-1003-1202 1-7/4-9/8 otonal 24 41 0-301-1503 1-11/9-11/8 utonal 30 42 0-502-1503 1-11/7-11/8 utonal 30 43 0-602-1503 1-3/2-11/8 otonal 30 44 0-903-1503 1-11/6-11/8 utonal 30 45 0-1003-1503 1-7/4-11/8 otonal 30 46 0-1202-1503 1-9/8-11/8 otonal 30 47 0-202-1703 1-20/11-5/4 utonal 34 48 0-501-1703 1-10/9-5/4 utonal 34 49 0-602-1703 1-3/2-5/4 otonal 34 50 0-702-1703 1-10/7-5/4 utonal 34 51 0-1003-1703 1-7/4-5/4 otonal 34 52 0-1103-1703 1-5/3-5/4 utonal 34 53 0-1202-1703 1-9/8-5/4 otonal 34 54 0-1503-1703 1-11/8-5/4 otonal 34