Harry/Chords
(Redirected from 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.
Triads
| 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 |
Tetrads
| Number | Chord | Transversal | Type | Complexity |
| 1 | 0-201-401-602 | 1-9/7-7/6-3/2 | swetismic | 12 |
| 2 | 0-201-401-702 | 1-9/7-7/6-10/7 | swetismic | 14 |
| 3 | 0-202-401-702 | 1-20/11-7/6-10/7 | swetismic | 14 |
| 4 | 0-202-501-702 | 1-20/11-10/9-10/7 | utonal | 14 |
| 5 | 0-301-501-702 | 1-11/9-10/9-10/7 | swetismic | 14 |
| 6 | 0-201-502-702 | 1-9/7-11/7-10/7 | otonal | 14 |
| 7 | 0-301-502-702 | 1-11/9-11/7-10/7 | swetismic | 14 |
| 8 | 0-201-401-903 | 1-9/7-7/6-11/6 | swetismic | 18 |
| 9 | 0-201-502-903 | 1-9/7-11/7-11/6 | swetismic | 18 |
| 10 | 0-301-502-903 | 1-11/9-11/7-11/6 | utonal | 18 |
| 11 | 0-201-602-903 | 1-9/7-3/2-11/6 | swetismic | 18 |
| 12 | 0-301-602-903 | 1-11/9-3/2-11/6 | rastmic | 18 |
| 13 | 0-401-602-903 | 1-7/6-3/2-11/6 | otonal | 18 |
| 14 | 0-201-702-903 | 1-9/7-10/7-11/6 | swetismic | 18 |
| 15 | 0-301-702-903 | 1-11/9-10/7-11/6 | swetismic | 18 |
| 16 | 0-401-702-903 | 1-7/6-10/7-11/6 | swetismic | 18 |
| 17 | 0-502-702-903 | 1-11/7-10/7-11/6 | swetismic | 18 |
| 18 | 0-301-501-1003 | 1-11/9-10/9-7/4 | werckismic | 20 |
| 19 | 0-301-502-1003 | 1-11/9-11/7-7/4 | werckismic | 20 |
| 20 | 0-301-602-1003 | 1-11/9-3/2-7/4 | jove | 20 |
| 21 | 0-401-602-1003 | 1-7/6-3/2-7/4 | ambitonal | 20 |
| 22 | 0-301-702-1003 | 1-11/9-10/7-7/4 | jove | 20 |
| 23 | 0-401-702-1003 | 1-7/6-10/7-7/4 | jove | 20 |
| 24 | 0-501-702-1003 | 1-10/9-10/7-7/4 | werckismic | 20 |
| 25 | 0-502-702-1003 | 1-11/7-10/7-7/4 | werckismic | 20 |
| 26 | 0-202-401-1103 | 1-20/11-7/6-5/3 | swetismic | 22 |
| 27 | 0-202-501-1103 | 1-20/11-10/9-5/3 | utonal | 22 |
| 28 | 0-401-602-1103 | 1-7/6-3/2-5/3 | otonal | 22 |
| 29 | 0-202-702-1103 | 1-20/11-10/7-5/3 | utonal | 22 |
| 30 | 0-401-702-1103 | 1-7/6-10/7-5/3 | swetismic | 22 |
| 31 | 0-501-702-1103 | 1-10/9-10/7-5/3 | utonal | 22 |
| 32 | 0-401-903-1103 | 1-7/6-11/6-5/3 | otonal | 22 |
| 33 | 0-602-903-1103 | 1-3/2-11/6-5/3 | otonal | 22 |
| 34 | 0-702-903-1103 | 1-10/7-11/6-5/3 | swetismic | 22 |
| 35 | 0-201-502-1202 | 1-9/7-11/7-9/8 | werckismic | 24 |
| 36 | 0-301-502-1202 | 1-11/9-11/7-9/8 | jove | 24 |
| 37 | 0-201-602-1202 | 1-9/7-3/2-9/8 | utonal | 24 |
| 38 | 0-301-602-1202 | 1-11/9-3/2-9/8 | rastmic | 24 |
| 39 | 0-201-702-1202 | 1-9/7-10/7-9/8 | werckismic | 24 |
| 40 | 0-301-702-1202 | 1-11/9-10/7-9/8 | jove | 24 |
| 41 | 0-502-702-1202 | 1-11/7-10/7-9/8 | werckismic | 24 |
| 42 | 0-201-903-1202 | 1-9/7-11/6-9/8 | jove | 24 |
| 43 | 0-301-903-1202 | 1-11/9-11/6-9/8 | rastmic | 24 |
| 44 | 0-502-903-1202 | 1-11/7-11/6-9/8 | jove | 24 |
| 45 | 0-602-903-1202 | 1-3/2-11/6-9/8 | rastmic | 24 |
| 46 | 0-702-903-1202 | 1-10/7-11/6-9/8 | jove | 24 |
| 47 | 0-301-1003-1202 | 1-11/9-7/4-9/8 | jove | 24 |
| 48 | 0-502-1003-1202 | 1-11/7-7/4-9/8 | werckismic | 24 |
| 49 | 0-602-1003-1202 | 1-3/2-7/4-9/8 | otonal | 24 |
| 50 | 0-702-1003-1202 | 1-10/7-7/4-9/8 | werckismic | 24 |
| 51 | 0-301-502-1503 | 1-11/9-11/7-11/8 | utonal | 30 |
| 52 | 0-301-602-1503 | 1-11/9-3/2-11/8 | rastmic | 30 |
| 53 | 0-301-903-1503 | 1-11/9-11/6-11/8 | utonal | 30 |
| 54 | 0-502-903-1503 | 1-11/7-11/6-11/8 | utonal | 30 |
| 55 | 0-602-903-1503 | 1-3/2-11/6-11/8 | ambitonal | 30 |
| 56 | 0-301-1003-1503 | 1-11/9-7/4-11/8 | werckismic | 30 |
| 57 | 0-502-1003-1503 | 1-11/7-7/4-11/8 | werckismic | 30 |
| 58 | 0-602-1003-1503 | 1-3/2-7/4-11/8 | otonal | 30 |
| 59 | 0-301-1202-1503 | 1-11/9-9/8-11/8 | rastmic | 30 |
| 60 | 0-502-1202-1503 | 1-11/7-9/8-11/8 | werckismic | 30 |
| 61 | 0-602-1202-1503 | 1-3/2-9/8-11/8 | otonal | 30 |
| 62 | 0-903-1202-1503 | 1-11/6-9/8-11/8 | rastmic | 30 |
| 63 | 0-1003-1202-1503 | 1-7/4-9/8-11/8 | otonal | 30 |
| 64 | 0-202-501-1703 | 1-20/11-10/9-5/4 | utonal | 34 |
| 65 | 0-202-702-1703 | 1-20/11-10/7-5/4 | utonal | 34 |
| 66 | 0-501-702-1703 | 1-10/9-10/7-5/4 | utonal | 34 |
| 67 | 0-501-1003-1703 | 1-10/9-7/4-5/4 | werckismic | 34 |
| 68 | 0-602-1003-1703 | 1-3/2-7/4-5/4 | otonal | 34 |
| 69 | 0-702-1003-1703 | 1-10/7-7/4-5/4 | werckismic | 34 |
| 70 | 0-202-1103-1703 | 1-20/11-5/3-5/4 | utonal | 34 |
| 71 | 0-501-1103-1703 | 1-10/9-5/3-5/4 | utonal | 34 |
| 72 | 0-602-1103-1703 | 1-3/2-5/3-5/4 | ambitonal | 34 |
| 73 | 0-702-1103-1703 | 1-10/7-5/3-5/4 | utonal | 34 |
| 74 | 0-602-1202-1703 | 1-3/2-9/8-5/4 | otonal | 34 |
| 75 | 0-702-1202-1703 | 1-10/7-9/8-5/4 | werckismic | 34 |
| 76 | 0-1003-1202-1703 | 1-7/4-9/8-5/4 | otonal | 34 |
| 77 | 0-602-1503-1703 | 1-3/2-11/8-5/4 | otonal | 34 |
| 78 | 0-1003-1503-1703 | 1-7/4-11/8-5/4 | otonal | 34 |
| 79 | 0-1202-1503-1703 | 1-9/8-11/8-5/4 | otonal | 34 |
Pentads
| Number | Chord | Transversal | Type | Complexity |
| 1 | 0-201-401-602-903 | 1-9/7-7/6-3/2-11/6 | swetismic | 18 |
| 2 | 0-201-401-702-903 | 1-9/7-7/6-10/7-11/6 | swetismic | 18 |
| 3 | 0-201-502-702-903 | 1-9/7-11/7-10/7-11/6 | swetismic | 18 |
| 4 | 0-301-502-702-903 | 1-11/9-11/7-10/7-11/6 | swetismic | 18 |
| 5 | 0-301-501-702-1003 | 1-11/9-10/9-10/7-7/4 | jove | 20 |
| 6 | 0-301-502-702-1003 | 1-11/9-11/7-10/7-7/4 | jove | 20 |
| 7 | 0-202-401-702-1103 | 1-20/11-7/6-10/7-5/3 | swetismic | 22 |
| 8 | 0-202-501-702-1103 | 1-20/11-10/9-10/7-5/3 | utonal | 22 |
| 9 | 0-401-602-903-1103 | 1-7/6-3/2-11/6-5/3 | otonal | 22 |
| 10 | 0-401-702-903-1103 | 1-7/6-10/7-11/6-5/3 | swetismic | 22 |
| 11 | 0-201-502-702-1202 | 1-9/7-11/7-10/7-9/8 | werckismic | 24 |
| 12 | 0-301-502-702-1202 | 1-11/9-11/7-10/7-9/8 | jove | 24 |
| 13 | 0-201-502-903-1202 | 1-9/7-11/7-11/6-9/8 | jove | 24 |
| 14 | 0-301-502-903-1202 | 1-11/9-11/7-11/6-9/8 | jove | 24 |
| 15 | 0-201-602-903-1202 | 1-9/7-3/2-11/6-9/8 | jove | 24 |
| 16 | 0-301-602-903-1202 | 1-11/9-3/2-11/6-9/8 | rastmic | 24 |
| 17 | 0-201-702-903-1202 | 1-9/7-10/7-11/6-9/8 | jove | 24 |
| 18 | 0-301-702-903-1202 | 1-11/9-10/7-11/6-9/8 | jove | 24 |
| 19 | 0-502-702-903-1202 | 1-11/7-10/7-11/6-9/8 | jove | 24 |
| 20 | 0-301-502-1003-1202 | 1-11/9-11/7-7/4-9/8 | jove | 24 |
| 21 | 0-301-602-1003-1202 | 1-11/9-3/2-7/4-9/8 | jove | 24 |
| 22 | 0-301-702-1003-1202 | 1-11/9-10/7-7/4-9/8 | jove | 24 |
| 23 | 0-502-702-1003-1202 | 1-11/7-10/7-7/4-9/8 | werckismic | 24 |
| 24 | 0-301-502-903-1503 | 1-11/9-11/7-11/6-11/8 | utonal | 30 |
| 25 | 0-301-602-903-1503 | 1-11/9-3/2-11/6-11/8 | rastmic | 30 |
| 26 | 0-301-502-1003-1503 | 1-11/9-11/7-7/4-11/8 | werckismic | 30 |
| 27 | 0-301-602-1003-1503 | 1-11/9-3/2-7/4-11/8 | jove | 30 |
| 28 | 0-301-502-1202-1503 | 1-11/9-11/7-9/8-11/8 | jove | 30 |
| 29 | 0-301-602-1202-1503 | 1-11/9-3/2-9/8-11/8 | rastmic | 30 |
| 30 | 0-301-903-1202-1503 | 1-11/9-11/6-9/8-11/8 | rastmic | 30 |
| 31 | 0-502-903-1202-1503 | 1-11/7-11/6-9/8-11/8 | jove | 30 |
| 32 | 0-602-903-1202-1503 | 1-3/2-11/6-9/8-11/8 | rastmic | 30 |
| 33 | 0-301-1003-1202-1503 | 1-11/9-7/4-9/8-11/8 | jove | 30 |
| 34 | 0-502-1003-1202-1503 | 1-11/7-7/4-9/8-11/8 | werckismic | 30 |
| 35 | 0-602-1003-1202-1503 | 1-3/2-7/4-9/8-11/8 | otonal | 30 |
| 36 | 0-202-501-702-1703 | 1-20/11-10/9-10/7-5/4 | utonal | 34 |
| 37 | 0-501-702-1003-1703 | 1-10/9-10/7-7/4-5/4 | werckismic | 34 |
| 38 | 0-202-501-1103-1703 | 1-20/11-10/9-5/3-5/4 | utonal | 34 |
| 39 | 0-202-702-1103-1703 | 1-20/11-10/7-5/3-5/4 | utonal | 34 |
| 40 | 0-501-702-1103-1703 | 1-10/9-10/7-5/3-5/4 | utonal | 34 |
| 41 | 0-602-1003-1202-1703 | 1-3/2-7/4-9/8-5/4 | otonal | 34 |
| 42 | 0-702-1003-1202-1703 | 1-10/7-7/4-9/8-5/4 | werckismic | 34 |
| 43 | 0-602-1003-1503-1703 | 1-3/2-7/4-11/8-5/4 | otonal | 34 |
| 44 | 0-602-1202-1503-1703 | 1-3/2-9/8-11/8-5/4 | otonal | 34 |
| 45 | 0-1003-1202-1503-1703 | 1-7/4-9/8-11/8-5/4 | otonal | 34 |
Hexads
| Number | Chord | Transversal | Type | Complexity |
| 1 | 0-201-502-702-903-1202 | 1-9/7-11/7-10/7-11/6-9/8 | jove | 24 |
| 2 | 0-301-502-702-903-1202 | 1-11/9-11/7-10/7-11/6-9/8 | jove | 24 |
| 3 | 0-301-502-702-1003-1202 | 1-11/9-11/7-10/7-7/4-9/8 | jove | 24 |
| 4 | 0-301-502-903-1202-1503 | 1-11/9-11/7-11/6-9/8-11/8 | jove | 30 |
| 5 | 0-301-602-903-1202-1503 | 1-11/9-3/2-11/6-9/8-11/8 | rastmic | 30 |
| 6 | 0-301-502-1003-1202-1503 | 1-11/9-11/7-7/4-9/8-11/8 | jove | 30 |
| 7 | 0-301-602-1003-1202-1503 | 1-11/9-3/2-7/4-9/8-11/8 | jove | 30 |
| 8 | 0-202-501-702-1103-1703 | 1-20/11-10/9-10/7-5/3-5/4 | utonal | 34 |
| 9 | 0-602-1003-1202-1503-1703 | 1-3/2-7/4-9/8-11/8-5/4 | otonal | 34 |