Chords of hemiwürschmidt: Difference between revisions
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[[Category:Lists of chords]] | |||
[[Category:Dyadic chords]] | |||
[[Category:11-limit]] | |||
[[Category:Hemiwürschmidt]] | |||
Revision as of 11:02, 25 April 2023
Below are listed the dyadic chords of 11-limit hemiwürschmidt temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, by 441/440 werckismic, and by 243/242 rastmic. Chords requiring any two of the above are labeled jove.
Hemiwürschmidt has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 40, and so would require the 68 note MOS. However, it will be observed that much smaller MOS still have quite a few chords.
Triads
| Number | Chord | Transversal | Type |
| 1 | 0-2-5 | 1-5/4-7/4 | otonal |
| 2 | 0-3-5 | 1-7/5-7/4 | utonal |
| 3 | 0-3-8 | 1-7/5-11/9 | werckismic |
| 4 | 0-5-8 | 1-7/4-11/9 | werckismic |
| 5 | 0-3-11 | 1-7/5-12/7 | swetismic |
| 6 | 0-8-11 | 1-11/9-12/7 | swetismic |
| 7 | 0-3-14 | 1-7/5-6/5 | otonal |
| 8 | 0-11-14 | 1-12/7-6/5 | utonal |
| 9 | 0-2-16 | 1-5/4-3/2 | otonal |
| 10 | 0-5-16 | 1-7/4-3/2 | otonal |
| 11 | 0-8-16 | 1-11/9-3/2 | rastmic |
| 12 | 0-11-16 | 1-12/7-3/2 | utonal |
| 13 | 0-14-16 | 1-6/5-3/2 | utonal |
| 14 | 0-8-24 | 1-11/9-11/6 | utonal |
| 15 | 0-16-24 | 1-3/2-11/6 | otonal |
| 16 | 0-3-27 | 1-7/5-9/7 | swetismic |
| 17 | 0-11-27 | 1-12/7-9/7 | otonal |
| 18 | 0-16-27 | 1-3/2-9/7 | utonal |
| 19 | 0-24-27 | 1-11/6-9/7 | swetismic |
| 20 | 0-3-30 | 1-7/5-9/5 | otonal |
| 21 | 0-14-30 | 1-6/5-9/5 | otonal |
| 22 | 0-16-30 | 1-3/2-9/5 | utonal |
| 23 | 0-27-30 | 1-9/7-9/5 | utonal |
| 24 | 0-2-32 | 1-5/4-9/8 | otonal |
| 25 | 0-5-32 | 1-7/4-9/8 | otonal |
| 26 | 0-8-32 | 1-11/9-9/8 | rastmic |
| 27 | 0-16-32 | 1-3/2-9/8 | ambitonal |
| 28 | 0-24-32 | 1-11/6-9/8 | rastmic |
| 29 | 0-27-32 | 1-9/7-9/8 | utonal |
| 30 | 0-30-32 | 1-9/5-9/8 | utonal |
| 31 | 0-3-35 | 1-7/5-11/7 | werckismic |
| 32 | 0-5-35 | 1-7/4-11/7 | werckismic |
| 33 | 0-8-35 | 1-11/9-11/7 | utonal |
| 34 | 0-11-35 | 1-12/7-11/7 | otonal |
| 35 | 0-24-35 | 1-11/6-11/7 | utonal |
| 36 | 0-27-35 | 1-9/7-11/7 | otonal |
| 37 | 0-30-35 | 1-9/5-11/7 | werckismic |
| 38 | 0-32-35 | 1-9/8-11/7 | werckismic |
| 39 | 0-3-38 | 1-7/5-11/10 | otonal |
| 40 | 0-8-38 | 1-11/9-11/10 | utonal |
| 41 | 0-11-38 | 1-12/7-11/10 | swetismic |
| 42 | 0-14-38 | 1-6/5-11/10 | otonal |
| 43 | 0-24-38 | 1-11/6-11/10 | utonal |
| 44 | 0-27-38 | 1-9/7-11/10 | swetismic |
| 45 | 0-30-38 | 1-9/5-11/10 | otonal |
| 46 | 0-35-38 | 1-11/7-11/10 | utonal |
| 47 | 0-2-40 | 1-5/4-11/8 | otonal |
| 48 | 0-5-40 | 1-7/4-11/8 | otonal |
| 49 | 0-8-40 | 1-11/9-11/8 | utonal |
| 50 | 0-16-40 | 1-3/2-11/8 | otonal |
| 51 | 0-24-40 | 1-11/6-11/8 | utonal |
| 52 | 0-32-40 | 1-9/8-11/8 | otonal |
| 53 | 0-35-40 | 1-11/7-11/8 | utonal |
| 54 | 0-38-40 | 1-11/10-11/8 | utonal |
Tetrads
| Number | Chord | Transversal | Type |
| 1 | 0-3-5-8 | 1-7/5-7/4-11/9 | werckismic |
| 2 | 0-3-8-11 | 1-7/5-11/9-12/7 | jove |
| 3 | 0-3-11-14 | 1-7/5-12/7-6/5 | swetismic |
| 4 | 0-2-5-16 | 1-5/4-7/4-3/2 | otonal |
| 5 | 0-5-8-16 | 1-7/4-11/9-3/2 | jove |
| 6 | 0-8-11-16 | 1-11/9-12/7-3/2 | jove |
| 7 | 0-11-14-16 | 1-12/7-6/5-3/2 | utonal |
| 8 | 0-8-16-24 | 1-11/9-3/2-11/6 | rastmic |
| 9 | 0-3-11-27 | 1-7/5-12/7-9/7 | swetismic |
| 10 | 0-11-16-27 | 1-12/7-3/2-9/7 | ambitonal |
| 11 | 0-16-24-27 | 1-3/2-11/6-9/7 | swetismic |
| 12 | 0-3-14-30 | 1-7/5-6/5-9/5 | otonal |
| 13 | 0-14-16-30 | 1-6/5-3/2-9/5 | ambitonal |
| 14 | 0-3-27-30 | 1-7/5-9/7-9/5 | swetismic |
| 15 | 0-16-27-30 | 1-3/2-9/7-9/5 | utonal |
| 16 | 0-2-5-32 | 1-5/4-7/4-9/8 | otonal |
| 17 | 0-5-8-32 | 1-7/4-11/9-9/8 | jove |
| 18 | 0-2-16-32 | 1-5/4-3/2-9/8 | otonal |
| 19 | 0-5-16-32 | 1-7/4-3/2-9/8 | otonal |
| 20 | 0-8-16-32 | 1-11/9-3/2-9/8 | rastmic |
| 21 | 0-8-24-32 | 1-11/9-11/6-9/8 | rastmic |
| 22 | 0-16-24-32 | 1-3/2-11/6-9/8 | rastmic |
| 23 | 0-16-27-32 | 1-3/2-9/7-9/8 | utonal |
| 24 | 0-24-27-32 | 1-11/6-9/7-9/8 | jove |
| 25 | 0-16-30-32 | 1-3/2-9/5-9/8 | utonal |
| 26 | 0-27-30-32 | 1-9/7-9/5-9/8 | utonal |
| 27 | 0-3-5-35 | 1-7/5-7/4-11/7 | werckismic |
| 28 | 0-3-8-35 | 1-7/5-11/9-11/7 | werckismic |
| 29 | 0-5-8-35 | 1-7/4-11/9-11/7 | werckismic |
| 30 | 0-3-11-35 | 1-7/5-12/7-11/7 | jove |
| 31 | 0-8-11-35 | 1-11/9-12/7-11/7 | swetismic |
| 32 | 0-8-24-35 | 1-11/9-11/6-11/7 | utonal |
| 33 | 0-3-27-35 | 1-7/5-9/7-11/7 | jove |
| 34 | 0-11-27-35 | 1-12/7-9/7-11/7 | otonal |
| 35 | 0-24-27-35 | 1-11/6-9/7-11/7 | swetismic |
| 36 | 0-3-30-35 | 1-7/5-9/5-11/7 | werckismic |
| 37 | 0-27-30-35 | 1-9/7-9/5-11/7 | werckismic |
| 38 | 0-5-32-35 | 1-7/4-9/8-11/7 | werckismic |
| 39 | 0-8-32-35 | 1-11/9-9/8-11/7 | jove |
| 40 | 0-24-32-35 | 1-11/6-9/8-11/7 | jove |
| 41 | 0-27-32-35 | 1-9/7-9/8-11/7 | werckismic |
| 42 | 0-30-32-35 | 1-9/5-9/8-11/7 | werckismic |
| 43 | 0-3-8-38 | 1-7/5-11/9-11/10 | werckismic |
| 44 | 0-3-11-38 | 1-7/5-12/7-11/10 | swetismic |
| 45 | 0-8-11-38 | 1-11/9-12/7-11/10 | swetismic |
| 46 | 0-3-14-38 | 1-7/5-6/5-11/10 | otonal |
| 47 | 0-11-14-38 | 1-12/7-6/5-11/10 | swetismic |
| 48 | 0-8-24-38 | 1-11/9-11/6-11/10 | utonal |
| 49 | 0-3-27-38 | 1-7/5-9/7-11/10 | swetismic |
| 50 | 0-11-27-38 | 1-12/7-9/7-11/10 | swetismic |
| 51 | 0-24-27-38 | 1-11/6-9/7-11/10 | swetismic |
| 52 | 0-3-30-38 | 1-7/5-9/5-11/10 | otonal |
| 53 | 0-14-30-38 | 1-6/5-9/5-11/10 | otonal |
| 54 | 0-27-30-38 | 1-9/7-9/5-11/10 | swetismic |
| 55 | 0-3-35-38 | 1-7/5-11/7-11/10 | werckismic |
| 56 | 0-8-35-38 | 1-11/9-11/7-11/10 | utonal |
| 57 | 0-11-35-38 | 1-12/7-11/7-11/10 | swetismic |
| 58 | 0-24-35-38 | 1-11/6-11/7-11/10 | utonal |
| 59 | 0-27-35-38 | 1-9/7-11/7-11/10 | swetismic |
| 60 | 0-30-35-38 | 1-9/5-11/7-11/10 | werckismic |
| 61 | 0-2-5-40 | 1-5/4-7/4-11/8 | otonal |
| 62 | 0-5-8-40 | 1-7/4-11/9-11/8 | werckismic |
| 63 | 0-2-16-40 | 1-5/4-3/2-11/8 | otonal |
| 64 | 0-5-16-40 | 1-7/4-3/2-11/8 | otonal |
| 65 | 0-8-16-40 | 1-11/9-3/2-11/8 | rastmic |
| 66 | 0-8-24-40 | 1-11/9-11/6-11/8 | utonal |
| 67 | 0-16-24-40 | 1-3/2-11/6-11/8 | ambitonal |
| 68 | 0-2-32-40 | 1-5/4-9/8-11/8 | otonal |
| 69 | 0-5-32-40 | 1-7/4-9/8-11/8 | otonal |
| 70 | 0-8-32-40 | 1-11/9-9/8-11/8 | rastmic |
| 71 | 0-16-32-40 | 1-3/2-9/8-11/8 | otonal |
| 72 | 0-24-32-40 | 1-11/6-9/8-11/8 | rastmic |
| 73 | 0-5-35-40 | 1-7/4-11/7-11/8 | werckismic |
| 74 | 0-8-35-40 | 1-11/9-11/7-11/8 | utonal |
| 75 | 0-24-35-40 | 1-11/6-11/7-11/8 | utonal |
| 76 | 0-32-35-40 | 1-9/8-11/7-11/8 | werckismic |
| 77 | 0-8-38-40 | 1-11/9-11/10-11/8 | utonal |
| 78 | 0-24-38-40 | 1-11/6-11/10-11/8 | utonal |
| 79 | 0-35-38-40 | 1-11/7-11/10-11/8 | utonal |
Pentads
| Number | Chord | Transversal | Type |
| 1 | 0-2-5-16-32 | 1-5/4-7/4-3/2-9/8 | otonal |
| 2 | 0-5-8-16-32 | 1-7/4-11/9-3/2-9/8 | jove |
| 3 | 0-8-16-24-32 | 1-11/9-3/2-11/6-9/8 | rastmic |
| 4 | 0-16-24-27-32 | 1-3/2-11/6-9/7-9/8 | jove |
| 5 | 0-16-27-30-32 | 1-3/2-9/7-9/5-9/8 | utonal |
| 6 | 0-3-5-8-35 | 1-7/5-7/4-11/9-11/7 | werckismic |
| 7 | 0-3-8-11-35 | 1-7/5-11/9-12/7-11/7 | jove |
| 8 | 0-3-11-27-35 | 1-7/5-12/7-9/7-11/7 | jove |
| 9 | 0-3-27-30-35 | 1-7/5-9/7-9/5-11/7 | jove |
| 10 | 0-5-8-32-35 | 1-7/4-11/9-9/8-11/7 | jove |
| 11 | 0-8-24-32-35 | 1-11/9-11/6-9/8-11/7 | jove |
| 12 | 0-24-27-32-35 | 1-11/6-9/7-9/8-11/7 | jove |
| 13 | 0-27-30-32-35 | 1-9/7-9/5-9/8-11/7 | werckismic |
| 14 | 0-3-8-11-38 | 1-7/5-11/9-12/7-11/10 | jove |
| 15 | 0-3-11-14-38 | 1-7/5-12/7-6/5-11/10 | swetismic |
| 16 | 0-3-11-27-38 | 1-7/5-12/7-9/7-11/10 | swetismic |
| 17 | 0-3-14-30-38 | 1-7/5-6/5-9/5-11/10 | otonal |
| 18 | 0-3-27-30-38 | 1-7/5-9/7-9/5-11/10 | swetismic |
| 19 | 0-3-8-35-38 | 1-7/5-11/9-11/7-11/10 | werckismic |
| 20 | 0-3-11-35-38 | 1-7/5-12/7-11/7-11/10 | jove |
| 21 | 0-8-11-35-38 | 1-11/9-12/7-11/7-11/10 | swetismic |
| 22 | 0-8-24-35-38 | 1-11/9-11/6-11/7-11/10 | utonal |
| 23 | 0-3-27-35-38 | 1-7/5-9/7-11/7-11/10 | jove |
| 24 | 0-11-27-35-38 | 1-12/7-9/7-11/7-11/10 | swetismic |
| 25 | 0-24-27-35-38 | 1-11/6-9/7-11/7-11/10 | swetismic |
| 26 | 0-3-30-35-38 | 1-7/5-9/5-11/7-11/10 | werckismic |
| 27 | 0-27-30-35-38 | 1-9/7-9/5-11/7-11/10 | jove |
| 28 | 0-2-5-16-40 | 1-5/4-7/4-3/2-11/8 | otonal |
| 29 | 0-5-8-16-40 | 1-7/4-11/9-3/2-11/8 | jove |
| 30 | 0-8-16-24-40 | 1-11/9-3/2-11/6-11/8 | rastmic |
| 31 | 0-2-5-32-40 | 1-5/4-7/4-9/8-11/8 | otonal |
| 32 | 0-5-8-32-40 | 1-7/4-11/9-9/8-11/8 | jove |
| 33 | 0-2-16-32-40 | 1-5/4-3/2-9/8-11/8 | otonal |
| 34 | 0-5-16-32-40 | 1-7/4-3/2-9/8-11/8 | otonal |
| 35 | 0-8-16-32-40 | 1-11/9-3/2-9/8-11/8 | rastmic |
| 36 | 0-8-24-32-40 | 1-11/9-11/6-9/8-11/8 | rastmic |
| 37 | 0-16-24-32-40 | 1-3/2-11/6-9/8-11/8 | rastmic |
| 38 | 0-5-8-35-40 | 1-7/4-11/9-11/7-11/8 | werckismic |
| 39 | 0-8-24-35-40 | 1-11/9-11/6-11/7-11/8 | utonal |
| 40 | 0-5-32-35-40 | 1-7/4-9/8-11/7-11/8 | werckismic |
| 41 | 0-8-32-35-40 | 1-11/9-9/8-11/7-11/8 | jove |
| 42 | 0-24-32-35-40 | 1-11/6-9/8-11/7-11/8 | jove |
| 43 | 0-8-24-38-40 | 1-11/9-11/6-11/10-11/8 | utonal |
| 44 | 0-8-35-38-40 | 1-11/9-11/7-11/10-11/8 | utonal |
| 45 | 0-24-35-38-40 | 1-11/6-11/7-11/10-11/8 | utonal |
Hexads
| Number | Chord | Transversal | Type |
| 1 | 0-3-8-11-35-38 | 1-7/5-11/9-12/7-11/7-11/10 | jove |
| 2 | 0-3-11-27-35-38 | 1-7/5-12/7-9/7-11/7-11/10 | jove |
| 3 | 0-3-27-30-35-38 | 1-7/5-9/7-9/5-11/7-11/10 | jove |
| 4 | 0-2-5-16-32-40 | 1-5/4-7/4-3/2-9/8-11/8 | otonal |
| 5 | 0-5-8-16-32-40 | 1-7/4-11/9-3/2-9/8-11/8 | jove |
| 6 | 0-8-16-24-32-40 | 1-11/9-3/2-11/6-9/8-11/8 | rastmic |
| 7 | 0-5-8-32-35-40 | 1-7/4-11/9-9/8-11/7-11/8 | jove |
| 8 | 0-8-24-32-35-40 | 1-11/9-11/6-9/8-11/7-11/8 | jove |
| 9 | 0-8-24-35-38-40 | 1-11/9-11/6-11/7-11/10-11/8 | utonal |