Chords of hemiwürschmidt: Difference between revisions
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Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[ | Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Hemimean clan#Hemiwürschmidt|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. | 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. | ||
Latest revision as of 05:58, 31 October 2024
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 |