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Changing the name migration to mohajira in the article's body and trying to make sense of the chord labels. |
m Lériendil moved page Chords of mohajira to Mohajira/Chords |
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Latest revision as of 21:50, 22 June 2025
Below are listed the dyadic chords of 11-limit mohajira temperament. Typing the chords requires consideration of the fact that mohajira conflates 9/8 and 10/9 and also 11/10 and 12/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. The chord is analyzed in terms of the transversal which employs 9/8 and 20/11, if this can be done without tempering out additional commas.
Chords requiring tempering only by 81/80 are labeled didymic, by 121/120 biyatismic, by 176/175 valinorsmic, by 243/242 rastmic, and by 385/384 keenanismic. Chords which require any two of 81/80, 121/120 or 243/242 are labeled urania, and any two of 121/120, 176/175 or 385/384 zeus.
mohajira has MOS of size 7, 10, 17, 24, 31, 55 and 86. Even the seven-note MOS, which is itself an essentially tempered chord, has for that reason quite a few chords, they become much more abundant with ten notes.
Triads
| Number | Chord | Transversal | Type |
| 1 | 0-1-2 | 1-11/9-3/2 | rastmic |
| 2 | 0-1-3 | 1-11/9-11/6 | utonal |
| 3 | 0-2-3 | 1-3/2-11/6 | otonal |
| 4 | 0-1-4 | 1-11/9-10/9 | otonal |
| 5 | 0-2-4 | 1-3/2-9/8 | ambitonal |
| 6 | 0-3-4 | 1-20/11-10/9 | utonal |
| 7 | 0-1-5 | 1-11/9-11/8 | utonal |
| 8 | 0-2-5 | 1-3/2-11/8 | otonal |
| 9 | 0-3-5 | 1-11/6-11/8 | utonal |
| 10 | 0-4-5 | 1-9/8-11/8 | otonal |
| 11 | 0-1-6 | 1-11/9-5/3 | biyatismic |
| 12 | 0-2-6 | 1-3/2-5/3 | otonal |
| 13 | 0-3-6 | 1-20/11-5/3 | utonal |
| 14 | 0-4-6 | 1-10/9-5/3 | utonal |
| 15 | 0-5-6 | 1-11/8-5/3 | biyatismic |
| 16 | 0-2-8 | 1-3/2-5/4 | otonal |
| 17 | 0-3-8 | 1-20/11-5/4 | utonal |
| 18 | 0-4-8 | 1-9/8-5/4 | otonal |
| 19 | 0-5-8 | 1-11/8-5/4 | otonal |
| 20 | 0-6-8 | 1-5/3-5/4 | utonal |
| 21 | 0-3-11 | 1-20/11-8/7 | valinorsmic |
| 22 | 0-5-11 | 1-11/8-8/7 | keenanismic |
| 23 | 0-6-11 | 1-5/3-8/7 | keenanismic |
| 24 | 0-8-11 | 1-5/4-8/7 | valinorsmic |
| 25 | 0-2-13 | 1-3/2-12/7 | utonal |
| 26 | 0-5-13 | 1-11/8-12/7 | keenanismic |
| 27 | 0-8-13 | 1-5/4-12/7 | keenanismic |
| 28 | 0-11-13 | 1-8/7-12/7 | otonal |
| 29 | 0-2-15 | 1-3/2-9/7 | utonal |
| 30 | 0-4-15 | 1-9/8-9/7 | utonal |
| 31 | 0-11-15 | 1-8/7-9/7 | otonal |
| 32 | 0-13-15 | 1-12/7-9/7 | otonal |
| 33 | 0-1-16 | 1-11/9-11/7 | utonal |
| 34 | 0-3-16 | 1-11/6-11/7 | utonal |
| 35 | 0-5-16 | 1-11/8-11/7 | utonal |
| 36 | 0-8-16 | 1-5/4-11/7 | valinorsmic |
| 37 | 0-11-16 | 1-8/7-11/7 | otonal |
| 38 | 0-13-16 | 1-12/7-11/7 | otonal |
| 39 | 0-15-16 | 1-9/7-11/7 | otonal |
| 40 | 0-3-19 | 1-20/11-10/7 | utonal |
| 41 | 0-4-19 | 1-10/9-10/7 | utonal |
| 42 | 0-6-19 | 1-5/3-10/7 | utonal |
| 43 | 0-8-19 | 1-5/4-10/7 | utonal |
| 44 | 0-11-19 | 1-8/7-10/7 | otonal |
| 45 | 0-13-19 | 1-12/7-10/7 | otonal |
| 46 | 0-15-19 | 1-9/7-10/7 | otonal |
| 47 | 0-16-19 | 1-11/7-10/7 | otonal |
Tetrads
| Number | Chord | Transversal | Type |
| 1 | 0-1-2-3 | 1-11/9-3/2-11/6 | rastmic |
| 2 | 0-1-2-4 | 1-11/9-3/2-9/8 | rastmic |
| 3 | 0-1-3-4 | 1-11/9-11/6-9/8 | rastmic |
| 4 | 0-2-3-4 | 1-3/2-11/6-9/8 | rastmic |
| 5 | 0-1-2-5 | 1-11/9-3/2-11/8 | rastmic |
| 6 | 0-1-3-5 | 1-11/9-11/6-11/8 | utonal |
| 7 | 0-2-3-5 | 1-3/2-11/6-11/8 | ambitonal |
| 8 | 0-1-4-5 | 1-11/9-9/8-11/8 | didymic |
| 9 | 0-2-4-5 | 1-3/2-9/8-11/8 | otonal |
| 10 | 0-3-4-5 | 1-11/6-9/8-11/8 | rastmic |
| 11 | 0-1-2-6 | 1-11/9-3/2-5/3 | urania |
| 12 | 0-1-3-6 | 1-11/9-20/11-5/3 | biyatismic |
| 13 | 0-2-3-6 | 1-3/2-11/6-5/3 | otonal |
| 14 | 0-1-4-6 | 1-11/9-10/9-5/3 | biyatismic |
| 15 | 0-2-4-6 | 1-3/2-9/8-5/3 | didymic |
| 16 | 0-3-4-6 | 1-20/11-10/9-5/3 | utonal |
| 17 | 0-1-5-6 | 1-11/9-11/8-5/3 | biyatismic |
| 18 | 0-2-5-6 | 1-3/2-11/8-5/3 | biyatismic |
| 19 | 0-3-5-6 | 1-20/11-11/8-5/3 | biyatismic |
| 20 | 0-4-5-6 | 1-9/8-11/8-5/3 | urania |
| 21 | 0-2-3-8 | 1-3/2-20/11-5/4 | biyatismic |
| 22 | 0-2-4-8 | 1-3/2-9/8-5/4 | otonal |
| 23 | 0-3-4-8 | 1-20/11-10/9-5/4 | utonal |
| 24 | 0-2-5-8 | 1-3/2-11/8-5/4 | otonal |
| 25 | 0-3-5-8 | 1-20/11-11/8-5/4 | biyatismic |
| 26 | 0-4-5-8 | 1-9/8-11/8-5/4 | otonal |
| 27 | 0-2-6-8 | 1-3/2-5/3-5/4 | ambitonal |
| 28 | 0-3-6-8 | 1-20/11-5/3-5/4 | utonal |
| 29 | 0-4-6-8 | 1-10/9-5/3-5/4 | utonal |
| 30 | 0-5-6-8 | 1-11/8-5/3-5/4 | biyatismic |
| 31 | 0-3-5-11 | 1-11/6-11/8-8/7 | keenanismic |
| 32 | 0-3-6-11 | 1-11/6-5/3-8/7 | keenanismic |
| 33 | 0-5-6-11 | 1-11/8-5/3-8/7 | zeus |
| 34 | 0-3-8-11 | 1-20/11-5/4-8/7 | valinorsmic |
| 35 | 0-5-8-11 | 1-11/8-5/4-8/7 | keenanismic |
| 36 | 0-6-8-11 | 1-5/3-5/4-8/7 | keenanismic |
| 37 | 0-2-5-13 | 1-3/2-11/8-12/7 | keenanismic |
| 38 | 0-2-8-13 | 1-3/2-5/4-12/7 | keenanismic |
| 39 | 0-5-8-13 | 1-11/8-5/4-12/7 | keenanismic |
| 40 | 0-5-11-13 | 1-11/8-8/7-12/7 | keenanismic |
| 41 | 0-8-11-13 | 1-5/4-8/7-12/7 | keenanismic |
| 42 | 0-2-4-15 | 1-3/2-9/8-9/7 | utonal |
| 43 | 0-2-13-15 | 1-3/2-12/7-9/7 | ambitonal |
| 44 | 0-11-13-15 | 1-8/7-12/7-9/7 | otonal |
| 45 | 0-1-3-16 | 1-11/9-11/6-11/7 | utonal |
| 46 | 0-1-5-16 | 1-11/9-11/8-11/7 | utonal |
| 47 | 0-3-5-16 | 1-11/6-11/8-11/7 | utonal |
| 48 | 0-3-8-16 | 1-20/11-5/4-11/7 | zeus |
| 49 | 0-5-8-16 | 1-11/8-5/4-11/7 | valinorsmic |
| 50 | 0-3-11-16 | 1-11/6-8/7-11/7 | keenanismic |
| 51 | 0-5-11-16 | 1-11/8-8/7-11/7 | keenanismic |
| 52 | 0-8-11-16 | 1-5/4-8/7-11/7 | valinorsmic |
| 53 | 0-5-13-16 | 1-11/8-12/7-11/7 | keenanismic |
| 54 | 0-8-13-16 | 1-5/4-12/7-11/7 | zeus |
| 55 | 0-11-13-16 | 1-8/7-12/7-11/7 | otonal |
| 56 | 0-11-15-16 | 1-8/7-9/7-11/7 | otonal |
| 57 | 0-13-15-16 | 1-12/7-9/7-11/7 | otonal |
| 58 | 0-3-4-19 | 1-20/11-10/9-10/7 | utonal |
| 59 | 0-3-6-19 | 1-20/11-5/3-10/7 | utonal |
| 60 | 0-4-6-19 | 1-10/9-5/3-10/7 | utonal |
| 61 | 0-3-8-19 | 1-20/11-5/4-10/7 | utonal |
| 62 | 0-4-8-19 | 1-10/9-5/4-10/7 | utonal |
| 63 | 0-6-8-19 | 1-5/3-5/4-10/7 | utonal |
| 64 | 0-3-11-19 | 1-20/11-8/7-10/7 | valinorsmic |
| 65 | 0-6-11-19 | 1-5/3-8/7-10/7 | keenanismic |
| 66 | 0-8-11-19 | 1-5/4-8/7-10/7 | valinorsmic |
| 67 | 0-8-13-19 | 1-5/4-12/7-10/7 | keenanismic |
| 68 | 0-11-13-19 | 1-8/7-12/7-10/7 | otonal |
| 69 | 0-4-15-19 | 1-9/8-9/7-10/7 | didymic |
| 70 | 0-11-15-19 | 1-8/7-9/7-10/7 | otonal |
| 71 | 0-13-15-19 | 1-12/7-9/7-10/7 | otonal |
| 72 | 0-3-16-19 | 1-20/11-11/7-10/7 | biyatismic |
| 73 | 0-8-16-19 | 1-5/4-11/7-10/7 | valinorsmic |
| 74 | 0-11-16-19 | 1-8/7-11/7-10/7 | otonal |
| 75 | 0-13-16-19 | 1-12/7-11/7-10/7 | otonal |
| 76 | 0-15-16-19 | 1-9/7-11/7-10/7 | otonal |
Pentads
| Number | Chord | Transversal | Type |
| 1 | 0-1-2-3-4 | 1-11/9-3/2-11/6-9/8 | rastmic |
| 2 | 0-1-2-3-5 | 1-11/9-3/2-11/6-11/8 | rastmic |
| 3 | 0-1-2-4-5 | 1-11/9-3/2-9/8-11/8 | rastmic |
| 4 | 0-1-3-4-5 | 1-11/9-11/6-9/8-11/8 | rastmic |
| 5 | 0-2-3-4-5 | 1-3/2-11/6-9/8-11/8 | rastmic |
| 6 | 0-1-2-3-6 | 1-11/9-3/2-20/11-5/3 | urania |
| 7 | 0-1-2-4-6 | 1-11/9-3/2-9/8-5/3 | urania |
| 8 | 0-1-3-4-6 | 1-11/9-20/11-10/9-5/3 | biyatismic |
| 9 | 0-2-3-4-6 | 1-3/2-20/11-9/8-5/3 | urania |
| 10 | 0-1-2-5-6 | 1-11/9-3/2-11/8-5/3 | urania |
| 11 | 0-1-3-5-6 | 1-11/9-20/11-11/8-5/3 | biyatismic |
| 12 | 0-2-3-5-6 | 1-3/2-20/11-11/8-5/3 | biyatismic |
| 13 | 0-1-4-5-6 | 1-11/9-9/8-11/8-5/3 | urania |
| 14 | 0-2-4-5-6 | 1-3/2-9/8-11/8-5/3 | urania |
| 15 | 0-3-4-5-6 | 1-20/11-9/8-11/8-5/3 | urania |
| 16 | 0-2-3-4-8 | 1-3/2-20/11-9/8-5/4 | urania |
| 17 | 0-2-3-5-8 | 1-3/2-20/11-11/8-5/4 | biyatismic |
| 18 | 0-2-4-5-8 | 1-3/2-9/8-11/8-5/4 | otonal |
| 19 | 0-3-4-5-8 | 1-20/11-9/8-11/8-5/4 | urania |
| 20 | 0-2-3-6-8 | 1-3/2-20/11-5/3-5/4 | biyatismic |
| 21 | 0-2-4-6-8 | 1-3/2-9/8-5/3-5/4 | didymic |
| 22 | 0-3-4-6-8 | 1-20/11-10/9-5/3-5/4 | utonal |
| 23 | 0-2-5-6-8 | 1-3/2-11/8-5/3-5/4 | biyatismic |
| 24 | 0-3-5-6-8 | 1-20/11-11/8-5/3-5/4 | biyatismic |
| 25 | 0-4-5-6-8 | 1-9/8-11/8-5/3-5/4 | urania |
| 26 | 0-3-5-6-11 | 1-20/11-11/8-5/3-8/7 | zeus |
| 27 | 0-3-5-8-11 | 1-20/11-11/8-5/4-8/7 | zeus |
| 28 | 0-3-6-8-11 | 1-20/11-5/3-5/4-8/7 | zeus |
| 29 | 0-5-6-8-11 | 1-11/8-5/3-5/4-8/7 | zeus |
| 30 | 0-2-5-8-13 | 1-3/2-11/8-5/4-12/7 | keenanismic |
| 31 | 0-5-8-11-13 | 1-11/8-5/4-8/7-12/7 | keenanismic |
| 32 | 0-1-3-5-16 | 1-11/9-11/6-11/8-11/7 | utonal |
| 33 | 0-3-5-8-16 | 1-20/11-11/8-5/4-11/7 | zeus |
| 34 | 0-3-5-11-16 | 1-11/6-11/8-8/7-11/7 | keenanismic |
| 35 | 0-3-8-11-16 | 1-20/11-5/4-8/7-11/7 | zeus |
| 36 | 0-5-8-11-16 | 1-11/8-5/4-8/7-11/7 | zeus |
| 37 | 0-5-8-13-16 | 1-11/8-5/4-12/7-11/7 | zeus |
| 38 | 0-5-11-13-16 | 1-11/8-8/7-12/7-11/7 | keenanismic |
| 39 | 0-8-11-13-16 | 1-5/4-8/7-12/7-11/7 | zeus |
| 40 | 0-11-13-15-16 | 1-8/7-12/7-9/7-11/7 | otonal |
| 41 | 0-3-4-6-19 | 1-20/11-10/9-5/3-10/7 | utonal |
| 42 | 0-3-4-8-19 | 1-20/11-10/9-5/4-10/7 | utonal |
| 43 | 0-3-6-8-19 | 1-20/11-5/3-5/4-10/7 | utonal |
| 44 | 0-4-6-8-19 | 1-10/9-5/3-5/4-10/7 | utonal |
| 45 | 0-3-6-11-19 | 1-20/11-5/3-8/7-10/7 | zeus |
| 46 | 0-3-8-11-19 | 1-20/11-5/4-8/7-10/7 | valinorsmic |
| 47 | 0-6-8-11-19 | 1-5/3-5/4-8/7-10/7 | keenanismic |
| 48 | 0-8-11-13-19 | 1-5/4-8/7-12/7-10/7 | keenanismic |
| 49 | 0-11-13-15-19 | 1-8/7-12/7-9/7-10/7 | otonal |
| 50 | 0-3-8-16-19 | 1-20/11-5/4-11/7-10/7 | zeus |
| 51 | 0-3-11-16-19 | 1-20/11-8/7-11/7-10/7 | zeus |
| 52 | 0-8-11-16-19 | 1-5/4-8/7-11/7-10/7 | valinorsmic |
| 53 | 0-8-13-16-19 | 1-5/4-12/7-11/7-10/7 | zeus |
| 54 | 0-11-13-16-19 | 1-8/7-12/7-11/7-10/7 | otonal |
| 55 | 0-11-15-16-19 | 1-8/7-9/7-11/7-10/7 | otonal |
| 56 | 0-13-15-16-19 | 1-12/7-9/7-11/7-10/7 | otonal |
Hexads
| Number | Chord | Transversal | Type |
| 1 | 0-1-2-3-4-5 | 1-11/9-3/2-11/6-9/8-11/8 | rastmic |
| 2 | 0-1-2-3-4-6 | 1-11/9-3/2-20/11-9/8-5/3 | urania |
| 3 | 0-1-2-3-5-6 | 1-11/9-3/2-20/11-11/8-5/3 | urania |
| 4 | 0-1-2-4-5-6 | 1-11/9-3/2-9/8-11/8-5/3 | urania |
| 5 | 0-1-3-4-5-6 | 1-11/9-20/11-9/8-11/8-5/3 | urania |
| 6 | 0-2-3-4-5-6 | 1-3/2-20/11-9/8-11/8-5/3 | urania |
| 7 | 0-2-3-4-5-8 | 1-3/2-20/11-9/8-11/8-5/4 | urania |
| 8 | 0-2-3-4-6-8 | 1-3/2-20/11-9/8-5/3-5/4 | urania |
| 9 | 0-2-3-5-6-8 | 1-3/2-20/11-11/8-5/3-5/4 | biyatismic |
| 10 | 0-2-4-5-6-8 | 1-3/2-9/8-11/8-5/3-5/4 | urania |
| 11 | 0-3-4-5-6-8 | 1-20/11-9/8-11/8-5/3-5/4 | urania |
| 12 | 0-3-5-6-8-11 | 1-20/11-11/8-5/3-5/4-8/7 | zeus |
| 13 | 0-3-5-8-11-16 | 1-20/11-11/8-5/4-8/7-11/7 | zeus |
| 14 | 0-5-8-11-13-16 | 1-11/8-5/4-8/7-12/7-11/7 | zeus |
| 15 | 0-3-4-6-8-19 | 1-20/11-10/9-5/3-5/4-10/7 | utonal |
| 16 | 0-3-6-8-11-19 | 1-20/11-5/3-5/4-8/7-10/7 | zeus |
| 17 | 0-3-8-11-16-19 | 1-20/11-5/4-8/7-11/7-10/7 | zeus |
| 18 | 0-8-11-13-16-19 | 1-5/4-8/7-12/7-11/7-10/7 | zeus |
| 19 | 0-11-13-15-16-19 | 1-8/7-12/7-9/7-11/7-10/7 | otonal |
Septads
| Number | Chord | Transversal | Type |
| 1 | 0-1-2-3-4-5-6 | 1-11/9-3/2-20/11-9/8-11/8-5/3 | urania |
| 2 | 0-2-3-4-5-6-8 | 1-3/2-20/11-9/8-11/8-5/3-5/4 | urania |