Valentine/Chords
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Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Starling temperaments#Valentine%20temperament-11-limit|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. 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. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11. If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine. Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha. In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves. =Triads= || Number || Chord || Transversal || Type || || 1 || 0-2-4 || 1-11/10-6/5 || otonal || || 2 || 0-2-5 || 1-11/10-5/4 || valinorsmic || || 3 || 0-3-5 || 1-8/7-5/4 || valinorsmic || || 4 || 0-2-7 || 1-11/10-11/8 || utonal || || 5 || 0-3-7 || 1-8/7-11/8 || keenanismic || || 6 || 0-4-7 || 1-6/5-11/8 || keenanismic || || 7 || 0-5-7 || 1-5/4-11/8 || otonal || || 8 || 0-3-8 || 1-8/7-10/7 || otonal || || 9 || 0-4-8 || 1-6/5-10/7 || starling || || 10 || 0-5-8 || 1-5/4-10/7 || utonal || || 11 || 0-2-9 || 1-12/11-3/2 || utonal || || 12 || 0-4-9 || 1-6/5-3/2 || utonal || || 13 || 0-5-9 || 1-5/4-3/2 || otonal || || 14 || 0-7-9 || 1-11/8-3/2 || otonal || || 15 || 0-2-10 || 1-11/10-11/7 || utonal || || 16 || 0-3-10 || 1-8/7-11/7 || otonal || || 17 || 0-5-10 || 1-5/4-11/7 || valinorsmic || || 18 || 0-7-10 || 1-11/8-11/7 || utonal || || 19 || 0-8-10 || 1-10/7-11/7 || otonal || || 20 || 0-2-11 || 1-12/11-18/11 || otonal || || 21 || 0-3-11 || 1-8/7-18/11 || werckismic || || 22 || 0-4-11 || 1-6/5-18/11 || biyatismic || || 23 || 0-7-11 || 1-11/8-18/11 || biyatismic || || 24 || 0-8-11 || 1-10/7-18/11 || werckismic || || 25 || 0-9-11 || 1-3/2-18/11 || utonal || || 26 || 0-2-12 || 1-12/11-12/7 || utonal || || 27 || 0-3-12 || 1-8/7-12/7 || otonal || || 28 || 0-4-12 || 1-6/5-12/7 || utonal || || 29 || 0-5-12 || 1-5/4-12/7 || keenanismic || || 30 || 0-7-12 || 1-11/8-12/7 || keenanismic || || 31 || 0-8-12 || 1-10/7-12/7 || otonal || || 32 || 0-9-12 || 1-3/2-12/7 || utonal || || 33 || 0-10-12 || 1-11/7-12/7 || otonal || || 34 || 0-2-13 || 1-11/10-9/5 || otonal || || 35 || 0-3-13 || 1-8/7-9/5 || werckismic || || 36 || 0-4-13 || 1-6/5-9/5 || otonal || || 37 || 0-5-13 || 1-5/4-9/5 || starling || || 38 || 0-8-13 || 1-10/7-9/5 || starling || || 39 || 0-9-13 || 1-3/2-9/5 || utonal || || 40 || 0-10-13 || 1-11/7-9/5 || werckismic || || 41 || 0-11-13 || 1-18/11-9/5 || utonal || || 42 || 0-5-18 || 1-5/4-9/8 || otonal || || 43 || 0-7-18 || 1-11/8-9/8 || otonal || || 44 || 0-8-18 || 1-10/7-9/8 || werckismic || || 45 || 0-9-18 || 1-3/2-9/8 || ambitonal || || 46 || 0-10-18 || 1-11/7-9/8 || werckismic || || 47 || 0-11-18 || 1-18/11-9/8 || utonal || || 48 || 0-13-18 || 1-9/5-9/8 || utonal || || 49 || 0-3-21 || 1-8/7-9/7 || otonal || || 50 || 0-8-21 || 1-10/7-9/7 || otonal || || 51 || 0-9-21 || 1-3/2-9/7 || utonal || || 52 || 0-10-21 || 1-11/7-9/7 || otonal || || 53 || 0-11-21 || 1-18/11-9/7 || utonal || || 54 || 0-12-21 || 1-12/7-9/7 || otonal || || 55 || 0-13-21 || 1-9/5-9/7 || utonal || || 56 || 0-18-21 || 1-9/8-9/7 || utonal || =Tetrads= || Number || Chord || Transversal || Type || || 1 || 0-2-4-7 || 1-11/10-6/5-11/8 || zeus || || 2 || 0-2-5-7 || 1-11/10-5/4-11/8 || valinorsmic || || 3 || 0-3-5-7 || 1-8/7-5/4-11/8 || zeus || || 4 || 0-3-5-8 || 1-8/7-5/4-10/7 || valinorsmic || || 5 || 0-2-4-9 || 1-12/11-6/5-3/2 || utonal || || 6 || 0-2-5-9 || 1-11/10-5/4-3/2 || zeus || || 7 || 0-2-7-9 || 1-11/10-11/8-3/2 || biyatismic || || 8 || 0-4-7-9 || 1-6/5-11/8-3/2 || zeus || || 9 || 0-5-7-9 || 1-5/4-11/8-3/2 || otonal || || 10 || 0-2-5-10 || 1-11/10-5/4-11/7 || valinorsmic || || 11 || 0-3-5-10 || 1-8/7-5/4-11/7 || valinorsmic || || 12 || 0-2-7-10 || 1-11/10-11/8-11/7 || utonal || || 13 || 0-3-7-10 || 1-8/7-11/8-11/7 || keenanismic || || 14 || 0-5-7-10 || 1-5/4-11/8-11/7 || valinorsmic || || 15 || 0-3-8-10 || 1-8/7-10/7-11/7 || otonal || || 16 || 0-5-8-10 || 1-5/4-10/7-11/7 || valinorsmic || || 17 || 0-2-4-11 || 1-11/10-6/5-18/11 || biyatismic || || 18 || 0-2-7-11 || 1-11/10-11/8-18/11 || biyatismic || || 19 || 0-3-7-11 || 1-8/7-11/8-18/11 || valentine || || 20 || 0-4-7-11 || 1-6/5-11/8-18/11 || zeus || || 21 || 0-3-8-11 || 1-8/7-10/7-18/11 || werckismic || || 22 || 0-4-8-11 || 1-6/5-10/7-18/11 || valentine || || 23 || 0-2-9-11 || 1-12/11-3/2-18/11 || ambitonal || || 24 || 0-4-9-11 || 1-6/5-3/2-18/11 || biyatismic || || 25 || 0-7-9-11 || 1-11/8-3/2-18/11 || biyatismic || || 26 || 0-2-4-12 || 1-12/11-6/5-12/7 || utonal || || 27 || 0-2-5-12 || 1-11/10-5/4-12/7 || zeus || || 28 || 0-3-5-12 || 1-8/7-5/4-12/7 || zeus || || 29 || 0-2-7-12 || 1-11/10-11/8-12/7 || zeus || || 30 || 0-3-7-12 || 1-8/7-11/8-12/7 || keenanismic || || 31 || 0-4-7-12 || 1-6/5-11/8-12/7 || keenanismic || || 32 || 0-5-7-12 || 1-5/4-11/8-12/7 || keenanismic || || 33 || 0-3-8-12 || 1-8/7-10/7-12/7 || otonal || || 34 || 0-4-8-12 || 1-6/5-10/7-12/7 || starling || || 35 || 0-5-8-12 || 1-5/4-10/7-12/7 || keenanismic || || 36 || 0-2-9-12 || 1-12/11-3/2-12/7 || utonal || || 37 || 0-4-9-12 || 1-6/5-3/2-12/7 || utonal || || 38 || 0-5-9-12 || 1-5/4-3/2-12/7 || keenanismic || || 39 || 0-7-9-12 || 1-11/8-3/2-12/7 || zeus || || 40 || 0-2-10-12 || 1-11/10-11/7-12/7 || biyatismic || || 41 || 0-3-10-12 || 1-8/7-11/7-12/7 || otonal || || 42 || 0-5-10-12 || 1-5/4-11/7-12/7 || zeus || || 43 || 0-7-10-12 || 1-11/8-11/7-12/7 || zeus || || 44 || 0-8-10-12 || 1-10/7-11/7-12/7 || otonal || || 45 || 0-2-4-13 || 1-11/10-6/5-9/5 || otonal || || 46 || 0-2-5-13 || 1-11/10-5/4-9/5 || thrush || || 47 || 0-3-5-13 || 1-8/7-5/4-9/5 || thrush || || 48 || 0-3-8-13 || 1-8/7-10/7-9/5 || thrush || || 49 || 0-4-8-13 || 1-6/5-10/7-9/5 || starling || || 50 || 0-5-8-13 || 1-5/4-10/7-9/5 || starling || || 51 || 0-2-9-13 || 1-11/10-3/2-9/5 || biyatismic || || 52 || 0-4-9-13 || 1-6/5-3/2-9/5 || ambitonal || || 53 || 0-5-9-13 || 1-5/4-3/2-9/5 || starling || || 54 || 0-2-10-13 || 1-11/10-11/7-9/5 || werckismic || || 55 || 0-3-10-13 || 1-8/7-11/7-9/5 || werckismic || || 56 || 0-5-10-13 || 1-5/4-11/7-9/5 || thrush || || 57 || 0-8-10-13 || 1-10/7-11/7-9/5 || thrush || || 58 || 0-2-11-13 || 1-11/10-18/11-9/5 || biyatismic || || 59 || 0-3-11-13 || 1-8/7-18/11-9/5 || werckismic || || 60 || 0-4-11-13 || 1-6/5-18/11-9/5 || biyatismic || || 61 || 0-8-11-13 || 1-10/7-18/11-9/5 || thrush || || 62 || 0-9-11-13 || 1-3/2-18/11-9/5 || utonal || || 63 || 0-5-7-18 || 1-5/4-11/8-9/8 || otonal || || 64 || 0-5-8-18 || 1-5/4-10/7-9/8 || werckismic || || 65 || 0-5-9-18 || 1-5/4-3/2-9/8 || otonal || || 66 || 0-7-9-18 || 1-11/8-3/2-9/8 || otonal || || 67 || 0-5-10-18 || 1-5/4-11/7-9/8 || thrush || || 68 || 0-7-10-18 || 1-11/8-11/7-9/8 || werckismic || || 69 || 0-8-10-18 || 1-10/7-11/7-9/8 || werckismic || || 70 || 0-7-11-18 || 1-11/8-18/11-9/8 || biyatismic || || 71 || 0-8-11-18 || 1-10/7-18/11-9/8 || werckismic || || 72 || 0-9-11-18 || 1-3/2-18/11-9/8 || utonal || || 73 || 0-5-13-18 || 1-5/4-9/5-9/8 || starling || || 74 || 0-8-13-18 || 1-10/7-9/5-9/8 || thrush || || 75 || 0-9-13-18 || 1-3/2-9/5-9/8 || utonal || || 76 || 0-10-13-18 || 1-11/7-9/5-9/8 || werckismic || || 77 || 0-11-13-18 || 1-18/11-9/5-9/8 || utonal || || 78 || 0-3-8-21 || 1-8/7-10/7-9/7 || otonal || || 79 || 0-3-10-21 || 1-8/7-11/7-9/7 || otonal || || 80 || 0-8-10-21 || 1-10/7-11/7-9/7 || otonal || || 81 || 0-3-11-21 || 1-8/7-18/11-9/7 || werckismic || || 82 || 0-8-11-21 || 1-10/7-18/11-9/7 || werckismic || || 83 || 0-9-11-21 || 1-3/2-18/11-9/7 || utonal || || 84 || 0-3-12-21 || 1-8/7-12/7-9/7 || otonal || || 85 || 0-8-12-21 || 1-10/7-12/7-9/7 || otonal || || 86 || 0-9-12-21 || 1-3/2-12/7-9/7 || ambitonal || || 87 || 0-10-12-21 || 1-11/7-12/7-9/7 || otonal || || 88 || 0-3-13-21 || 1-8/7-9/5-9/7 || werckismic || || 89 || 0-8-13-21 || 1-10/7-9/5-9/7 || starling || || 90 || 0-9-13-21 || 1-3/2-9/5-9/7 || utonal || || 91 || 0-10-13-21 || 1-11/7-9/5-9/7 || werckismic || || 92 || 0-11-13-21 || 1-18/11-9/5-9/7 || utonal || || 93 || 0-8-18-21 || 1-10/7-9/8-9/7 || werckismic || || 94 || 0-9-18-21 || 1-3/2-9/8-9/7 || utonal || || 95 || 0-10-18-21 || 1-11/7-9/8-9/7 || werckismic || || 96 || 0-11-18-21 || 1-18/11-9/8-9/7 || utonal || || 97 || 0-13-18-21 || 1-9/5-9/8-9/7 || utonal || =Pentads= || Number || Chord || Transversal || Type || || 1 || 0-2-4-7-9 || 1-11/10-6/5-11/8-3/2 || zeus || || 2 || 0-2-5-7-9 || 1-11/10-5/4-11/8-3/2 || zeus || || 3 || 0-2-5-7-10 || 1-11/10-5/4-11/8-11/7 || valinorsmic || || 4 || 0-3-5-7-10 || 1-8/7-5/4-11/8-11/7 || zeus || || 5 || 0-3-5-8-10 || 1-8/7-5/4-10/7-11/7 || valinorsmic || || 6 || 0-2-4-7-11 || 1-11/10-6/5-11/8-18/11 || zeus || || 7 || 0-2-4-9-11 || 1-11/10-6/5-3/2-18/11 || biyatismic || || 8 || 0-2-7-9-11 || 1-11/10-11/8-3/2-18/11 || biyatismic || || 9 || 0-4-7-9-11 || 1-6/5-11/8-3/2-18/11 || zeus || || 10 || 0-2-4-7-12 || 1-11/10-6/5-11/8-12/7 || zeus || || 11 || 0-2-5-7-12 || 1-11/10-5/4-11/8-12/7 || zeus || || 12 || 0-3-5-7-12 || 1-8/7-5/4-11/8-12/7 || zeus || || 13 || 0-3-5-8-12 || 1-8/7-5/4-10/7-12/7 || zeus || || 14 || 0-2-4-9-12 || 1-12/11-6/5-3/2-12/7 || utonal || || 15 || 0-2-5-9-12 || 1-11/10-5/4-3/2-12/7 || zeus || || 16 || 0-2-7-9-12 || 1-11/10-11/8-3/2-12/7 || zeus || || 17 || 0-4-7-9-12 || 1-6/5-11/8-3/2-12/7 || zeus || || 18 || 0-5-7-9-12 || 1-5/4-11/8-3/2-12/7 || zeus || || 19 || 0-2-5-10-12 || 1-11/10-5/4-11/7-12/7 || zeus || || 20 || 0-3-5-10-12 || 1-8/7-5/4-11/7-12/7 || zeus || || 21 || 0-2-7-10-12 || 1-11/10-11/8-11/7-12/7 || zeus || || 22 || 0-3-7-10-12 || 1-8/7-11/8-11/7-12/7 || zeus || || 23 || 0-5-7-10-12 || 1-5/4-11/8-11/7-12/7 || zeus || || 24 || 0-3-8-10-12 || 1-8/7-10/7-11/7-12/7 || otonal || || 25 || 0-5-8-10-12 || 1-5/4-10/7-11/7-12/7 || zeus || || 26 || 0-3-5-8-13 || 1-8/7-5/4-10/7-9/5 || thrush || || 27 || 0-2-4-9-13 || 1-11/10-6/5-3/2-9/5 || biyatismic || || 28 || 0-2-5-9-13 || 1-11/10-5/4-3/2-9/5 || valentine || || 29 || 0-2-5-10-13 || 1-11/10-5/4-11/7-9/5 || thrush || || 30 || 0-3-5-10-13 || 1-8/7-5/4-11/7-9/5 || thrush || || 31 || 0-3-8-10-13 || 1-8/7-10/7-11/7-9/5 || thrush || || 32 || 0-5-8-10-13 || 1-5/4-10/7-11/7-9/5 || thrush || || 33 || 0-2-4-11-13 || 1-11/10-6/5-18/11-9/5 || biyatismic || || 34 || 0-3-8-11-13 || 1-8/7-10/7-18/11-9/5 || thrush || || 35 || 0-4-8-11-13 || 1-6/5-10/7-18/11-9/5 || valentine || || 36 || 0-2-9-11-13 || 1-11/10-3/2-18/11-9/5 || biyatismic || || 37 || 0-4-9-11-13 || 1-6/5-3/2-18/11-9/5 || biyatismic || || 38 || 0-5-7-9-18 || 1-5/4-11/8-3/2-9/8 || otonal || || 39 || 0-5-7-10-18 || 1-5/4-11/8-11/7-9/8 || thrush || || 40 || 0-5-8-10-18 || 1-5/4-10/7-11/7-9/8 || thrush || || 41 || 0-7-9-11-18 || 1-11/8-3/2-18/11-9/8 || biyatismic || || 42 || 0-5-8-13-18 || 1-5/4-10/7-9/5-9/8 || thrush || || 43 || 0-5-9-13-18 || 1-5/4-3/2-9/5-9/8 || starling || || 44 || 0-5-10-13-18 || 1-5/4-11/7-9/5-9/8 || thrush || || 45 || 0-8-10-13-18 || 1-10/7-11/7-9/5-9/8 || thrush || || 46 || 0-8-11-13-18 || 1-10/7-18/11-9/5-9/8 || thrush || || 47 || 0-9-11-13-18 || 1-3/2-18/11-9/5-9/8 || utonal || || 48 || 0-3-8-10-21 || 1-8/7-10/7-11/7-9/7 || otonal || || 49 || 0-3-8-11-21 || 1-8/7-10/7-18/11-9/7 || werckismic || || 50 || 0-3-8-12-21 || 1-8/7-10/7-12/7-9/7 || otonal || || 51 || 0-3-10-12-21 || 1-8/7-11/7-12/7-9/7 || otonal || || 52 || 0-8-10-12-21 || 1-10/7-11/7-12/7-9/7 || otonal || || 53 || 0-3-8-13-21 || 1-8/7-10/7-9/5-9/7 || thrush || || 54 || 0-3-10-13-21 || 1-8/7-11/7-9/5-9/7 || werckismic || || 55 || 0-8-10-13-21 || 1-10/7-11/7-9/5-9/7 || thrush || || 56 || 0-3-11-13-21 || 1-8/7-18/11-9/5-9/7 || werckismic || || 57 || 0-8-11-13-21 || 1-10/7-18/11-9/5-9/7 || thrush || || 58 || 0-9-11-13-21 || 1-3/2-18/11-9/5-9/7 || utonal || || 59 || 0-8-10-18-21 || 1-10/7-11/7-9/8-9/7 || werckismic || || 60 || 0-8-11-18-21 || 1-10/7-18/11-9/8-9/7 || werckismic || || 61 || 0-9-11-18-21 || 1-3/2-18/11-9/8-9/7 || utonal || || 62 || 0-8-13-18-21 || 1-10/7-9/5-9/8-9/7 || thrush || || 63 || 0-9-13-18-21 || 1-3/2-9/5-9/8-9/7 || utonal || || 64 || 0-10-13-18-21 || 1-11/7-9/5-9/8-9/7 || werckismic || || 65 || 0-11-13-18-21 || 1-18/11-9/5-9/8-9/7 || utonal || =Hexads= || Number || Chord || Transversal || Type || || 1 || 0-2-4-7-9-11 || 1-11/10-6/5-11/8-3/2-18/11 || zeus || || 2 || 0-2-4-7-9-12 || 1-11/10-6/5-11/8-3/2-12/7 || zeus || || 3 || 0-2-5-7-9-12 || 1-11/10-5/4-11/8-3/2-12/7 || zeus || || 4 || 0-2-5-7-10-12 || 1-11/10-5/4-11/8-11/7-12/7 || zeus || || 5 || 0-3-5-7-10-12 || 1-8/7-5/4-11/8-11/7-12/7 || zeus || || 6 || 0-3-5-8-10-12 || 1-8/7-5/4-10/7-11/7-12/7 || zeus || || 7 || 0-3-5-8-10-13 || 1-8/7-5/4-10/7-11/7-9/5 || thrush || || 8 || 0-2-4-9-11-13 || 1-11/10-6/5-3/2-18/11-9/5 || biyatismic || || 9 || 0-5-8-10-13-18 || 1-5/4-10/7-11/7-9/5-9/8 || thrush || || 10 || 0-3-8-10-12-21 || 1-8/7-10/7-11/7-12/7-9/7 || otonal || || 11 || 0-3-8-10-13-21 || 1-8/7-10/7-11/7-9/5-9/7 || thrush || || 12 || 0-3-8-11-13-21 || 1-8/7-10/7-18/11-9/5-9/7 || thrush || || 13 || 0-8-10-13-18-21 || 1-10/7-11/7-9/5-9/8-9/7 || thrush || || 14 || 0-8-11-13-18-21 || 1-10/7-18/11-9/5-9/8-9/7 || thrush || || 15 || 0-9-11-13-18-21 || 1-3/2-18/11-9/5-9/8-9/7 || utonal ||
Original HTML content:
<html><head><title>Chords of valentine</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-11-limit">valentine temperament</a>. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. 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. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.<br />
<br />
If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.<br />
<br />
Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a> is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.<br />
<br />
In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-4<br />
</td>
<td>1-11/10-6/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5<br />
</td>
<td>1-11/10-5/4<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-5<br />
</td>
<td>1-8/7-5/4<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-7<br />
</td>
<td>1-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-7<br />
</td>
<td>1-8/7-11/8<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-4-7<br />
</td>
<td>1-6/5-11/8<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-5-7<br />
</td>
<td>1-5/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-3-8<br />
</td>
<td>1-8/7-10/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-4-8<br />
</td>
<td>1-6/5-10/7<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-5-8<br />
</td>
<td>1-5/4-10/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-2-9<br />
</td>
<td>1-12/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-4-9<br />
</td>
<td>1-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-5-9<br />
</td>
<td>1-5/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-7-9<br />
</td>
<td>1-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-2-10<br />
</td>
<td>1-11/10-11/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-3-10<br />
</td>
<td>1-8/7-11/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-5-10<br />
</td>
<td>1-5/4-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-7-10<br />
</td>
<td>1-11/8-11/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-8-10<br />
</td>
<td>1-10/7-11/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-2-11<br />
</td>
<td>1-12/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-3-11<br />
</td>
<td>1-8/7-18/11<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-4-11<br />
</td>
<td>1-6/5-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-7-11<br />
</td>
<td>1-11/8-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-8-11<br />
</td>
<td>1-10/7-18/11<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-9-11<br />
</td>
<td>1-3/2-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-2-12<br />
</td>
<td>1-12/11-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-3-12<br />
</td>
<td>1-8/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-4-12<br />
</td>
<td>1-6/5-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-5-12<br />
</td>
<td>1-5/4-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-7-12<br />
</td>
<td>1-11/8-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-8-12<br />
</td>
<td>1-10/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-9-12<br />
</td>
<td>1-3/2-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-10-12<br />
</td>
<td>1-11/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-2-13<br />
</td>
<td>1-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-3-13<br />
</td>
<td>1-8/7-9/5<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-4-13<br />
</td>
<td>1-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-5-13<br />
</td>
<td>1-5/4-9/5<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-8-13<br />
</td>
<td>1-10/7-9/5<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-9-13<br />
</td>
<td>1-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-10-13<br />
</td>
<td>1-11/7-9/5<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-11-13<br />
</td>
<td>1-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-5-18<br />
</td>
<td>1-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-7-18<br />
</td>
<td>1-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-8-18<br />
</td>
<td>1-10/7-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-9-18<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-10-18<br />
</td>
<td>1-11/7-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-11-18<br />
</td>
<td>1-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-13-18<br />
</td>
<td>1-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-3-21<br />
</td>
<td>1-8/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-8-21<br />
</td>
<td>1-10/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-9-21<br />
</td>
<td>1-3/2-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-10-21<br />
</td>
<td>1-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-11-21<br />
</td>
<td>1-18/11-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-12-21<br />
</td>
<td>1-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-13-21<br />
</td>
<td>1-9/5-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-18-21<br />
</td>
<td>1-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tetrads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-4-7<br />
</td>
<td>1-11/10-6/5-11/8<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5-7<br />
</td>
<td>1-11/10-5/4-11/8<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-3-5-7<br />
</td>
<td>1-8/7-5/4-11/8<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-3-5-8<br />
</td>
<td>1-8/7-5/4-10/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-2-4-9<br />
</td>
<td>1-12/11-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-5-9<br />
</td>
<td>1-11/10-5/4-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-2-7-9<br />
</td>
<td>1-11/10-11/8-3/2<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-4-7-9<br />
</td>
<td>1-6/5-11/8-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-5-7-9<br />
</td>
<td>1-5/4-11/8-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-2-5-10<br />
</td>
<td>1-11/10-5/4-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-3-5-10<br />
</td>
<td>1-8/7-5/4-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-2-7-10<br />
</td>
<td>1-11/10-11/8-11/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-3-7-10<br />
</td>
<td>1-8/7-11/8-11/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-5-7-10<br />
</td>
<td>1-5/4-11/8-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-3-8-10<br />
</td>
<td>1-8/7-10/7-11/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-5-8-10<br />
</td>
<td>1-5/4-10/7-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-2-4-11<br />
</td>
<td>1-11/10-6/5-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-2-7-11<br />
</td>
<td>1-11/10-11/8-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-3-7-11<br />
</td>
<td>1-8/7-11/8-18/11<br />
</td>
<td>valentine<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-4-7-11<br />
</td>
<td>1-6/5-11/8-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-3-8-11<br />
</td>
<td>1-8/7-10/7-18/11<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-4-8-11<br />
</td>
<td>1-6/5-10/7-18/11<br />
</td>
<td>valentine<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-2-9-11<br />
</td>
<td>1-12/11-3/2-18/11<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-4-9-11<br />
</td>
<td>1-6/5-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-7-9-11<br />
</td>
<td>1-11/8-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-2-4-12<br />
</td>
<td>1-12/11-6/5-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-2-5-12<br />
</td>
<td>1-11/10-5/4-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-3-5-12<br />
</td>
<td>1-8/7-5/4-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-2-7-12<br />
</td>
<td>1-11/10-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-3-7-12<br />
</td>
<td>1-8/7-11/8-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-4-7-12<br />
</td>
<td>1-6/5-11/8-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-5-7-12<br />
</td>
<td>1-5/4-11/8-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-3-8-12<br />
</td>
<td>1-8/7-10/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-4-8-12<br />
</td>
<td>1-6/5-10/7-12/7<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-5-8-12<br />
</td>
<td>1-5/4-10/7-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-2-9-12<br />
</td>
<td>1-12/11-3/2-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-4-9-12<br />
</td>
<td>1-6/5-3/2-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-5-9-12<br />
</td>
<td>1-5/4-3/2-12/7<br />
</td>
<td>keenanismic<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-7-9-12<br />
</td>
<td>1-11/8-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-2-10-12<br />
</td>
<td>1-11/10-11/7-12/7<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-3-10-12<br />
</td>
<td>1-8/7-11/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-5-10-12<br />
</td>
<td>1-5/4-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-7-10-12<br />
</td>
<td>1-11/8-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-8-10-12<br />
</td>
<td>1-10/7-11/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-2-4-13<br />
</td>
<td>1-11/10-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-2-5-13<br />
</td>
<td>1-11/10-5/4-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-3-5-13<br />
</td>
<td>1-8/7-5/4-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-3-8-13<br />
</td>
<td>1-8/7-10/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-4-8-13<br />
</td>
<td>1-6/5-10/7-9/5<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-5-8-13<br />
</td>
<td>1-5/4-10/7-9/5<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-2-9-13<br />
</td>
<td>1-11/10-3/2-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-4-9-13<br />
</td>
<td>1-6/5-3/2-9/5<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-5-9-13<br />
</td>
<td>1-5/4-3/2-9/5<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-2-10-13<br />
</td>
<td>1-11/10-11/7-9/5<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-3-10-13<br />
</td>
<td>1-8/7-11/7-9/5<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-5-10-13<br />
</td>
<td>1-5/4-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-8-10-13<br />
</td>
<td>1-10/7-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-2-11-13<br />
</td>
<td>1-11/10-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-3-11-13<br />
</td>
<td>1-8/7-18/11-9/5<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-4-11-13<br />
</td>
<td>1-6/5-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-8-11-13<br />
</td>
<td>1-10/7-18/11-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-9-11-13<br />
</td>
<td>1-3/2-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-5-7-18<br />
</td>
<td>1-5/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-5-8-18<br />
</td>
<td>1-5/4-10/7-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-5-9-18<br />
</td>
<td>1-5/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-7-9-18<br />
</td>
<td>1-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>0-5-10-18<br />
</td>
<td>1-5/4-11/7-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>0-7-10-18<br />
</td>
<td>1-11/8-11/7-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>0-8-10-18<br />
</td>
<td>1-10/7-11/7-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>0-7-11-18<br />
</td>
<td>1-11/8-18/11-9/8<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>0-8-11-18<br />
</td>
<td>1-10/7-18/11-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>0-9-11-18<br />
</td>
<td>1-3/2-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>0-5-13-18<br />
</td>
<td>1-5/4-9/5-9/8<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>0-8-13-18<br />
</td>
<td>1-10/7-9/5-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>0-9-13-18<br />
</td>
<td>1-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>0-10-13-18<br />
</td>
<td>1-11/7-9/5-9/8<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>0-11-13-18<br />
</td>
<td>1-18/11-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>0-3-8-21<br />
</td>
<td>1-8/7-10/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>79<br />
</td>
<td>0-3-10-21<br />
</td>
<td>1-8/7-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>80<br />
</td>
<td>0-8-10-21<br />
</td>
<td>1-10/7-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>81<br />
</td>
<td>0-3-11-21<br />
</td>
<td>1-8/7-18/11-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>82<br />
</td>
<td>0-8-11-21<br />
</td>
<td>1-10/7-18/11-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>83<br />
</td>
<td>0-9-11-21<br />
</td>
<td>1-3/2-18/11-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>84<br />
</td>
<td>0-3-12-21<br />
</td>
<td>1-8/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>85<br />
</td>
<td>0-8-12-21<br />
</td>
<td>1-10/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>86<br />
</td>
<td>0-9-12-21<br />
</td>
<td>1-3/2-12/7-9/7<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>87<br />
</td>
<td>0-10-12-21<br />
</td>
<td>1-11/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>88<br />
</td>
<td>0-3-13-21<br />
</td>
<td>1-8/7-9/5-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>89<br />
</td>
<td>0-8-13-21<br />
</td>
<td>1-10/7-9/5-9/7<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>90<br />
</td>
<td>0-9-13-21<br />
</td>
<td>1-3/2-9/5-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>91<br />
</td>
<td>0-10-13-21<br />
</td>
<td>1-11/7-9/5-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>92<br />
</td>
<td>0-11-13-21<br />
</td>
<td>1-18/11-9/5-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>93<br />
</td>
<td>0-8-18-21<br />
</td>
<td>1-10/7-9/8-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>94<br />
</td>
<td>0-9-18-21<br />
</td>
<td>1-3/2-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>95<br />
</td>
<td>0-10-18-21<br />
</td>
<td>1-11/7-9/8-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>96<br />
</td>
<td>0-11-18-21<br />
</td>
<td>1-18/11-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>97<br />
</td>
<td>0-13-18-21<br />
</td>
<td>1-9/5-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Pentads"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-4-7-9<br />
</td>
<td>1-11/10-6/5-11/8-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-5-7-9<br />
</td>
<td>1-11/10-5/4-11/8-3/2<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-5-7-10<br />
</td>
<td>1-11/10-5/4-11/8-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-3-5-7-10<br />
</td>
<td>1-8/7-5/4-11/8-11/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-5-8-10<br />
</td>
<td>1-8/7-5/4-10/7-11/7<br />
</td>
<td>valinorsmic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-2-4-7-11<br />
</td>
<td>1-11/10-6/5-11/8-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-2-4-9-11<br />
</td>
<td>1-11/10-6/5-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-2-7-9-11<br />
</td>
<td>1-11/10-11/8-3/2-18/11<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-4-7-9-11<br />
</td>
<td>1-6/5-11/8-3/2-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-2-4-7-12<br />
</td>
<td>1-11/10-6/5-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-2-5-7-12<br />
</td>
<td>1-11/10-5/4-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-3-5-7-12<br />
</td>
<td>1-8/7-5/4-11/8-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-3-5-8-12<br />
</td>
<td>1-8/7-5/4-10/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-2-4-9-12<br />
</td>
<td>1-12/11-6/5-3/2-12/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-2-5-9-12<br />
</td>
<td>1-11/10-5/4-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-2-7-9-12<br />
</td>
<td>1-11/10-11/8-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-4-7-9-12<br />
</td>
<td>1-6/5-11/8-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-5-7-9-12<br />
</td>
<td>1-5/4-11/8-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-2-5-10-12<br />
</td>
<td>1-11/10-5/4-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-3-5-10-12<br />
</td>
<td>1-8/7-5/4-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-2-7-10-12<br />
</td>
<td>1-11/10-11/8-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-3-7-10-12<br />
</td>
<td>1-8/7-11/8-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-5-7-10-12<br />
</td>
<td>1-5/4-11/8-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-3-8-10-12<br />
</td>
<td>1-8/7-10/7-11/7-12/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-5-8-10-12<br />
</td>
<td>1-5/4-10/7-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-3-5-8-13<br />
</td>
<td>1-8/7-5/4-10/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-2-4-9-13<br />
</td>
<td>1-11/10-6/5-3/2-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-2-5-9-13<br />
</td>
<td>1-11/10-5/4-3/2-9/5<br />
</td>
<td>valentine<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-2-5-10-13<br />
</td>
<td>1-11/10-5/4-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-3-5-10-13<br />
</td>
<td>1-8/7-5/4-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-3-8-10-13<br />
</td>
<td>1-8/7-10/7-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-5-8-10-13<br />
</td>
<td>1-5/4-10/7-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-2-4-11-13<br />
</td>
<td>1-11/10-6/5-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-3-8-11-13<br />
</td>
<td>1-8/7-10/7-18/11-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-4-8-11-13<br />
</td>
<td>1-6/5-10/7-18/11-9/5<br />
</td>
<td>valentine<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-2-9-11-13<br />
</td>
<td>1-11/10-3/2-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-4-9-11-13<br />
</td>
<td>1-6/5-3/2-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-5-7-9-18<br />
</td>
<td>1-5/4-11/8-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-5-7-10-18<br />
</td>
<td>1-5/4-11/8-11/7-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-5-8-10-18<br />
</td>
<td>1-5/4-10/7-11/7-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-7-9-11-18<br />
</td>
<td>1-11/8-3/2-18/11-9/8<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-5-8-13-18<br />
</td>
<td>1-5/4-10/7-9/5-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-5-9-13-18<br />
</td>
<td>1-5/4-3/2-9/5-9/8<br />
</td>
<td>starling<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-5-10-13-18<br />
</td>
<td>1-5/4-11/7-9/5-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-8-10-13-18<br />
</td>
<td>1-10/7-11/7-9/5-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-8-11-13-18<br />
</td>
<td>1-10/7-18/11-9/5-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-9-11-13-18<br />
</td>
<td>1-3/2-18/11-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-3-8-10-21<br />
</td>
<td>1-8/7-10/7-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-3-8-11-21<br />
</td>
<td>1-8/7-10/7-18/11-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-3-8-12-21<br />
</td>
<td>1-8/7-10/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-3-10-12-21<br />
</td>
<td>1-8/7-11/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-8-10-12-21<br />
</td>
<td>1-10/7-11/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-3-8-13-21<br />
</td>
<td>1-8/7-10/7-9/5-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-3-10-13-21<br />
</td>
<td>1-8/7-11/7-9/5-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-8-10-13-21<br />
</td>
<td>1-10/7-11/7-9/5-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-3-11-13-21<br />
</td>
<td>1-8/7-18/11-9/5-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-8-11-13-21<br />
</td>
<td>1-10/7-18/11-9/5-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-9-11-13-21<br />
</td>
<td>1-3/2-18/11-9/5-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-8-10-18-21<br />
</td>
<td>1-10/7-11/7-9/8-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-8-11-18-21<br />
</td>
<td>1-10/7-18/11-9/8-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-9-11-18-21<br />
</td>
<td>1-3/2-18/11-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-8-13-18-21<br />
</td>
<td>1-10/7-9/5-9/8-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-9-13-18-21<br />
</td>
<td>1-3/2-9/5-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-10-13-18-21<br />
</td>
<td>1-11/7-9/5-9/8-9/7<br />
</td>
<td>werckismic<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-11-13-18-21<br />
</td>
<td>1-18/11-9/5-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Hexads"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexads</h1>
<table class="wiki_table">
<tr>
<td>Number<br />
</td>
<td>Chord<br />
</td>
<td>Transversal<br />
</td>
<td>Type<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0-2-4-7-9-11<br />
</td>
<td>1-11/10-6/5-11/8-3/2-18/11<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-2-4-7-9-12<br />
</td>
<td>1-11/10-6/5-11/8-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-2-5-7-9-12<br />
</td>
<td>1-11/10-5/4-11/8-3/2-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-2-5-7-10-12<br />
</td>
<td>1-11/10-5/4-11/8-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-3-5-7-10-12<br />
</td>
<td>1-8/7-5/4-11/8-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-3-5-8-10-12<br />
</td>
<td>1-8/7-5/4-10/7-11/7-12/7<br />
</td>
<td>zeus<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-3-5-8-10-13<br />
</td>
<td>1-8/7-5/4-10/7-11/7-9/5<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-2-4-9-11-13<br />
</td>
<td>1-11/10-6/5-3/2-18/11-9/5<br />
</td>
<td>biyatismic<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-5-8-10-13-18<br />
</td>
<td>1-5/4-10/7-11/7-9/5-9/8<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-3-8-10-12-21<br />
</td>
<td>1-8/7-10/7-11/7-12/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-3-8-10-13-21<br />
</td>
<td>1-8/7-10/7-11/7-9/5-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-3-8-11-13-21<br />
</td>
<td>1-8/7-10/7-18/11-9/5-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-8-10-13-18-21<br />
</td>
<td>1-10/7-11/7-9/5-9/8-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-8-11-13-18-21<br />
</td>
<td>1-10/7-18/11-9/5-9/8-9/7<br />
</td>
<td>thrush<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-9-11-13-18-21<br />
</td>
<td>1-3/2-18/11-9/5-9/8-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
</table>
</body></html>