Chords of octacot: Difference between revisions

Revision as of 01:49, 28 December 2011

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Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Tetracot family#Octacot|octacot temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot. 

Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the [[88cET|88 cents temperament]] is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.

=Triads=
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-4 || 1-10/9-11/9 || otonal ||
|| 2 || 0-2-5 || 1-10/9-9/7 || sensamagic ||
|| 3 || 0-3-5 || 1-7/6-9/7 || sensamagic ||
|| 4 || 0-2-7 || 1-10/9-10/7 || utonal ||
|| 5 || 0-3-7 || 1-7/6-10/7 || swetismic ||
|| 6 || 0-4-7 || 1-11/9-10/7 || swetismic ||
|| 7 || 0-5-7 || 1-9/7-10/7 || otonal ||
|| 8 || 0-3-8 || 1-7/6-3/2 || otonal ||
|| 9 || 0-4-8 || 1-11/9-3/2 || rastmic ||
|| 10 || 0-5-8 || 1-9/7-3/2 || utonal ||
|| 11 || 0-2-9 || 1-11/10-11/7 || utonal ||
|| 12 || 0-4-9 || 1-11/9-11/7 || utonal ||
|| 13 || 0-5-9 || 1-9/7-11/7 || otonal ||
|| 14 || 0-7-9 || 1-10/7-11/7 || otonal ||
|| 15 || 0-2-10 || 1-10/9-5/3 || utonal ||
|| 16 || 0-3-10 || 1-7/6-5/3 || otonal ||
|| 17 || 0-5-10 || 1-9/7-5/3 || sensamagic ||
|| 18 || 0-7-10 || 1-10/7-5/3 || utonal ||
|| 19 || 0-8-10 || 1-3/2-5/3 || otonal ||
|| 20 || 0-2-11 || 1-10/9-7/4 || werkismic ||
|| 21 || 0-3-11 || 1-7/6-7/4 || utonal ||
|| 22 || 0-4-11 || 1-11/9-7/4 || werkismic ||
|| 23 || 0-7-11 || 1-10/7-7/4 || werkismic ||
|| 24 || 0-8-11 || 1-3/2-7/4 || otonal ||
|| 25 || 0-9-11 || 1-11/7-7/4 || werkismic ||
|| 26 || 0-2-12 || 1-11/10-11/6 || utonal ||
|| 27 || 0-3-12 || 1-7/6-11/6 || otonal ||
|| 28 || 0-4-12 || 1-11/9-11/6 || utonal ||
|| 29 || 0-5-12 || 1-9/7-11/6 || swetismic ||
|| 30 || 0-7-12 || 1-10/7-11/6 || swetismic ||
|| 31 || 0-8-12 || 1-3/2-11/6 || otonal ||
|| 32 || 0-9-12 || 1-11/7-11/6 || utonal ||
|| 33 || 0-10-12 || 1-5/3-11/6 || otonal ||
|| 34 || 0-4-16 || 1-11/9-9/8 || rastmic ||
|| 35 || 0-5-16 || 1-9/7-9/8 || utonal ||
|| 36 || 0-7-16 || 1-10/7-9/8 || werkismic ||
|| 37 || 0-8-16 || 1-3/2-9/8 || ambitonal ||
|| 38 || 0-9-16 || 1-11/7-9/8 || werkismic ||
|| 39 || 0-11-16 || 1-7/4-9/8 || otonal ||
|| 40 || 0-12-16 || 1-11/6-9/8 || rastmic ||
|| 41 || 0-2-18 || 1-10/9-5/4 || utonal ||
|| 42 || 0-7-18 || 1-10/7-5/4 || utonal ||
|| 43 || 0-8-18 || 1-3/2-5/4 || otonal ||
|| 44 || 0-9-18 || 1-11/7-5/4 || cassacot ||
|| 45 || 0-10-18 || 1-5/3-5/4 || utonal ||
|| 46 || 0-11-18 || 1-7/4-5/4 || otonal ||
|| 47 || 0-16-18 || 1-9/8-5/4 || otonal ||
|| 48 || 0-2-20 || 1-11/10-11/8 || utonal ||
|| 49 || 0-4-20 || 1-11/9-11/8 || utonal ||
|| 50 || 0-8-20 || 1-3/2-11/8 || otonal ||
|| 51 || 0-9-20 || 1-11/7-11/8 || utonal ||
|| 52 || 0-10-20 || 1-5/3-11/8 || ptolemismic ||
|| 53 || 0-11-20 || 1-7/4-11/8 || otonal ||
|| 54 || 0-12-20 || 1-11/6-11/8 || utonal ||
|| 55 || 0-16-20 || 1-9/8-11/8 || otonal ||
|| 56 || 0-18-20 || 1-5/4-11/8 || otonal ||

=Tetrads=
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-4-7 || 1-10/9-11/9-10/7 || octarod ||
|| 2 || 0-2-5-7 || 1-10/9-9/7-10/7 || sensamagic ||
|| 3 || 0-3-5-7 || 1-7/6-9/7-10/7 || octarod ||
|| 4 || 0-3-5-8 || 1-7/6-9/7-3/2 || sensamagic ||
|| 5 || 0-2-4-9 || 1-11/10-11/9-11/7 || utonal ||
|| 6 || 0-2-5-9 || 1-10/9-9/7-11/7 || octarod ||
|| 7 || 0-2-7-9 || 1-10/9-10/7-11/7 || ptolemismic ||
|| 8 || 0-4-7-9 || 1-11/9-10/7-11/7 || octarod ||
|| 9 || 0-5-7-9 || 1-9/7-10/7-11/7 || otonal ||
|| 10 || 0-2-5-10 || 1-10/9-9/7-5/3 || sensamagic ||
|| 11 || 0-3-5-10 || 1-7/6-9/7-5/3 || sensamagic ||
|| 12 || 0-2-7-10 || 1-10/9-10/7-5/3 || utonal ||
|| 13 || 0-3-7-10 || 1-7/6-10/7-5/3 || swetismic ||
|| 14 || 0-5-7-10 || 1-9/7-10/7-5/3 || sensamagic ||
|| 15 || 0-3-8-10 || 1-7/6-3/2-5/3 || otonal ||
|| 16 || 0-5-8-10 || 1-9/7-3/2-5/3 || sensamagic ||
|| 17 || 0-2-4-11 || 1-10/9-11/9-7/4 || octagari ||
|| 18 || 0-2-7-11 || 1-10/9-10/7-7/4 || werkismic ||
|| 19 || 0-3-7-11 || 1-7/6-10/7-7/4 || jove ||
|| 20 || 0-4-7-11 || 1-11/9-10/7-7/4 || jove ||
|| 21 || 0-3-8-11 || 1-7/6-3/2-7/4 || ambitonal ||
|| 22 || 0-4-8-11 || 1-11/9-3/2-7/4 || jove ||
|| 23 || 0-2-9-11 || 1-10/9-11/7-7/4 || octagari ||
|| 24 || 0-4-9-11 || 1-11/9-11/7-7/4 || werkismic ||
|| 25 || 0-7-9-11 || 1-10/7-11/7-7/4 || octagari ||
|| 26 || 0-2-4-12 || 1-11/10-11/9-11/6 || utonal ||
|| 27 || 0-2-5-12 || 1-10/9-9/7-11/6 || octarod ||
|| 28 || 0-3-5-12 || 1-7/6-9/7-11/6 || octarod ||
|| 29 || 0-2-7-12 || 1-10/9-10/7-11/6 || octarod ||
|| 30 || 0-3-7-12 || 1-7/6-10/7-11/6 || swetismic ||
|| 31 || 0-4-7-12 || 1-11/9-10/7-11/6 || swetismic ||
|| 32 || 0-5-7-12 || 1-9/7-10/7-11/6 || swetismic ||
|| 33 || 0-3-8-12 || 1-7/6-3/2-11/6 || otonal ||
|| 34 || 0-4-8-12 || 1-11/9-3/2-11/6 || rastmic ||
|| 35 || 0-5-8-12 || 1-9/7-3/2-11/6 || swetismic ||
|| 36 || 0-2-9-12 || 1-11/10-11/7-11/6 || utonal ||
|| 37 || 0-4-9-12 || 1-11/9-11/7-11/6 || utonal ||
|| 38 || 0-5-9-12 || 1-9/7-11/7-11/6 || swetismic ||
|| 39 || 0-7-9-12 || 1-10/7-11/7-11/6 || octarod ||
|| 40 || 0-2-10-12 || 1-10/9-5/3-11/6 || ptolemismic ||
|| 41 || 0-3-10-12 || 1-7/6-5/3-11/6 || otonal ||
|| 42 || 0-5-10-12 || 1-9/7-5/3-11/6 || octarod ||
|| 43 || 0-7-10-12 || 1-10/7-5/3-11/6 || octarod ||
|| 44 || 0-8-10-12 || 1-3/2-5/3-11/6 || otonal ||
|| 45 || 0-4-7-16 || 1-11/9-10/7-9/8 || jove ||
|| 46 || 0-5-7-16 || 1-9/7-10/7-9/8 || werkismic ||
|| 47 || 0-4-8-16 || 1-11/9-3/2-9/8 || rastmic ||
|| 48 || 0-5-8-16 || 1-9/7-3/2-9/8 || utonal ||
|| 49 || 0-4-9-16 || 1-11/9-11/7-9/8 || jove ||
|| 50 || 0-5-9-16 || 1-9/7-11/7-9/8 || werkismic ||
|| 51 || 0-7-9-16 || 1-10/7-11/7-9/8 || octagari ||
|| 52 || 0-4-11-16 || 1-11/9-7/4-9/8 || jove ||
|| 53 || 0-7-11-16 || 1-10/7-7/4-9/8 || werkismic ||
|| 54 || 0-8-11-16 || 1-3/2-7/4-9/8 || otonal ||
|| 55 || 0-9-11-16 || 1-11/7-7/4-9/8 || werkismic ||
|| 56 || 0-4-12-16 || 1-11/9-11/6-9/8 || rastmic ||
|| 57 || 0-5-12-16 || 1-9/7-11/6-9/8 || jove ||
|| 58 || 0-7-12-16 || 1-10/7-11/6-9/8 || jove ||
|| 59 || 0-8-12-16 || 1-3/2-11/6-9/8 || rastmic ||
|| 60 || 0-9-12-16 || 1-11/7-11/6-9/8 || jove ||
|| 61 || 0-2-7-18 || 1-10/9-10/7-5/4 || utonal ||
|| 62 || 0-2-9-18 || 1-10/9-11/7-5/4 || octagari ||
|| 63 || 0-7-9-18 || 1-10/7-11/7-5/4 || octagari ||
|| 64 || 0-2-10-18 || 1-10/9-5/3-5/4 || utonal ||
|| 65 || 0-7-10-18 || 1-10/7-5/3-5/4 || utonal ||
|| 66 || 0-8-10-18 || 1-3/2-5/3-5/4 || ambitonal ||
|| 67 || 0-2-11-18 || 1-10/9-7/4-5/4 || werkismic ||
|| 68 || 0-7-11-18 || 1-10/7-7/4-5/4 || werkismic ||
|| 69 || 0-8-11-18 || 1-3/2-7/4-5/4 || otonal ||
|| 70 || 0-9-11-18 || 1-11/7-7/4-5/4 || octagari ||
|| 71 || 0-7-16-18 || 1-10/7-9/8-5/4 || werkismic ||
|| 72 || 0-8-16-18 || 1-3/2-9/8-5/4 || otonal ||
|| 73 || 0-9-16-18 || 1-11/7-9/8-5/4 || octagari ||
|| 74 || 0-11-16-18 || 1-7/4-9/8-5/4 || otonal ||
|| 75 || 0-2-4-20 || 1-11/10-11/9-11/8 || utonal ||
|| 76 || 0-4-8-20 || 1-11/9-3/2-11/8 || rastmic ||
|| 77 || 0-2-9-20 || 1-11/10-11/7-11/8 || utonal ||
|| 78 || 0-4-9-20 || 1-11/9-11/7-11/8 || utonal ||
|| 79 || 0-2-10-20 || 1-10/9-5/3-11/8 || ptolemismic ||
|| 80 || 0-8-10-20 || 1-3/2-5/3-11/8 || ptolemismic ||
|| 81 || 0-2-11-20 || 1-10/9-7/4-11/8 || octagari ||
|| 82 || 0-4-11-20 || 1-11/9-7/4-11/8 || werkismic ||
|| 83 || 0-8-11-20 || 1-3/2-7/4-11/8 || otonal ||
|| 84 || 0-9-11-20 || 1-11/7-7/4-11/8 || werkismic ||
|| 85 || 0-2-12-20 || 1-11/10-11/6-11/8 || utonal ||
|| 86 || 0-4-12-20 || 1-11/9-11/6-11/8 || utonal ||
|| 87 || 0-8-12-20 || 1-3/2-11/6-11/8 || ambitonal ||
|| 88 || 0-9-12-20 || 1-11/7-11/6-11/8 || utonal ||
|| 89 || 0-10-12-20 || 1-5/3-11/6-11/8 || ptolemismic ||
|| 90 || 0-4-16-20 || 1-11/9-9/8-11/8 || rastmic ||
|| 91 || 0-8-16-20 || 1-3/2-9/8-11/8 || otonal ||
|| 92 || 0-9-16-20 || 1-11/7-9/8-11/8 || werkismic ||
|| 93 || 0-11-16-20 || 1-7/4-9/8-11/8 || otonal ||
|| 94 || 0-12-16-20 || 1-11/6-9/8-11/8 || rastmic ||
|| 95 || 0-2-18-20 || 1-10/9-5/4-11/8 || ptolemismic ||
|| 96 || 0-8-18-20 || 1-3/2-5/4-11/8 || otonal ||
|| 97 || 0-9-18-20 || 1-11/7-5/4-11/8 || octagari ||
|| 98 || 0-10-18-20 || 1-5/3-5/4-11/8 || ptolemismic ||
|| 99 || 0-11-18-20 || 1-7/4-5/4-11/8 || otonal ||
|| 100 || 0-16-18-20 || 1-9/8-5/4-11/8 || otonal ||

=Pentads=
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-4-7-9 || 1-10/9-11/9-10/7-11/7 || octarod ||
|| 2 || 0-2-5-7-9 || 1-10/9-9/7-10/7-11/7 || octarod ||
|| 3 || 0-2-5-7-10 || 1-10/9-9/7-10/7-5/3 || sensamagic ||
|| 4 || 0-3-5-7-10 || 1-7/6-9/7-10/7-5/3 || octarod ||
|| 5 || 0-3-5-8-10 || 1-7/6-9/7-3/2-5/3 || sensamagic ||
|| 6 || 0-2-4-7-11 || 1-10/9-11/9-10/7-7/4 || octacot ||
|| 7 || 0-2-4-9-11 || 1-10/9-11/9-11/7-7/4 || octagari ||
|| 8 || 0-2-7-9-11 || 1-10/9-10/7-11/7-7/4 || octagari ||
|| 9 || 0-4-7-9-11 || 1-11/9-10/7-11/7-7/4 || octacot ||
|| 10 || 0-2-4-7-12 || 1-10/9-11/9-10/7-11/6 || octarod ||
|| 11 || 0-2-5-7-12 || 1-10/9-9/7-10/7-11/6 || octarod ||
|| 12 || 0-3-5-7-12 || 1-7/6-9/7-10/7-11/6 || octarod ||
|| 13 || 0-3-5-8-12 || 1-7/6-9/7-3/2-11/6 || octarod ||
|| 14 || 0-2-4-9-12 || 1-11/10-11/9-11/7-11/6 || utonal ||
|| 15 || 0-2-5-9-12 || 1-10/9-9/7-11/7-11/6 || octarod ||
|| 16 || 0-2-7-9-12 || 1-10/9-10/7-11/7-11/6 || octarod ||
|| 17 || 0-4-7-9-12 || 1-11/9-10/7-11/7-11/6 || octarod ||
|| 18 || 0-5-7-9-12 || 1-9/7-10/7-11/7-11/6 || octarod ||
|| 19 || 0-2-5-10-12 || 1-10/9-9/7-5/3-11/6 || octarod ||
|| 20 || 0-3-5-10-12 || 1-7/6-9/7-5/3-11/6 || octarod ||
|| 21 || 0-2-7-10-12 || 1-10/9-10/7-5/3-11/6 || octarod ||
|| 22 || 0-3-7-10-12 || 1-7/6-10/7-5/3-11/6 || octarod ||
|| 23 || 0-5-7-10-12 || 1-9/7-10/7-5/3-11/6 || octarod ||
|| 24 || 0-3-8-10-12 || 1-7/6-3/2-5/3-11/6 || otonal ||
|| 25 || 0-5-8-10-12 || 1-9/7-3/2-5/3-11/6 || octarod ||
|| 26 || 0-4-7-9-16 || 1-11/9-10/7-11/7-9/8 || octacot ||
|| 27 || 0-5-7-9-16 || 1-9/7-10/7-11/7-9/8 || octagari ||
|| 28 || 0-4-7-11-16 || 1-11/9-10/7-7/4-9/8 || jove ||
|| 29 || 0-4-8-11-16 || 1-11/9-3/2-7/4-9/8 || jove ||
|| 30 || 0-4-9-11-16 || 1-11/9-11/7-7/4-9/8 || jove ||
|| 31 || 0-7-9-11-16 || 1-10/7-11/7-7/4-9/8 || octagari ||
|| 32 || 0-4-7-12-16 || 1-11/9-10/7-11/6-9/8 || jove ||
|| 33 || 0-5-7-12-16 || 1-9/7-10/7-11/6-9/8 || jove ||
|| 34 || 0-4-8-12-16 || 1-11/9-3/2-11/6-9/8 || rastmic ||
|| 35 || 0-5-8-12-16 || 1-9/7-3/2-11/6-9/8 || jove- ||
|| 36 || 0-4-9-12-16 || 1-11/9-11/7-11/6-9/8 || jove ||
|| 37 || 0-5-9-12-16 || 1-9/7-11/7-11/6-9/8 || jove ||
|| 38 || 0-7-9-12-16 || 1-10/7-11/7-11/6-9/8 || octacot ||
|| 39 || 0-2-7-9-18 || 1-10/9-10/7-11/7-5/4 || octagari ||
|| 40 || 0-2-7-10-18 || 1-10/9-10/7-5/3-5/4 || utonal ||
|| 41 || 0-2-7-11-18 || 1-10/9-10/7-7/4-5/4 || werkismic ||
|| 42 || 0-2-9-11-18 || 1-10/9-11/7-7/4-5/4 || octagari ||
|| 43 || 0-7-9-11-18 || 1-10/7-11/7-7/4-5/4 || octagari ||
|| 44 || 0-7-9-16-18 || 1-10/7-11/7-9/8-5/4 || octagari ||
|| 45 || 0-7-11-16-18 || 1-10/7-7/4-9/8-5/4 || werkismic ||
|| 46 || 0-8-11-16-18 || 1-3/2-7/4-9/8-5/4 || otonal ||
|| 47 || 0-9-11-16-18 || 1-11/7-7/4-9/8-5/4 || octagari ||
|| 48 || 0-2-4-9-20 || 1-11/10-11/9-11/7-11/8 || utonal ||
|| 49 || 0-2-4-11-20 || 1-10/9-11/9-7/4-11/8 || octagari ||
|| 50 || 0-4-8-11-20 || 1-11/9-3/2-7/4-11/8 || jove ||
|| 51 || 0-2-9-11-20 || 1-10/9-11/7-7/4-11/8 || octagari ||
|| 52 || 0-4-9-11-20 || 1-11/9-11/7-7/4-11/8 || werkismic ||
|| 53 || 0-2-4-12-20 || 1-11/10-11/9-11/6-11/8 || utonal ||
|| 54 || 0-4-8-12-20 || 1-11/9-3/2-11/6-11/8 || rastmic ||
|| 55 || 0-2-9-12-20 || 1-11/10-11/7-11/6-11/8 || utonal ||
|| 56 || 0-4-9-12-20 || 1-11/9-11/7-11/6-11/8 || utonal ||
|| 57 || 0-2-10-12-20 || 1-10/9-5/3-11/6-11/8 || ptolemismic ||
|| 58 || 0-8-10-12-20 || 1-3/2-5/3-11/6-11/8 || ptolemismic ||
|| 59 || 0-4-8-16-20 || 1-11/9-3/2-9/8-11/8 || rastmic ||
|| 60 || 0-4-9-16-20 || 1-11/9-11/7-9/8-11/8 || jove ||
|| 61 || 0-4-11-16-20 || 1-11/9-7/4-9/8-11/8 || jove ||
|| 62 || 0-8-11-16-20 || 1-3/2-7/4-9/8-11/8 || otonal ||
|| 63 || 0-9-11-16-20 || 1-11/7-7/4-9/8-11/8 || werkismic ||
|| 64 || 0-4-12-16-20 || 1-11/9-11/6-9/8-11/8 || rastmic ||
|| 65 || 0-8-12-16-20 || 1-3/2-11/6-9/8-11/8 || rastmic ||
|| 66 || 0-9-12-16-20 || 1-11/7-11/6-9/8-11/8 || jove ||
|| 67 || 0-2-9-18-20 || 1-10/9-11/7-5/4-11/8 || octagari ||
|| 68 || 0-2-10-18-20 || 1-10/9-5/3-5/4-11/8 || ptolemismic ||
|| 69 || 0-8-10-18-20 || 1-3/2-5/3-5/4-11/8 || ptolemismic ||
|| 70 || 0-2-11-18-20 || 1-10/9-7/4-5/4-11/8 || octagari ||
|| 71 || 0-8-11-18-20 || 1-3/2-7/4-5/4-11/8 || otonal ||
|| 72 || 0-9-11-18-20 || 1-11/7-7/4-5/4-11/8 || octagari ||
|| 73 || 0-8-16-18-20 || 1-3/2-9/8-5/4-11/8 || otonal ||
|| 74 || 0-9-16-18-20 || 1-11/7-9/8-5/4-11/8 || octagari ||
|| 75 || 0-11-16-18-20 || 1-7/4-9/8-5/4-11/8 || otonal ||

=Hexads=
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-4-7-9-11 || 1-10/9-11/9-10/7-11/7-7/4 || octacot ||
|| 2 || 0-2-4-7-9-12 || 1-10/9-11/9-10/7-11/7-11/6 || octarod ||
|| 3 || 0-2-5-7-9-12 || 1-10/9-9/7-10/7-11/7-11/6 || octarod ||
|| 4 || 0-2-5-7-10-12 || 1-10/9-9/7-10/7-5/3-11/6 || octarod ||
|| 5 || 0-3-5-7-10-12 || 1-7/6-9/7-10/7-5/3-11/6 || octarod ||
|| 6 || 0-3-5-8-10-12 || 1-7/6-9/7-3/2-5/3-11/6 || octarod ||
|| 7 || 0-4-7-9-11-16 || 1-11/9-10/7-11/7-7/4-9/8 || octacot ||
|| 8 || 0-4-7-9-12-16 || 1-11/9-10/7-11/7-11/6-9/8 || octacot ||
|| 9 || 0-5-7-9-12-16 || 1-9/7-10/7-11/7-11/6-9/8 || octacot ||
|| 10 || 0-2-7-9-11-18 || 1-10/9-10/7-11/7-7/4-5/4 || octagari ||
|| 11 || 0-7-9-11-16-18 || 1-10/7-11/7-7/4-9/8-5/4 || octagari ||
|| 12 || 0-2-4-9-11-20 || 1-10/9-11/9-11/7-7/4-11/8 || octagari ||
|| 13 || 0-2-4-9-12-20 || 1-11/10-11/9-11/7-11/6-11/8 || utonal ||
|| 14 || 0-4-8-11-16-20 || 1-11/9-3/2-7/4-9/8-11/8 || jove ||
|| 15 || 0-4-9-11-16-20 || 1-11/9-11/7-7/4-9/8-11/8 || jove ||
|| 16 || 0-4-8-12-16-20 || 1-11/9-3/2-11/6-9/8-11/8 || rastmic ||
|| 17 || 0-4-9-12-16-20 || 1-11/9-11/7-11/6-9/8-11/8 || jove ||
|| 18 || 0-2-9-11-18-20 || 1-10/9-11/7-7/4-5/4-11/8 || octagari ||
|| 19 || 0-8-11-16-18-20 || 1-3/2-7/4-9/8-5/4-11/8 || otonal ||
|| 20 || 0-9-11-16-18-20 || 1-11/7-7/4-9/8-5/4-11/8 || octagari ||

Original HTML content:

<html><head><title>Chords of octacot</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="/Tetracot%20family#Octacot">octacot temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot. <br />
<br />
Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the <a class="wiki_link" href="/88cET">88 cents temperament</a> is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4<br />
</td>
        <td>1-10/9-11/9<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5<br />
</td>
        <td>1-10/9-9/7<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-5<br />
</td>
        <td>1-7/6-9/7<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-7<br />
</td>
        <td>1-10/9-10/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-7<br />
</td>
        <td>1-7/6-10/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-4-7<br />
</td>
        <td>1-11/9-10/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-5-7<br />
</td>
        <td>1-9/7-10/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-3-8<br />
</td>
        <td>1-7/6-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-4-8<br />
</td>
        <td>1-11/9-3/2<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-5-8<br />
</td>
        <td>1-9/7-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-2-9<br />
</td>
        <td>1-11/10-11/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-4-9<br />
</td>
        <td>1-11/9-11/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-5-9<br />
</td>
        <td>1-9/7-11/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-7-9<br />
</td>
        <td>1-10/7-11/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-2-10<br />
</td>
        <td>1-10/9-5/3<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-3-10<br />
</td>
        <td>1-7/6-5/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-5-10<br />
</td>
        <td>1-9/7-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-7-10<br />
</td>
        <td>1-10/7-5/3<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-8-10<br />
</td>
        <td>1-3/2-5/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-2-11<br />
</td>
        <td>1-10/9-7/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-3-11<br />
</td>
        <td>1-7/6-7/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-4-11<br />
</td>
        <td>1-11/9-7/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-7-11<br />
</td>
        <td>1-10/7-7/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-8-11<br />
</td>
        <td>1-3/2-7/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-9-11<br />
</td>
        <td>1-11/7-7/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-2-12<br />
</td>
        <td>1-11/10-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-3-12<br />
</td>
        <td>1-7/6-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-4-12<br />
</td>
        <td>1-11/9-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-5-12<br />
</td>
        <td>1-9/7-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-7-12<br />
</td>
        <td>1-10/7-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-8-12<br />
</td>
        <td>1-3/2-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-9-12<br />
</td>
        <td>1-11/7-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-10-12<br />
</td>
        <td>1-5/3-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-4-16<br />
</td>
        <td>1-11/9-9/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-5-16<br />
</td>
        <td>1-9/7-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-7-16<br />
</td>
        <td>1-10/7-9/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-8-16<br />
</td>
        <td>1-3/2-9/8<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-9-16<br />
</td>
        <td>1-11/7-9/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-11-16<br />
</td>
        <td>1-7/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-12-16<br />
</td>
        <td>1-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-2-18<br />
</td>
        <td>1-10/9-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-7-18<br />
</td>
        <td>1-10/7-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-8-18<br />
</td>
        <td>1-3/2-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-9-18<br />
</td>
        <td>1-11/7-5/4<br />
</td>
        <td>cassacot<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-10-18<br />
</td>
        <td>1-5/3-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-11-18<br />
</td>
        <td>1-7/4-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-16-18<br />
</td>
        <td>1-9/8-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-2-20<br />
</td>
        <td>1-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-4-20<br />
</td>
        <td>1-11/9-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-8-20<br />
</td>
        <td>1-3/2-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-9-20<br />
</td>
        <td>1-11/7-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-10-20<br />
</td>
        <td>1-5/3-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-11-20<br />
</td>
        <td>1-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-12-20<br />
</td>
        <td>1-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-16-20<br />
</td>
        <td>1-9/8-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-18-20<br />
</td>
        <td>1-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4-7<br />
</td>
        <td>1-10/9-11/9-10/7<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-7<br />
</td>
        <td>1-10/9-9/7-10/7<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-5-7<br />
</td>
        <td>1-7/6-9/7-10/7<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-3-5-8<br />
</td>
        <td>1-7/6-9/7-3/2<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-2-4-9<br />
</td>
        <td>1-11/10-11/9-11/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-5-9<br />
</td>
        <td>1-10/9-9/7-11/7<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-2-7-9<br />
</td>
        <td>1-10/9-10/7-11/7<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-4-7-9<br />
</td>
        <td>1-11/9-10/7-11/7<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-7-9<br />
</td>
        <td>1-9/7-10/7-11/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-5-10<br />
</td>
        <td>1-10/9-9/7-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-5-10<br />
</td>
        <td>1-7/6-9/7-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-2-7-10<br />
</td>
        <td>1-10/9-10/7-5/3<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-3-7-10<br />
</td>
        <td>1-7/6-10/7-5/3<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-5-7-10<br />
</td>
        <td>1-9/7-10/7-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-3-8-10<br />
</td>
        <td>1-7/6-3/2-5/3<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-5-8-10<br />
</td>
        <td>1-9/7-3/2-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-2-4-11<br />
</td>
        <td>1-10/9-11/9-7/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-2-7-11<br />
</td>
        <td>1-10/9-10/7-7/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-3-7-11<br />
</td>
        <td>1-7/6-10/7-7/4<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-4-7-11<br />
</td>
        <td>1-11/9-10/7-7/4<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-3-8-11<br />
</td>
        <td>1-7/6-3/2-7/4<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-4-8-11<br />
</td>
        <td>1-11/9-3/2-7/4<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-2-9-11<br />
</td>
        <td>1-10/9-11/7-7/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-4-9-11<br />
</td>
        <td>1-11/9-11/7-7/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-7-9-11<br />
</td>
        <td>1-10/7-11/7-7/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-2-4-12<br />
</td>
        <td>1-11/10-11/9-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-2-5-12<br />
</td>
        <td>1-10/9-9/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-3-5-12<br />
</td>
        <td>1-7/6-9/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-2-7-12<br />
</td>
        <td>1-10/9-10/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-3-7-12<br />
</td>
        <td>1-7/6-10/7-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-4-7-12<br />
</td>
        <td>1-11/9-10/7-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-5-7-12<br />
</td>
        <td>1-9/7-10/7-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-3-8-12<br />
</td>
        <td>1-7/6-3/2-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-4-8-12<br />
</td>
        <td>1-11/9-3/2-11/6<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-5-8-12<br />
</td>
        <td>1-9/7-3/2-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-2-9-12<br />
</td>
        <td>1-11/10-11/7-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-4-9-12<br />
</td>
        <td>1-11/9-11/7-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-5-9-12<br />
</td>
        <td>1-9/7-11/7-11/6<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-7-9-12<br />
</td>
        <td>1-10/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-2-10-12<br />
</td>
        <td>1-10/9-5/3-11/6<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-3-10-12<br />
</td>
        <td>1-7/6-5/3-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-5-10-12<br />
</td>
        <td>1-9/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-7-10-12<br />
</td>
        <td>1-10/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-8-10-12<br />
</td>
        <td>1-3/2-5/3-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-4-7-16<br />
</td>
        <td>1-11/9-10/7-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-5-7-16<br />
</td>
        <td>1-9/7-10/7-9/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-4-8-16<br />
</td>
        <td>1-11/9-3/2-9/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-5-8-16<br />
</td>
        <td>1-9/7-3/2-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-4-9-16<br />
</td>
        <td>1-11/9-11/7-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-5-9-16<br />
</td>
        <td>1-9/7-11/7-9/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-7-9-16<br />
</td>
        <td>1-10/7-11/7-9/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-4-11-16<br />
</td>
        <td>1-11/9-7/4-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-7-11-16<br />
</td>
        <td>1-10/7-7/4-9/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-8-11-16<br />
</td>
        <td>1-3/2-7/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-9-11-16<br />
</td>
        <td>1-11/7-7/4-9/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-4-12-16<br />
</td>
        <td>1-11/9-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-5-12-16<br />
</td>
        <td>1-9/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-7-12-16<br />
</td>
        <td>1-10/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-8-12-16<br />
</td>
        <td>1-3/2-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-9-12-16<br />
</td>
        <td>1-11/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-2-7-18<br />
</td>
        <td>1-10/9-10/7-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-2-9-18<br />
</td>
        <td>1-10/9-11/7-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-7-9-18<br />
</td>
        <td>1-10/7-11/7-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-2-10-18<br />
</td>
        <td>1-10/9-5/3-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-7-10-18<br />
</td>
        <td>1-10/7-5/3-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-8-10-18<br />
</td>
        <td>1-3/2-5/3-5/4<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-2-11-18<br />
</td>
        <td>1-10/9-7/4-5/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-7-11-18<br />
</td>
        <td>1-10/7-7/4-5/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-8-11-18<br />
</td>
        <td>1-3/2-7/4-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-9-11-18<br />
</td>
        <td>1-11/7-7/4-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-7-16-18<br />
</td>
        <td>1-10/7-9/8-5/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-8-16-18<br />
</td>
        <td>1-3/2-9/8-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-9-16-18<br />
</td>
        <td>1-11/7-9/8-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-11-16-18<br />
</td>
        <td>1-7/4-9/8-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-2-4-20<br />
</td>
        <td>1-11/10-11/9-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>76<br />
</td>
        <td>0-4-8-20<br />
</td>
        <td>1-11/9-3/2-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>0-2-9-20<br />
</td>
        <td>1-11/10-11/7-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>78<br />
</td>
        <td>0-4-9-20<br />
</td>
        <td>1-11/9-11/7-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>0-2-10-20<br />
</td>
        <td>1-10/9-5/3-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>80<br />
</td>
        <td>0-8-10-20<br />
</td>
        <td>1-3/2-5/3-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>0-2-11-20<br />
</td>
        <td>1-10/9-7/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>82<br />
</td>
        <td>0-4-11-20<br />
</td>
        <td>1-11/9-7/4-11/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>0-8-11-20<br />
</td>
        <td>1-3/2-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>84<br />
</td>
        <td>0-9-11-20<br />
</td>
        <td>1-11/7-7/4-11/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>0-2-12-20<br />
</td>
        <td>1-11/10-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>86<br />
</td>
        <td>0-4-12-20<br />
</td>
        <td>1-11/9-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>0-8-12-20<br />
</td>
        <td>1-3/2-11/6-11/8<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>88<br />
</td>
        <td>0-9-12-20<br />
</td>
        <td>1-11/7-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>89<br />
</td>
        <td>0-10-12-20<br />
</td>
        <td>1-5/3-11/6-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>0-4-16-20<br />
</td>
        <td>1-11/9-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>0-8-16-20<br />
</td>
        <td>1-3/2-9/8-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>92<br />
</td>
        <td>0-9-16-20<br />
</td>
        <td>1-11/7-9/8-11/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>0-11-16-20<br />
</td>
        <td>1-7/4-9/8-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>94<br />
</td>
        <td>0-12-16-20<br />
</td>
        <td>1-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>95<br />
</td>
        <td>0-2-18-20<br />
</td>
        <td>1-10/9-5/4-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>96<br />
</td>
        <td>0-8-18-20<br />
</td>
        <td>1-3/2-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>97<br />
</td>
        <td>0-9-18-20<br />
</td>
        <td>1-11/7-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>98<br />
</td>
        <td>0-10-18-20<br />
</td>
        <td>1-5/3-5/4-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>99<br />
</td>
        <td>0-11-18-20<br />
</td>
        <td>1-7/4-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>100<br />
</td>
        <td>0-16-18-20<br />
</td>
        <td>1-9/8-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4-7-9<br />
</td>
        <td>1-10/9-11/9-10/7-11/7<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-7-9<br />
</td>
        <td>1-10/9-9/7-10/7-11/7<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-5-7-10<br />
</td>
        <td>1-10/9-9/7-10/7-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-3-5-7-10<br />
</td>
        <td>1-7/6-9/7-10/7-5/3<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-5-8-10<br />
</td>
        <td>1-7/6-9/7-3/2-5/3<br />
</td>
        <td>sensamagic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-4-7-11<br />
</td>
        <td>1-10/9-11/9-10/7-7/4<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-2-4-9-11<br />
</td>
        <td>1-10/9-11/9-11/7-7/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-2-7-9-11<br />
</td>
        <td>1-10/9-10/7-11/7-7/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-4-7-9-11<br />
</td>
        <td>1-11/9-10/7-11/7-7/4<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-4-7-12<br />
</td>
        <td>1-10/9-11/9-10/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-2-5-7-12<br />
</td>
        <td>1-10/9-9/7-10/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-3-5-7-12<br />
</td>
        <td>1-7/6-9/7-10/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-3-5-8-12<br />
</td>
        <td>1-7/6-9/7-3/2-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-2-4-9-12<br />
</td>
        <td>1-11/10-11/9-11/7-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-2-5-9-12<br />
</td>
        <td>1-10/9-9/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-2-7-9-12<br />
</td>
        <td>1-10/9-10/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-4-7-9-12<br />
</td>
        <td>1-11/9-10/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-5-7-9-12<br />
</td>
        <td>1-9/7-10/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-2-5-10-12<br />
</td>
        <td>1-10/9-9/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-3-5-10-12<br />
</td>
        <td>1-7/6-9/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-2-7-10-12<br />
</td>
        <td>1-10/9-10/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-3-7-10-12<br />
</td>
        <td>1-7/6-10/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-5-7-10-12<br />
</td>
        <td>1-9/7-10/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-3-8-10-12<br />
</td>
        <td>1-7/6-3/2-5/3-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-5-8-10-12<br />
</td>
        <td>1-9/7-3/2-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-4-7-9-16<br />
</td>
        <td>1-11/9-10/7-11/7-9/8<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-5-7-9-16<br />
</td>
        <td>1-9/7-10/7-11/7-9/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-4-7-11-16<br />
</td>
        <td>1-11/9-10/7-7/4-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-4-8-11-16<br />
</td>
        <td>1-11/9-3/2-7/4-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-4-9-11-16<br />
</td>
        <td>1-11/9-11/7-7/4-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-7-9-11-16<br />
</td>
        <td>1-10/7-11/7-7/4-9/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-4-7-12-16<br />
</td>
        <td>1-11/9-10/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-5-7-12-16<br />
</td>
        <td>1-9/7-10/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-4-8-12-16<br />
</td>
        <td>1-11/9-3/2-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-5-8-12-16<br />
</td>
        <td>1-9/7-3/2-11/6-9/8<br />
</td>
        <td>jove-<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-4-9-12-16<br />
</td>
        <td>1-11/9-11/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-5-9-12-16<br />
</td>
        <td>1-9/7-11/7-11/6-9/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-7-9-12-16<br />
</td>
        <td>1-10/7-11/7-11/6-9/8<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-2-7-9-18<br />
</td>
        <td>1-10/9-10/7-11/7-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-2-7-10-18<br />
</td>
        <td>1-10/9-10/7-5/3-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-2-7-11-18<br />
</td>
        <td>1-10/9-10/7-7/4-5/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-2-9-11-18<br />
</td>
        <td>1-10/9-11/7-7/4-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-7-9-11-18<br />
</td>
        <td>1-10/7-11/7-7/4-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-7-9-16-18<br />
</td>
        <td>1-10/7-11/7-9/8-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-7-11-16-18<br />
</td>
        <td>1-10/7-7/4-9/8-5/4<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-8-11-16-18<br />
</td>
        <td>1-3/2-7/4-9/8-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-9-11-16-18<br />
</td>
        <td>1-11/7-7/4-9/8-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-2-4-9-20<br />
</td>
        <td>1-11/10-11/9-11/7-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-2-4-11-20<br />
</td>
        <td>1-10/9-11/9-7/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-4-8-11-20<br />
</td>
        <td>1-11/9-3/2-7/4-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-2-9-11-20<br />
</td>
        <td>1-10/9-11/7-7/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-4-9-11-20<br />
</td>
        <td>1-11/9-11/7-7/4-11/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-2-4-12-20<br />
</td>
        <td>1-11/10-11/9-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-4-8-12-20<br />
</td>
        <td>1-11/9-3/2-11/6-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-2-9-12-20<br />
</td>
        <td>1-11/10-11/7-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-4-9-12-20<br />
</td>
        <td>1-11/9-11/7-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-2-10-12-20<br />
</td>
        <td>1-10/9-5/3-11/6-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-8-10-12-20<br />
</td>
        <td>1-3/2-5/3-11/6-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-4-8-16-20<br />
</td>
        <td>1-11/9-3/2-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-4-9-16-20<br />
</td>
        <td>1-11/9-11/7-9/8-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-4-11-16-20<br />
</td>
        <td>1-11/9-7/4-9/8-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-8-11-16-20<br />
</td>
        <td>1-3/2-7/4-9/8-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-9-11-16-20<br />
</td>
        <td>1-11/7-7/4-9/8-11/8<br />
</td>
        <td>werkismic<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-4-12-16-20<br />
</td>
        <td>1-11/9-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-8-12-16-20<br />
</td>
        <td>1-3/2-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-9-12-16-20<br />
</td>
        <td>1-11/7-11/6-9/8-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-2-9-18-20<br />
</td>
        <td>1-10/9-11/7-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-2-10-18-20<br />
</td>
        <td>1-10/9-5/3-5/4-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-8-10-18-20<br />
</td>
        <td>1-3/2-5/3-5/4-11/8<br />
</td>
        <td>ptolemismic<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-2-11-18-20<br />
</td>
        <td>1-10/9-7/4-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-8-11-18-20<br />
</td>
        <td>1-3/2-7/4-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-9-11-18-20<br />
</td>
        <td>1-11/7-7/4-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-8-16-18-20<br />
</td>
        <td>1-3/2-9/8-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-9-16-18-20<br />
</td>
        <td>1-11/7-9/8-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-11-16-18-20<br />
</td>
        <td>1-7/4-9/8-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4-7-9-11<br />
</td>
        <td>1-10/9-11/9-10/7-11/7-7/4<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-4-7-9-12<br />
</td>
        <td>1-10/9-11/9-10/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-5-7-9-12<br />
</td>
        <td>1-10/9-9/7-10/7-11/7-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-5-7-10-12<br />
</td>
        <td>1-10/9-9/7-10/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-5-7-10-12<br />
</td>
        <td>1-7/6-9/7-10/7-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-3-5-8-10-12<br />
</td>
        <td>1-7/6-9/7-3/2-5/3-11/6<br />
</td>
        <td>octarod<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-4-7-9-11-16<br />
</td>
        <td>1-11/9-10/7-11/7-7/4-9/8<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-4-7-9-12-16<br />
</td>
        <td>1-11/9-10/7-11/7-11/6-9/8<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-7-9-12-16<br />
</td>
        <td>1-9/7-10/7-11/7-11/6-9/8<br />
</td>
        <td>octacot<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-7-9-11-18<br />
</td>
        <td>1-10/9-10/7-11/7-7/4-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-7-9-11-16-18<br />
</td>
        <td>1-10/7-11/7-7/4-9/8-5/4<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-2-4-9-11-20<br />
</td>
        <td>1-10/9-11/9-11/7-7/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-2-4-9-12-20<br />
</td>
        <td>1-11/10-11/9-11/7-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-4-8-11-16-20<br />
</td>
        <td>1-11/9-3/2-7/4-9/8-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-4-9-11-16-20<br />
</td>
        <td>1-11/9-11/7-7/4-9/8-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-4-8-12-16-20<br />
</td>
        <td>1-11/9-3/2-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-4-9-12-16-20<br />
</td>
        <td>1-11/9-11/7-11/6-9/8-11/8<br />
</td>
        <td>jove<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-2-9-11-18-20<br />
</td>
        <td>1-10/9-11/7-7/4-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-8-11-16-18-20<br />
</td>
        <td>1-3/2-7/4-9/8-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-9-11-16-18-20<br />
</td>
        <td>1-11/7-7/4-9/8-5/4-11/8<br />
</td>
        <td>octagari<br />
</td>
    </tr>
</table>

</body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-28 01:43:46 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-28 01:49:22 UTC</tt>.<br>
-: The original revision id was <tt>288623796</tt>.<br>
+: The original revision id was <tt>288623986</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 8: / Line 8: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Tetracot family#Octacot|octacot temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.
-Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the [[88cET|88 cent temperament]] is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cent temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.
+Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the [[88cET|88 cents temperament]] is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.
 =Triads=
@@ Line 277: / Line 277: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chords of octacot&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/Tetracot%20family#Octacot"&gt;octacot temperament&lt;/a&gt;. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot. &lt;br /&gt;
 &lt;br /&gt;
-Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the &lt;a class="wiki_link" href="/88cET"&gt;88 cent temperament&lt;/a&gt; is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cent temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.&lt;br /&gt;
+Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the &lt;a class="wiki_link" href="/88cET"&gt;88 cents temperament&lt;/a&gt; is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h1&gt;

Chords of octacot: Difference between revisions

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