Sqrtphi/Chords
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Below are listed the 15-limit [[Dyadic chord|dyadic chords]] of [[Kleismic family#Sqrtphi|sqrtphi temperament]], subject to the condition that no interval smaller than [[12_11|12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 325/324 are labeled marveltwin, by 364/363 gentle, by 540/539 swetismic, by 676/675 island, and by 1575/1573 nicolic. [[Rank and codimension|Codimension]] two temperaments are labeled swetismic-gentle, island-gentle and kleismic-marveltwin according to two commas which define it. Sqrtphi has MOS of size 5, 8, 11, 14, 17, 20, 23, 26, 49 and 72. The largest chords on these lists have complexity 70, and so would require the 72 note MOS, but there are many chords of much lower complexity. Sqrtphi has a generator very close to √φ, which can be chosen to be exactly √φ. Either way, aside from the dyadic chords, chords with stacks of φ are interesting since φ² - φ = 1, resulting in a relationship between difference tones. Though it isn't the "official" 13/8 of sqrtphi, φ is 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-1-2-9-10 or 0-1-8-9-10 work a stack of φs into chords which composers might find of interest. =Triads= || Number || Chord || Transversal || Type || || 1 || 0-1-9 || 1-11/7-11/6 || utonal || || 2 || 0-8-9 || 1-7/6-11/6 || otonal || || 3 || 0-1-10 || 1-11/7-13/9 || gentle || || 4 || 0-5-10 || 1-6/5-13/9 || marveltwin || || 5 || 0-9-10 || 1-11/6-13/9 || gentle || || 6 || 0-5-13 || 1-6/5-7/5 || otonal || || 7 || 0-8-13 || 1-7/6-7/5 || utonal || || 8 || 0-1-14 || 1-11/7-11/10 || utonal || || 9 || 0-5-14 || 1-6/5-11/10 || otonal || || 10 || 0-9-14 || 1-11/6-11/10 || utonal || || 11 || 0-13-14 || 1-7/5-11/10 || otonal || || 12 || 0-1-15 || 1-11/7-26/15 || gentle || || 13 || 0-5-15 || 1-6/5-26/15 || otonal || || 14 || 0-10-15 || 1-13/9-26/15 || utonal || || 15 || 0-14-15 || 1-11/10-26/15 || gentle || || 16 || 0-1-16 || 1-11/7-15/11 || nicolic || || 17 || 0-8-16 || 1-7/6-15/11 || swetismic || || 18 || 0-15-16 || 1-26/15-15/11 || nicolic || || 19 || 0-5-21 || 1-6/5-18/11 || utonal || || 20 || 0-8-21 || 1-7/6-18/11 || swetismic || || 21 || 0-13-21 || 1-7/5-18/11 || swetismic || || 22 || 0-16-21 || 1-15/11-18/11 || otonal || || 23 || 0-1-22 || 1-11/7-9/7 || otonal || || 24 || 0-8-22 || 1-7/6-9/7 || swetismic || || 25 || 0-9-22 || 1-11/6-9/7 || swetismic || || 26 || 0-13-22 || 1-7/5-9/7 || swetismic || || 27 || 0-14-22 || 1-11/10-9/7 || swetismic || || 28 || 0-21-22 || 1-18/11-9/7 || utonal || || 29 || 0-9-25 || 1-11/6-5/4 || otonal || || 30 || 0-10-25 || 1-13/9-5/4 || island || || 31 || 0-15-25 || 1-26/15-5/4 || island || || 32 || 0-16-25 || 1-15/11-5/4 || utonal || || 33 || 0-5-30 || 1-6/5-3/2 || utonal || || 34 || 0-8-30 || 1-7/6-3/2 || otonal || || 35 || 0-9-30 || 1-11/6-3/2 || otonal || || 36 || 0-14-30 || 1-11/10-3/2 || otonal || || 37 || 0-15-30 || 1-26/15-3/2 || island || || 38 || 0-16-30 || 1-15/11-3/2 || utonal || || 39 || 0-21-30 || 1-18/11-3/2 || utonal || || 40 || 0-22-30 || 1-9/7-3/2 || utonal || || 41 || 0-25-30 || 1-5/4-3/2 || otonal || || 42 || 0-1-31 || 1-11/7-13/11 || gentle || || 43 || 0-9-31 || 1-11/6-13/11 || gentle || || 44 || 0-10-31 || 1-13/9-13/11 || utonal || || 45 || 0-15-31 || 1-26/15-13/11 || utonal || || 46 || 0-16-31 || 1-15/11-13/11 || otonal || || 47 || 0-21-31 || 1-18/11-13/11 || otonal || || 48 || 0-22-31 || 1-9/7-13/11 || gentle || || 49 || 0-30-31 || 1-3/2-13/11 || gentle || || 50 || 0-5-35 || 1-6/5-9/5 || otonal || || 51 || 0-10-35 || 1-13/9-9/5 || marveltwin || || 52 || 0-13-35 || 1-7/5-9/5 || otonal || || 53 || 0-14-35 || 1-11/10-9/5 || otonal || || 54 || 0-21-35 || 1-18/11-9/5 || utonal || || 55 || 0-22-35 || 1-9/7-9/5 || utonal || || 56 || 0-25-35 || 1-5/4-9/5 || marveltwin || || 57 || 0-30-35 || 1-3/2-9/5 || utonal || || 58 || 0-8-38 || 1-7/6-7/4 || utonal || || 59 || 0-13-38 || 1-7/5-7/4 || utonal || || 60 || 0-16-38 || 1-15/11-7/4 || swetismic || || 61 || 0-22-38 || 1-9/7-7/4 || swetismic || || 62 || 0-25-38 || 1-5/4-7/4 || otonal || || 63 || 0-30-38 || 1-3/2-7/4 || otonal || || 64 || 0-1-39 || 1-11/7-11/8 || utonal || || 65 || 0-8-39 || 1-7/6-11/8 || gentle || || 66 || 0-9-39 || 1-11/6-11/8 || utonal || || 67 || 0-14-39 || 1-11/10-11/8 || utonal || || 68 || 0-25-39 || 1-5/4-11/8 || otonal || || 69 || 0-30-39 || 1-3/2-11/8 || otonal || || 70 || 0-31-39 || 1-13/11-11/8 || gentle || || 71 || 0-38-39 || 1-7/4-11/8 || otonal || || 72 || 0-10-45 || 1-13/9-13/10 || utonal || || 73 || 0-14-45 || 1-11/10-13/10 || otonal || || 74 || 0-15-45 || 1-26/15-13/10 || utonal || || 75 || 0-30-45 || 1-3/2-13/10 || otonal || || 76 || 0-31-45 || 1-13/11-13/10 || utonal || || 77 || 0-35-45 || 1-9/5-13/10 || otonal || || 78 || 0-15-60 || 1-26/15-9/8 || island || || 79 || 0-21-60 || 1-18/11-9/8 || utonal || || 80 || 0-22-60 || 1-9/7-9/8 || utonal || || 81 || 0-25-60 || 1-5/4-9/8 || otonal || || 82 || 0-30-60 || 1-3/2-9/8 || ambitonal || || 83 || 0-35-60 || 1-9/5-9/8 || utonal || || 84 || 0-38-60 || 1-7/4-9/8 || otonal || || 85 || 0-39-60 || 1-11/8-9/8 || otonal || || 86 || 0-45-60 || 1-13/10-9/8 || island || || 87 || 0-10-70 || 1-13/9-13/8 || utonal || || 88 || 0-25-70 || 1-5/4-13/8 || otonal || || 89 || 0-31-70 || 1-13/11-13/8 || utonal || || 90 || 0-35-70 || 1-9/5-13/8 || marveltwin || || 91 || 0-39-70 || 1-11/8-13/8 || otonal || || 92 || 0-45-70 || 1-13/10-13/8 || utonal || || 93 || 0-60-70 || 1-9/8-13/8 || otonal || =Tetrads= || Number || Chord || Transversal || Type || || 1 || 0-1-9-10 || 1-11/7-11/6-13/9 || gentle || || 2 || 0-1-9-14 || 1-11/7-11/6-11/10 || utonal || || 3 || 0-5-13-14 || 1-6/5-7/5-11/10 || otonal || || 4 || 0-1-10-15 || 1-11/7-13/9-26/15 || gentle || || 5 || 0-5-10-15 || 1-6/5-13/9-26/15 || marveltwin || || 6 || 0-1-14-15 || 1-11/7-11/10-26/15 || gentle || || 7 || 0-5-14-15 || 1-6/5-11/10-26/15 || gentle || || 8 || 0-1-15-16 || 1-11/7-26/15-15/11 || island-gentle || || 9 || 0-5-13-21 || 1-6/5-7/5-18/11 || swetismic || || 10 || 0-8-13-21 || 1-7/6-7/5-18/11 || swetismic || || 11 || 0-8-16-21 || 1-7/6-15/11-18/11 || swetismic || || 12 || 0-1-9-22 || 1-11/7-11/6-9/7 || swetismic || || 13 || 0-8-9-22 || 1-7/6-11/6-9/7 || swetismic || || 14 || 0-8-13-22 || 1-7/6-7/5-9/7 || swetismic || || 15 || 0-1-14-22 || 1-11/7-11/10-9/7 || swetismic || || 16 || 0-9-14-22 || 1-11/6-11/10-9/7 || swetismic || || 17 || 0-13-14-22 || 1-7/5-11/10-9/7 || swetismic || || 18 || 0-8-21-22 || 1-7/6-18/11-9/7 || swetismic || || 19 || 0-13-21-22 || 1-7/5-18/11-9/7 || swetismic || || 20 || 0-9-10-25 || 1-11/6-13/9-5/4 || island-gentle || || 21 || 0-10-15-25 || 1-13/9-26/15-5/4 || island || || 22 || 0-15-16-25 || 1-26/15-15/11-5/4 || island-gentle || || 23 || 0-8-9-30 || 1-7/6-11/6-3/2 || otonal || || 24 || 0-5-14-30 || 1-6/5-11/10-3/2 || otonal || || 25 || 0-9-14-30 || 1-11/6-11/10-3/2 || utonal || || 26 || 0-5-15-30 || 1-6/5-26/15-3/2 || island || || 27 || 0-14-15-30 || 1-11/10-26/15-3/2 || island-gentle || || 28 || 0-8-16-30 || 1-7/6-15/11-3/2 || swetismic || || 29 || 0-15-16-30 || 1-26/15-15/11-3/2 || island-gentle || || 30 || 0-5-21-30 || 1-6/5-18/11-3/2 || utonal || || 31 || 0-8-21-30 || 1-7/6-18/11-3/2 || swetismic || || 32 || 0-16-21-30 || 1-15/11-18/11-3/2 || otonal || || 33 || 0-8-22-30 || 1-7/6-9/7-3/2 || swetismic || || 34 || 0-9-22-30 || 1-11/6-9/7-3/2 || swetismic || || 35 || 0-14-22-30 || 1-11/10-9/7-3/2 || swetismic || || 36 || 0-21-22-30 || 1-18/11-9/7-3/2 || utonal || || 37 || 0-9-25-30 || 1-11/6-5/4-3/2 || otonal || || 38 || 0-15-25-30 || 1-26/15-5/4-3/2 || island || || 39 || 0-16-25-30 || 1-15/11-5/4-3/2 || utonal || || 40 || 0-1-9-31 || 1-11/7-11/6-13/11 || gentle || || 41 || 0-1-10-31 || 1-11/7-13/9-13/11 || gentle || || 42 || 0-9-10-31 || 1-11/6-13/9-13/11 || gentle || || 43 || 0-1-15-31 || 1-11/7-26/15-13/11 || gentle || || 44 || 0-10-15-31 || 1-13/9-26/15-13/11 || utonal || || 45 || 0-1-16-31 || 1-11/7-15/11-13/11 || island-gentle || || 46 || 0-15-16-31 || 1-26/15-15/11-13/11 || nicolic || || 47 || 0-16-21-31 || 1-15/11-18/11-13/11 || otonal || || 48 || 0-1-22-31 || 1-11/7-9/7-13/11 || gentle || || 49 || 0-9-22-31 || 1-11/6-9/7-13/11 || swetismic-gentle || || 50 || 0-21-22-31 || 1-18/11-9/7-13/11 || gentle || || 51 || 0-9-30-31 || 1-11/6-3/2-13/11 || gentle || || 52 || 0-15-30-31 || 1-26/15-3/2-13/11 || island-gentle || || 53 || 0-16-30-31 || 1-15/11-3/2-13/11 || gentle || || 54 || 0-21-30-31 || 1-18/11-3/2-13/11 || gentle || || 55 || 0-22-30-31 || 1-9/7-3/2-13/11 || gentle || || 56 || 0-5-10-35 || 1-6/5-13/9-9/5 || marveltwin || || 57 || 0-5-13-35 || 1-6/5-7/5-9/5 || otonal || || 58 || 0-5-14-35 || 1-6/5-11/10-9/5 || otonal || || 59 || 0-13-14-35 || 1-7/5-11/10-9/5 || otonal || || 60 || 0-5-21-35 || 1-6/5-18/11-9/5 || utonal || || 61 || 0-13-21-35 || 1-7/5-18/11-9/5 || swetismic || || 62 || 0-13-22-35 || 1-7/5-9/7-9/5 || swetismic || || 63 || 0-14-22-35 || 1-11/10-9/7-9/5 || swetismic || || 64 || 0-21-22-35 || 1-18/11-9/7-9/5 || utonal || || 65 || 0-10-25-35 || 1-13/9-5/4-9/5 || kleismic-marveltwin || || 66 || 0-5-30-35 || 1-6/5-3/2-9/5 || ambitonal || || 67 || 0-14-30-35 || 1-11/10-3/2-9/5 || otonal || || 68 || 0-21-30-35 || 1-18/11-3/2-9/5 || utonal || || 69 || 0-22-30-35 || 1-9/7-3/2-9/5 || utonal || || 70 || 0-25-30-35 || 1-5/4-3/2-9/5 || marveltwin || || 71 || 0-8-13-38 || 1-7/6-7/5-7/4 || utonal || || 72 || 0-8-16-38 || 1-7/6-15/11-7/4 || swetismic || || 73 || 0-8-22-38 || 1-7/6-9/7-7/4 || swetismic || || 74 || 0-13-22-38 || 1-7/5-9/7-7/4 || swetismic || || 75 || 0-16-25-38 || 1-15/11-5/4-7/4 || swetismic || || 76 || 0-8-30-38 || 1-7/6-3/2-7/4 || ambitonal || || 77 || 0-16-30-38 || 1-15/11-3/2-7/4 || swetismic || || 78 || 0-22-30-38 || 1-9/7-3/2-7/4 || swetismic || || 79 || 0-25-30-38 || 1-5/4-3/2-7/4 || otonal || || 80 || 0-1-9-39 || 1-11/7-11/6-11/8 || utonal || || 81 || 0-8-9-39 || 1-7/6-11/6-11/8 || gentle || || 82 || 0-1-14-39 || 1-11/7-11/10-11/8 || utonal || || 83 || 0-9-14-39 || 1-11/6-11/10-11/8 || utonal || || 84 || 0-9-25-39 || 1-11/6-5/4-11/8 || otonal || || 85 || 0-8-30-39 || 1-7/6-3/2-11/8 || gentle || || 86 || 0-9-30-39 || 1-11/6-3/2-11/8 || ambitonal || || 87 || 0-14-30-39 || 1-11/10-3/2-11/8 || utonal || || 88 || 0-25-30-39 || 1-5/4-3/2-11/8 || otonal || || 89 || 0-1-31-39 || 1-11/7-13/11-11/8 || gentle || || 90 || 0-9-31-39 || 1-11/6-13/11-11/8 || gentle || || 91 || 0-30-31-39 || 1-3/2-13/11-11/8 || gentle || || 92 || 0-8-38-39 || 1-7/6-7/4-11/8 || gentle || || 93 || 0-25-38-39 || 1-5/4-7/4-11/8 || otonal || || 94 || 0-30-38-39 || 1-3/2-7/4-11/8 || otonal || || 95 || 0-10-15-45 || 1-13/9-26/15-13/10 || utonal || || 96 || 0-14-15-45 || 1-11/10-26/15-13/10 || gentle || || 97 || 0-14-30-45 || 1-11/10-3/2-13/10 || otonal || || 98 || 0-15-30-45 || 1-26/15-3/2-13/10 || island || || 99 || 0-10-31-45 || 1-13/9-13/11-13/10 || utonal || || 100 || 0-15-31-45 || 1-26/15-13/11-13/10 || utonal || || 101 || 0-30-31-45 || 1-3/2-13/11-13/10 || gentle || || 102 || 0-10-35-45 || 1-13/9-9/5-13/10 || marveltwin || || 103 || 0-14-35-45 || 1-11/10-9/5-13/10 || otonal || || 104 || 0-30-35-45 || 1-3/2-9/5-13/10 || otonal || || 105 || 0-21-22-60 || 1-18/11-9/7-9/8 || utonal || || 106 || 0-15-25-60 || 1-26/15-5/4-9/8 || island || || 107 || 0-15-30-60 || 1-26/15-3/2-9/8 || island || || 108 || 0-21-30-60 || 1-18/11-3/2-9/8 || utonal || || 109 || 0-22-30-60 || 1-9/7-3/2-9/8 || utonal || || 110 || 0-25-30-60 || 1-5/4-3/2-9/8 || otonal || || 111 || 0-21-35-60 || 1-18/11-9/5-9/8 || utonal || || 112 || 0-22-35-60 || 1-9/7-9/5-9/8 || utonal || || 113 || 0-25-35-60 || 1-5/4-9/5-9/8 || marveltwin || || 114 || 0-30-35-60 || 1-3/2-9/5-9/8 || utonal || || 115 || 0-22-38-60 || 1-9/7-7/4-9/8 || swetismic || || 116 || 0-25-38-60 || 1-5/4-7/4-9/8 || otonal || || 117 || 0-30-38-60 || 1-3/2-7/4-9/8 || otonal || || 118 || 0-25-39-60 || 1-5/4-11/8-9/8 || otonal || || 119 || 0-30-39-60 || 1-3/2-11/8-9/8 || otonal || || 120 || 0-38-39-60 || 1-7/4-11/8-9/8 || otonal || || 121 || 0-15-45-60 || 1-26/15-13/10-9/8 || island || || 122 || 0-30-45-60 || 1-3/2-13/10-9/8 || island || || 123 || 0-35-45-60 || 1-9/5-13/10-9/8 || island || || 124 || 0-10-25-70 || 1-13/9-5/4-13/8 || island || || 125 || 0-10-31-70 || 1-13/9-13/11-13/8 || utonal || || 126 || 0-10-35-70 || 1-13/9-9/5-13/8 || marveltwin || || 127 || 0-25-35-70 || 1-5/4-9/5-13/8 || marveltwin || || 128 || 0-25-39-70 || 1-5/4-11/8-13/8 || otonal || || 129 || 0-31-39-70 || 1-13/11-11/8-13/8 || gentle || || 130 || 0-10-45-70 || 1-13/9-13/10-13/8 || utonal || || 131 || 0-31-45-70 || 1-13/11-13/10-13/8 || utonal || || 132 || 0-35-45-70 || 1-9/5-13/10-13/8 || marveltwin || || 133 || 0-25-60-70 || 1-5/4-9/8-13/8 || otonal || || 134 || 0-35-60-70 || 1-9/5-9/8-13/8 || marveltwin || || 135 || 0-39-60-70 || 1-11/8-9/8-13/8 || otonal || || 136 || 0-45-60-70 || 1-13/10-9/8-13/8 || island || =Pentads= || Number || Chord || Transversal || Type || || 1 || 0-1-9-14-22 || 1-11/7-11/6-11/10-9/7 || swetismic || || 2 || 0-8-13-21-22 || 1-7/6-7/5-18/11-9/7 || swetismic || || 3 || 0-5-14-15-30 || 1-6/5-11/10-26/15-3/2 || island-gentle || || 4 || 0-8-16-21-30 || 1-7/6-15/11-18/11-3/2 || swetismic || || 5 || 0-8-9-22-30 || 1-7/6-11/6-9/7-3/2 || swetismic || || 6 || 0-9-14-22-30 || 1-11/6-11/10-9/7-3/2 || swetismic || || 7 || 0-8-21-22-30 || 1-7/6-18/11-9/7-3/2 || swetismic || || 8 || 0-15-16-25-30 || 1-26/15-15/11-5/4-3/2 || island-gentle || || 9 || 0-1-9-10-31 || 1-11/7-11/6-13/9-13/11 || gentle || || 10 || 0-1-10-15-31 || 1-11/7-13/9-26/15-13/11 || gentle || || 11 || 0-1-15-16-31 || 1-11/7-26/15-15/11-13/11 || island-gentle || || 12 || 0-1-9-22-31 || 1-11/7-11/6-9/7-13/11 || swetismic-gentle || || 13 || 0-15-16-30-31 || 1-26/15-15/11-3/2-13/11 || island-gentle || || 14 || 0-16-21-30-31 || 1-15/11-18/11-3/2-13/11 || gentle || || 15 || 0-9-22-30-31 || 1-11/6-9/7-3/2-13/11 || swetismic-gentle || || 16 || 0-21-22-30-31 || 1-18/11-9/7-3/2-13/11 || gentle || || 17 || 0-5-13-14-35 || 1-6/5-7/5-11/10-9/5 || otonal || || 18 || 0-5-13-21-35 || 1-6/5-7/5-18/11-9/5 || swetismic || || 19 || 0-13-14-22-35 || 1-7/5-11/10-9/7-9/5 || swetismic || || 20 || 0-13-21-22-35 || 1-7/5-18/11-9/7-9/5 || swetismic || || 21 || 0-5-14-30-35 || 1-6/5-11/10-3/2-9/5 || otonal || || 22 || 0-5-21-30-35 || 1-6/5-18/11-3/2-9/5 || utonal || || 23 || 0-14-22-30-35 || 1-11/10-9/7-3/2-9/5 || swetismic || || 24 || 0-21-22-30-35 || 1-18/11-9/7-3/2-9/5 || utonal || || 25 || 0-8-13-22-38 || 1-7/6-7/5-9/7-7/4 || swetismic || || 26 || 0-8-16-30-38 || 1-7/6-15/11-3/2-7/4 || swetismic || || 27 || 0-8-22-30-38 || 1-7/6-9/7-3/2-7/4 || swetismic || || 28 || 0-16-25-30-38 || 1-15/11-5/4-3/2-7/4 || swetismic || || 29 || 0-1-9-14-39 || 1-11/7-11/6-11/10-11/8 || utonal || || 30 || 0-8-9-30-39 || 1-7/6-11/6-3/2-11/8 || gentle || || 31 || 0-9-14-30-39 || 1-11/6-11/10-3/2-11/8 || utonal || || 32 || 0-9-25-30-39 || 1-11/6-5/4-3/2-11/8 || otonal || || 33 || 0-1-9-31-39 || 1-11/7-11/6-13/11-11/8 || gentle || || 34 || 0-9-30-31-39 || 1-11/6-3/2-13/11-11/8 || gentle || || 35 || 0-8-30-38-39 || 1-7/6-3/2-7/4-11/8 || gentle || || 36 || 0-25-30-38-39 || 1-5/4-3/2-7/4-11/8 || otonal || || 37 || 0-14-15-30-45 || 1-11/10-26/15-3/2-13/10 || island-gentle || || 38 || 0-10-15-31-45 || 1-13/9-26/15-13/11-13/10 || utonal || || 39 || 0-15-30-31-45 || 1-26/15-3/2-13/11-13/10 || island-gentle || || 40 || 0-14-30-35-45 || 1-11/10-3/2-9/5-13/10 || otonal || || 41 || 0-21-22-30-60 || 1-18/11-9/7-3/2-9/8 || utonal || || 42 || 0-15-25-30-60 || 1-26/15-5/4-3/2-9/8 || island || || 43 || 0-21-22-35-60 || 1-18/11-9/7-9/5-9/8 || utonal || || 44 || 0-21-30-35-60 || 1-18/11-3/2-9/5-9/8 || utonal || || 45 || 0-22-30-35-60 || 1-9/7-3/2-9/5-9/8 || utonal || || 46 || 0-25-30-35-60 || 1-5/4-3/2-9/5-9/8 || marveltwin || || 47 || 0-22-30-38-60 || 1-9/7-3/2-7/4-9/8 || swetismic || || 48 || 0-25-30-38-60 || 1-5/4-3/2-7/4-9/8 || otonal || || 49 || 0-25-30-39-60 || 1-5/4-3/2-11/8-9/8 || otonal || || 50 || 0-25-38-39-60 || 1-5/4-7/4-11/8-9/8 || otonal || || 51 || 0-30-38-39-60 || 1-3/2-7/4-11/8-9/8 || otonal || || 52 || 0-15-30-45-60 || 1-26/15-3/2-13/10-9/8 || island || || 53 || 0-30-35-45-60 || 1-3/2-9/5-13/10-9/8 || island || || 54 || 0-10-25-35-70 || 1-13/9-5/4-9/5-13/8 || kleismic-marveltwin || || 55 || 0-10-31-45-70 || 1-13/9-13/11-13/10-13/8 || utonal || || 56 || 0-10-35-45-70 || 1-13/9-9/5-13/10-13/8 || marveltwin || || 57 || 0-25-35-60-70 || 1-5/4-9/5-9/8-13/8 || marveltwin || || 58 || 0-25-39-60-70 || 1-5/4-11/8-9/8-13/8 || otonal || || 59 || 0-35-45-60-70 || 1-9/5-13/10-9/8-13/8 || kleismic-marveltwin || =Hexads= || Number || Chord || Transversal || Type || || 1 || 0-21-22-30-35-60 || 1-18/11-9/7-3/2-9/5-9/8 ||utonal || || 2 || 0-25-30-38-39-60 || 1-5/4-3/2-7/4-11/8-9/8 || otonal ||
Original HTML content:
<html><head><title>Chords of sqrtphi</title></head><body>Below are listed the 15-limit <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of <a class="wiki_link" href="/Kleismic%20family#Sqrtphi">sqrtphi temperament</a>, subject to the condition that no interval smaller than <a class="wiki_link" href="/12_11">12/11</a>, at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 325/324 are labeled marveltwin, by 364/363 gentle, by 540/539 swetismic, by 676/675 island, and by 1575/1573 nicolic. <a class="wiki_link" href="/Rank%20and%20codimension">Codimension</a> two temperaments are labeled swetismic-gentle, island-gentle and kleismic-marveltwin according to two commas which define it. <br />
<br />
Sqrtphi has MOS of size 5, 8, 11, 14, 17, 20, 23, 26, 49 and 72. The largest chords on these lists have complexity 70, and so would require the 72 note MOS, but there are many chords of much lower complexity. Sqrtphi has a generator very close to √φ, which can be chosen to be exactly √φ. Either way, aside from the dyadic chords, chords with stacks of φ are interesting since φ² - φ = 1, resulting in a relationship between difference tones. Though it isn't the "official" 13/8 of sqrtphi, φ is 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-1-2-9-10 or 0-1-8-9-10 work a stack of φs into chords which composers might find of interest.<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>0-1-9<br />
</td>
<td>1-11/7-11/6<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-8-9<br />
</td>
<td>1-7/6-11/6<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-1-10<br />
</td>
<td>1-11/7-13/9<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-5-10<br />
</td>
<td>1-6/5-13/9<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-9-10<br />
</td>
<td>1-11/6-13/9<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-5-13<br />
</td>
<td>1-6/5-7/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-8-13<br />
</td>
<td>1-7/6-7/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-1-14<br />
</td>
<td>1-11/7-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-5-14<br />
</td>
<td>1-6/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-9-14<br />
</td>
<td>1-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-13-14<br />
</td>
<td>1-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-1-15<br />
</td>
<td>1-11/7-26/15<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-5-15<br />
</td>
<td>1-6/5-26/15<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-10-15<br />
</td>
<td>1-13/9-26/15<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-14-15<br />
</td>
<td>1-11/10-26/15<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-1-16<br />
</td>
<td>1-11/7-15/11<br />
</td>
<td>nicolic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-8-16<br />
</td>
<td>1-7/6-15/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-15-16<br />
</td>
<td>1-26/15-15/11<br />
</td>
<td>nicolic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-5-21<br />
</td>
<td>1-6/5-18/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-8-21<br />
</td>
<td>1-7/6-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-13-21<br />
</td>
<td>1-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-16-21<br />
</td>
<td>1-15/11-18/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-1-22<br />
</td>
<td>1-11/7-9/7<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-8-22<br />
</td>
<td>1-7/6-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-9-22<br />
</td>
<td>1-11/6-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-13-22<br />
</td>
<td>1-7/5-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-14-22<br />
</td>
<td>1-11/10-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-21-22<br />
</td>
<td>1-18/11-9/7<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-9-25<br />
</td>
<td>1-11/6-5/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-10-25<br />
</td>
<td>1-13/9-5/4<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-15-25<br />
</td>
<td>1-26/15-5/4<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-16-25<br />
</td>
<td>1-15/11-5/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-5-30<br />
</td>
<td>1-6/5-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-8-30<br />
</td>
<td>1-7/6-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-9-30<br />
</td>
<td>1-11/6-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-14-30<br />
</td>
<td>1-11/10-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-15-30<br />
</td>
<td>1-26/15-3/2<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-16-30<br />
</td>
<td>1-15/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-21-30<br />
</td>
<td>1-18/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-22-30<br />
</td>
<td>1-9/7-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-25-30<br />
</td>
<td>1-5/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-1-31<br />
</td>
<td>1-11/7-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-9-31<br />
</td>
<td>1-11/6-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-10-31<br />
</td>
<td>1-13/9-13/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-15-31<br />
</td>
<td>1-26/15-13/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-16-31<br />
</td>
<td>1-15/11-13/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-21-31<br />
</td>
<td>1-18/11-13/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-22-31<br />
</td>
<td>1-9/7-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-30-31<br />
</td>
<td>1-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-5-35<br />
</td>
<td>1-6/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-10-35<br />
</td>
<td>1-13/9-9/5<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-13-35<br />
</td>
<td>1-7/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-14-35<br />
</td>
<td>1-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-21-35<br />
</td>
<td>1-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-22-35<br />
</td>
<td>1-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-25-35<br />
</td>
<td>1-5/4-9/5<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-30-35<br />
</td>
<td>1-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-8-38<br />
</td>
<td>1-7/6-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-13-38<br />
</td>
<td>1-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-16-38<br />
</td>
<td>1-15/11-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-22-38<br />
</td>
<td>1-9/7-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-25-38<br />
</td>
<td>1-5/4-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-30-38<br />
</td>
<td>1-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-1-39<br />
</td>
<td>1-11/7-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-8-39<br />
</td>
<td>1-7/6-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-9-39<br />
</td>
<td>1-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>0-14-39<br />
</td>
<td>1-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>0-25-39<br />
</td>
<td>1-5/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>0-30-39<br />
</td>
<td>1-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>0-31-39<br />
</td>
<td>1-13/11-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>0-38-39<br />
</td>
<td>1-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>0-10-45<br />
</td>
<td>1-13/9-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>0-14-45<br />
</td>
<td>1-11/10-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>0-15-45<br />
</td>
<td>1-26/15-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>0-30-45<br />
</td>
<td>1-3/2-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>0-31-45<br />
</td>
<td>1-13/11-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>0-35-45<br />
</td>
<td>1-9/5-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>0-15-60<br />
</td>
<td>1-26/15-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>79<br />
</td>
<td>0-21-60<br />
</td>
<td>1-18/11-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>80<br />
</td>
<td>0-22-60<br />
</td>
<td>1-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>81<br />
</td>
<td>0-25-60<br />
</td>
<td>1-5/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>82<br />
</td>
<td>0-30-60<br />
</td>
<td>1-3/2-9/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>83<br />
</td>
<td>0-35-60<br />
</td>
<td>1-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>84<br />
</td>
<td>0-38-60<br />
</td>
<td>1-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>85<br />
</td>
<td>0-39-60<br />
</td>
<td>1-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>86<br />
</td>
<td>0-45-60<br />
</td>
<td>1-13/10-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>87<br />
</td>
<td>0-10-70<br />
</td>
<td>1-13/9-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>88<br />
</td>
<td>0-25-70<br />
</td>
<td>1-5/4-13/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>89<br />
</td>
<td>0-31-70<br />
</td>
<td>1-13/11-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>90<br />
</td>
<td>0-35-70<br />
</td>
<td>1-9/5-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>91<br />
</td>
<td>0-39-70<br />
</td>
<td>1-11/8-13/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>92<br />
</td>
<td>0-45-70<br />
</td>
<td>1-13/10-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>93<br />
</td>
<td>0-60-70<br />
</td>
<td>1-9/8-13/8<br />
</td>
<td>otonal<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>0-1-9-10<br />
</td>
<td>1-11/7-11/6-13/9<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-1-9-14<br />
</td>
<td>1-11/7-11/6-11/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-5-13-14<br />
</td>
<td>1-6/5-7/5-11/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-1-10-15<br />
</td>
<td>1-11/7-13/9-26/15<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-5-10-15<br />
</td>
<td>1-6/5-13/9-26/15<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-1-14-15<br />
</td>
<td>1-11/7-11/10-26/15<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-5-14-15<br />
</td>
<td>1-6/5-11/10-26/15<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-1-15-16<br />
</td>
<td>1-11/7-26/15-15/11<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-5-13-21<br />
</td>
<td>1-6/5-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-8-13-21<br />
</td>
<td>1-7/6-7/5-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-8-16-21<br />
</td>
<td>1-7/6-15/11-18/11<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-1-9-22<br />
</td>
<td>1-11/7-11/6-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-8-9-22<br />
</td>
<td>1-7/6-11/6-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-8-13-22<br />
</td>
<td>1-7/6-7/5-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-1-14-22<br />
</td>
<td>1-11/7-11/10-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-9-14-22<br />
</td>
<td>1-11/6-11/10-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-13-14-22<br />
</td>
<td>1-7/5-11/10-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-8-21-22<br />
</td>
<td>1-7/6-18/11-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-13-21-22<br />
</td>
<td>1-7/5-18/11-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-9-10-25<br />
</td>
<td>1-11/6-13/9-5/4<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-10-15-25<br />
</td>
<td>1-13/9-26/15-5/4<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-15-16-25<br />
</td>
<td>1-26/15-15/11-5/4<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-8-9-30<br />
</td>
<td>1-7/6-11/6-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-5-14-30<br />
</td>
<td>1-6/5-11/10-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-9-14-30<br />
</td>
<td>1-11/6-11/10-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-5-15-30<br />
</td>
<td>1-6/5-26/15-3/2<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-14-15-30<br />
</td>
<td>1-11/10-26/15-3/2<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-8-16-30<br />
</td>
<td>1-7/6-15/11-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-15-16-30<br />
</td>
<td>1-26/15-15/11-3/2<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-5-21-30<br />
</td>
<td>1-6/5-18/11-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-8-21-30<br />
</td>
<td>1-7/6-18/11-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-16-21-30<br />
</td>
<td>1-15/11-18/11-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-8-22-30<br />
</td>
<td>1-7/6-9/7-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-9-22-30<br />
</td>
<td>1-11/6-9/7-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-14-22-30<br />
</td>
<td>1-11/10-9/7-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-21-22-30<br />
</td>
<td>1-18/11-9/7-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-9-25-30<br />
</td>
<td>1-11/6-5/4-3/2<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-15-25-30<br />
</td>
<td>1-26/15-5/4-3/2<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-16-25-30<br />
</td>
<td>1-15/11-5/4-3/2<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-1-9-31<br />
</td>
<td>1-11/7-11/6-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-1-10-31<br />
</td>
<td>1-11/7-13/9-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-9-10-31<br />
</td>
<td>1-11/6-13/9-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-1-15-31<br />
</td>
<td>1-11/7-26/15-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-10-15-31<br />
</td>
<td>1-13/9-26/15-13/11<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-1-16-31<br />
</td>
<td>1-11/7-15/11-13/11<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-15-16-31<br />
</td>
<td>1-26/15-15/11-13/11<br />
</td>
<td>nicolic<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-16-21-31<br />
</td>
<td>1-15/11-18/11-13/11<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-1-22-31<br />
</td>
<td>1-11/7-9/7-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-9-22-31<br />
</td>
<td>1-11/6-9/7-13/11<br />
</td>
<td>swetismic-gentle<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-21-22-31<br />
</td>
<td>1-18/11-9/7-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-9-30-31<br />
</td>
<td>1-11/6-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-15-30-31<br />
</td>
<td>1-26/15-3/2-13/11<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-16-30-31<br />
</td>
<td>1-15/11-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-21-30-31<br />
</td>
<td>1-18/11-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-22-30-31<br />
</td>
<td>1-9/7-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-5-10-35<br />
</td>
<td>1-6/5-13/9-9/5<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-5-13-35<br />
</td>
<td>1-6/5-7/5-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-5-14-35<br />
</td>
<td>1-6/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-13-14-35<br />
</td>
<td>1-7/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>0-5-21-35<br />
</td>
<td>1-6/5-18/11-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>0-13-21-35<br />
</td>
<td>1-7/5-18/11-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>0-13-22-35<br />
</td>
<td>1-7/5-9/7-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>0-14-22-35<br />
</td>
<td>1-11/10-9/7-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>0-21-22-35<br />
</td>
<td>1-18/11-9/7-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>0-10-25-35<br />
</td>
<td>1-13/9-5/4-9/5<br />
</td>
<td>kleismic-marveltwin<br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>0-5-30-35<br />
</td>
<td>1-6/5-3/2-9/5<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>0-14-30-35<br />
</td>
<td>1-11/10-3/2-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>0-21-30-35<br />
</td>
<td>1-18/11-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>0-22-30-35<br />
</td>
<td>1-9/7-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>0-25-30-35<br />
</td>
<td>1-5/4-3/2-9/5<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>0-8-13-38<br />
</td>
<td>1-7/6-7/5-7/4<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>0-8-16-38<br />
</td>
<td>1-7/6-15/11-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>0-8-22-38<br />
</td>
<td>1-7/6-9/7-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>0-13-22-38<br />
</td>
<td>1-7/5-9/7-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>0-16-25-38<br />
</td>
<td>1-15/11-5/4-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>0-8-30-38<br />
</td>
<td>1-7/6-3/2-7/4<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>0-16-30-38<br />
</td>
<td>1-15/11-3/2-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>0-22-30-38<br />
</td>
<td>1-9/7-3/2-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>79<br />
</td>
<td>0-25-30-38<br />
</td>
<td>1-5/4-3/2-7/4<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>80<br />
</td>
<td>0-1-9-39<br />
</td>
<td>1-11/7-11/6-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>81<br />
</td>
<td>0-8-9-39<br />
</td>
<td>1-7/6-11/6-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>82<br />
</td>
<td>0-1-14-39<br />
</td>
<td>1-11/7-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>83<br />
</td>
<td>0-9-14-39<br />
</td>
<td>1-11/6-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>84<br />
</td>
<td>0-9-25-39<br />
</td>
<td>1-11/6-5/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>85<br />
</td>
<td>0-8-30-39<br />
</td>
<td>1-7/6-3/2-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>86<br />
</td>
<td>0-9-30-39<br />
</td>
<td>1-11/6-3/2-11/8<br />
</td>
<td>ambitonal<br />
</td>
</tr>
<tr>
<td>87<br />
</td>
<td>0-14-30-39<br />
</td>
<td>1-11/10-3/2-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>88<br />
</td>
<td>0-25-30-39<br />
</td>
<td>1-5/4-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>89<br />
</td>
<td>0-1-31-39<br />
</td>
<td>1-11/7-13/11-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>90<br />
</td>
<td>0-9-31-39<br />
</td>
<td>1-11/6-13/11-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>91<br />
</td>
<td>0-30-31-39<br />
</td>
<td>1-3/2-13/11-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>92<br />
</td>
<td>0-8-38-39<br />
</td>
<td>1-7/6-7/4-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>93<br />
</td>
<td>0-25-38-39<br />
</td>
<td>1-5/4-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>94<br />
</td>
<td>0-30-38-39<br />
</td>
<td>1-3/2-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>95<br />
</td>
<td>0-10-15-45<br />
</td>
<td>1-13/9-26/15-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>96<br />
</td>
<td>0-14-15-45<br />
</td>
<td>1-11/10-26/15-13/10<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>97<br />
</td>
<td>0-14-30-45<br />
</td>
<td>1-11/10-3/2-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>98<br />
</td>
<td>0-15-30-45<br />
</td>
<td>1-26/15-3/2-13/10<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>99<br />
</td>
<td>0-10-31-45<br />
</td>
<td>1-13/9-13/11-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>100<br />
</td>
<td>0-15-31-45<br />
</td>
<td>1-26/15-13/11-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>101<br />
</td>
<td>0-30-31-45<br />
</td>
<td>1-3/2-13/11-13/10<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>102<br />
</td>
<td>0-10-35-45<br />
</td>
<td>1-13/9-9/5-13/10<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>103<br />
</td>
<td>0-14-35-45<br />
</td>
<td>1-11/10-9/5-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>104<br />
</td>
<td>0-30-35-45<br />
</td>
<td>1-3/2-9/5-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>105<br />
</td>
<td>0-21-22-60<br />
</td>
<td>1-18/11-9/7-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>106<br />
</td>
<td>0-15-25-60<br />
</td>
<td>1-26/15-5/4-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>107<br />
</td>
<td>0-15-30-60<br />
</td>
<td>1-26/15-3/2-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>108<br />
</td>
<td>0-21-30-60<br />
</td>
<td>1-18/11-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>109<br />
</td>
<td>0-22-30-60<br />
</td>
<td>1-9/7-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>110<br />
</td>
<td>0-25-30-60<br />
</td>
<td>1-5/4-3/2-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>111<br />
</td>
<td>0-21-35-60<br />
</td>
<td>1-18/11-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>112<br />
</td>
<td>0-22-35-60<br />
</td>
<td>1-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>113<br />
</td>
<td>0-25-35-60<br />
</td>
<td>1-5/4-9/5-9/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>114<br />
</td>
<td>0-30-35-60<br />
</td>
<td>1-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>115<br />
</td>
<td>0-22-38-60<br />
</td>
<td>1-9/7-7/4-9/8<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>116<br />
</td>
<td>0-25-38-60<br />
</td>
<td>1-5/4-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>117<br />
</td>
<td>0-30-38-60<br />
</td>
<td>1-3/2-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>118<br />
</td>
<td>0-25-39-60<br />
</td>
<td>1-5/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>119<br />
</td>
<td>0-30-39-60<br />
</td>
<td>1-3/2-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>120<br />
</td>
<td>0-38-39-60<br />
</td>
<td>1-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>121<br />
</td>
<td>0-15-45-60<br />
</td>
<td>1-26/15-13/10-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>122<br />
</td>
<td>0-30-45-60<br />
</td>
<td>1-3/2-13/10-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>123<br />
</td>
<td>0-35-45-60<br />
</td>
<td>1-9/5-13/10-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>124<br />
</td>
<td>0-10-25-70<br />
</td>
<td>1-13/9-5/4-13/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>125<br />
</td>
<td>0-10-31-70<br />
</td>
<td>1-13/9-13/11-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>126<br />
</td>
<td>0-10-35-70<br />
</td>
<td>1-13/9-9/5-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>127<br />
</td>
<td>0-25-35-70<br />
</td>
<td>1-5/4-9/5-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>128<br />
</td>
<td>0-25-39-70<br />
</td>
<td>1-5/4-11/8-13/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>129<br />
</td>
<td>0-31-39-70<br />
</td>
<td>1-13/11-11/8-13/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>130<br />
</td>
<td>0-10-45-70<br />
</td>
<td>1-13/9-13/10-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>131<br />
</td>
<td>0-31-45-70<br />
</td>
<td>1-13/11-13/10-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>132<br />
</td>
<td>0-35-45-70<br />
</td>
<td>1-9/5-13/10-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>133<br />
</td>
<td>0-25-60-70<br />
</td>
<td>1-5/4-9/8-13/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>134<br />
</td>
<td>0-35-60-70<br />
</td>
<td>1-9/5-9/8-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>135<br />
</td>
<td>0-39-60-70<br />
</td>
<td>1-11/8-9/8-13/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>136<br />
</td>
<td>0-45-60-70<br />
</td>
<td>1-13/10-9/8-13/8<br />
</td>
<td>island<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>0-1-9-14-22<br />
</td>
<td>1-11/7-11/6-11/10-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-8-13-21-22<br />
</td>
<td>1-7/6-7/5-18/11-9/7<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0-5-14-15-30<br />
</td>
<td>1-6/5-11/10-26/15-3/2<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0-8-16-21-30<br />
</td>
<td>1-7/6-15/11-18/11-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0-8-9-22-30<br />
</td>
<td>1-7/6-11/6-9/7-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>0-9-14-22-30<br />
</td>
<td>1-11/6-11/10-9/7-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>0-8-21-22-30<br />
</td>
<td>1-7/6-18/11-9/7-3/2<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>0-15-16-25-30<br />
</td>
<td>1-26/15-15/11-5/4-3/2<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>0-1-9-10-31<br />
</td>
<td>1-11/7-11/6-13/9-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>0-1-10-15-31<br />
</td>
<td>1-11/7-13/9-26/15-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>0-1-15-16-31<br />
</td>
<td>1-11/7-26/15-15/11-13/11<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>0-1-9-22-31<br />
</td>
<td>1-11/7-11/6-9/7-13/11<br />
</td>
<td>swetismic-gentle<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>0-15-16-30-31<br />
</td>
<td>1-26/15-15/11-3/2-13/11<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>0-16-21-30-31<br />
</td>
<td>1-15/11-18/11-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>0-9-22-30-31<br />
</td>
<td>1-11/6-9/7-3/2-13/11<br />
</td>
<td>swetismic-gentle<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>0-21-22-30-31<br />
</td>
<td>1-18/11-9/7-3/2-13/11<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>0-5-13-14-35<br />
</td>
<td>1-6/5-7/5-11/10-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>0-5-13-21-35<br />
</td>
<td>1-6/5-7/5-18/11-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>0-13-14-22-35<br />
</td>
<td>1-7/5-11/10-9/7-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>0-13-21-22-35<br />
</td>
<td>1-7/5-18/11-9/7-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>0-5-14-30-35<br />
</td>
<td>1-6/5-11/10-3/2-9/5<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>0-5-21-30-35<br />
</td>
<td>1-6/5-18/11-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>0-14-22-30-35<br />
</td>
<td>1-11/10-9/7-3/2-9/5<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>0-21-22-30-35<br />
</td>
<td>1-18/11-9/7-3/2-9/5<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>0-8-13-22-38<br />
</td>
<td>1-7/6-7/5-9/7-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>0-8-16-30-38<br />
</td>
<td>1-7/6-15/11-3/2-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>0-8-22-30-38<br />
</td>
<td>1-7/6-9/7-3/2-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>0-16-25-30-38<br />
</td>
<td>1-15/11-5/4-3/2-7/4<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>0-1-9-14-39<br />
</td>
<td>1-11/7-11/6-11/10-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>0-8-9-30-39<br />
</td>
<td>1-7/6-11/6-3/2-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>0-9-14-30-39<br />
</td>
<td>1-11/6-11/10-3/2-11/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>0-9-25-30-39<br />
</td>
<td>1-11/6-5/4-3/2-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>0-1-9-31-39<br />
</td>
<td>1-11/7-11/6-13/11-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>0-9-30-31-39<br />
</td>
<td>1-11/6-3/2-13/11-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>0-8-30-38-39<br />
</td>
<td>1-7/6-3/2-7/4-11/8<br />
</td>
<td>gentle<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>0-25-30-38-39<br />
</td>
<td>1-5/4-3/2-7/4-11/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>0-14-15-30-45<br />
</td>
<td>1-11/10-26/15-3/2-13/10<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>0-10-15-31-45<br />
</td>
<td>1-13/9-26/15-13/11-13/10<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>0-15-30-31-45<br />
</td>
<td>1-26/15-3/2-13/11-13/10<br />
</td>
<td>island-gentle<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>0-14-30-35-45<br />
</td>
<td>1-11/10-3/2-9/5-13/10<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>0-21-22-30-60<br />
</td>
<td>1-18/11-9/7-3/2-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>0-15-25-30-60<br />
</td>
<td>1-26/15-5/4-3/2-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>0-21-22-35-60<br />
</td>
<td>1-18/11-9/7-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>0-21-30-35-60<br />
</td>
<td>1-18/11-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>0-22-30-35-60<br />
</td>
<td>1-9/7-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>0-25-30-35-60<br />
</td>
<td>1-5/4-3/2-9/5-9/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>0-22-30-38-60<br />
</td>
<td>1-9/7-3/2-7/4-9/8<br />
</td>
<td>swetismic<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>0-25-30-38-60<br />
</td>
<td>1-5/4-3/2-7/4-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>0-25-30-39-60<br />
</td>
<td>1-5/4-3/2-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>0-25-38-39-60<br />
</td>
<td>1-5/4-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>0-30-38-39-60<br />
</td>
<td>1-3/2-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>0-15-30-45-60<br />
</td>
<td>1-26/15-3/2-13/10-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>0-30-35-45-60<br />
</td>
<td>1-3/2-9/5-13/10-9/8<br />
</td>
<td>island<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>0-10-25-35-70<br />
</td>
<td>1-13/9-5/4-9/5-13/8<br />
</td>
<td>kleismic-marveltwin<br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>0-10-31-45-70<br />
</td>
<td>1-13/9-13/11-13/10-13/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>0-10-35-45-70<br />
</td>
<td>1-13/9-9/5-13/10-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>0-25-35-60-70<br />
</td>
<td>1-5/4-9/5-9/8-13/8<br />
</td>
<td>marveltwin<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>0-25-39-60-70<br />
</td>
<td>1-5/4-11/8-9/8-13/8<br />
</td>
<td>otonal<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>0-35-45-60-70<br />
</td>
<td>1-9/5-13/10-9/8-13/8<br />
</td>
<td>kleismic-marveltwin<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>0-21-22-30-35-60<br />
</td>
<td>1-18/11-9/7-3/2-9/5-9/8<br />
</td>
<td>utonal<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0-25-30-38-39-60<br />
</td>
<td>1-5/4-3/2-7/4-11/8-9/8<br />
</td>
<td>otonal<br />
</td>
</tr>
</table>
</body></html>