# Chords of sqrtphi

Below are listed the 15-limit dyadic chords of sqrtphi temperament, subject to the condition that no interval smaller than 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. 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 = √((1+√5)/2), 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 only 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-2-4-8-10 containing stacks of φs composers might find of interest.

 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