Chords of magic
Below are listed the dyadic chords of 11-limit magic temperament. Typing the chords requires consideration of the fact that magic conflates 10/9 and 11/10 and so also 9/5 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.
Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/224, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic. Finally, anything requiring three independent commas among those discussed above is labeled magic.
Magic has mos scales of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.
The chord names use ups and downs as described on the pergens page. The generator is vM3 and the enharmonic interval is ^5dd2. To simplify the names, lifts and drops are also used. One lift is 41 generators, octave-reduced. (41 because 41edo is a near-optimal tuning of magic.) Thus /1 = ^d2 = 20¢ - 8.2c, i.e. an up minus a tempered pythagorean comma. /C = ^Dbb and \C = vB#. ^C = /B# and vC = \Dbb.
| Genspan | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cents (41edo) | 0 | 380 | 761 | 1141 | 322 | 702 | 1083 | 263 | 644 | 1024 | 205 | 585 | 966 | 146 |
| Ratios | 1/1 | 5/4 | 14/9 | 27/14 | 6/5 | 3/2 | 15/8 | 7/6 | (16/11) | 9/5 | 9/8 | 7/5 | 7/4 | (12/11) |
| Interval | P1 | vM3 | vvA5
v\m6 |
^^d8
^/M7 |
^m3 | P5 | vM7 | vvA2
v\m3 |
^^d5
^/A4 |
^m7 | M2 | vA4
\d5 |
vvA6
v\m7 |
^^m2
^/A1 |
TODO: complete the tables
Triads
| # | Chord | Transversal | Type | Name | Comments |
|---|---|---|---|---|---|
| 1 | 0-1-2 | 1-5/4-14/9 | Marvel | v(vv#5) | |
| 2 | 0-2-4 | 1-14/9-6/5 | Sensamagic | ^m(vv#5) | |
| 3 | 0-1-5 | 1-5/4-3/2 | Otonal | v | |
| 4 | 0-4-5 | 1-6/5-3/2 | Utonal | ^m | |
| 5 | 0-2-7 | 1-14/9-7/6 | Utonal | ^/ | 1-9/7-3/2 |
| 6 | 0-5-7 | 1-3/2-7/6 | Otonal | v\m | |
| 7 | 0-1-8 | 1-5/4-16/11 | Keenanismic | v(^^b5) | |
| 8 | 0-4-8 | 1-6/5-16/11 | Ptolemismic | ^m(^^b5) | |
| 9 | 0-7-8 | 1-7/6-16/11 | Keenanismic | v\m(^^b5) | |
| 10 | 0-1-9 | 1-5/4-20/11 | Utonal | v^7no5 | |
| 11 | 0-2-9 | 1-14/9-9/5 | Sensamagic | ^m7(vv#5)no3 | |
| 12 | 0-4-9 | 1-6/5-9/5 | Otonal | ^m7no5 | or 1-3/2-5/3 = v6no3 |
| 13 | 0-5-9 | 1-3/2-9/5 | Utonal | ^m7no3 | |
| 14 | 0-7-9 | 1-7/6-9/5 | Sensamagic | v\m,v7no5 | |
| 15 | 0-8-9 | 1-16/11-20/11 | Otonal | v(^^^bb5) | 1-5/4-11/8 |
| 16 | 0-1-10 | 1-5/4-9/8 | Otonal | v,9no5 | |
| 17 | 0-2-10 | 1-14/9-9/8 | Pentacircle | 2(vv#5) | |
| 18 | 0-5-10 | 1-3/2-9/8 | Ambitonal | 2 | |
| 19 | 0-8-10 | 1-16/11-9/8 | Pentacircle | 2(^^b5) | |
| 20 | 0-9-10 | 1-9/5-9/8 | Utonal | ^9no35 | or ^7sus2no5 |
| 21 | 0-1-11 | 1-5/4-7/5 | Marvel | v(\b5) | |
| 22 | 0-2-11 | 1-14/9-7/5 | Utonal | ^/,^7no5 | 1-9/7-9/5 |
| 23 | 0-4-11 | 1-6/5-7/5 | Otonal | ^m(\b5) | |
| 24 | 0-7-11 | 1-7/6-7/5 | Utonal | v\m(\b5) | |
| 25 | 0-9-11 | 1-9/5-7/5 | Otonal | ^/(^b5) | 1-9/7-10/7 |
| 26 | 0-10-11 | 1-9/8-7/5 | Marvel | v,7no5 | 1-5/4-16/9 |
| 27 | 0-1-12 | 1-5/4-7/4 | Otonal | v,v/7 | |
| 28 | 0-2-12 | 1-14/9-7/4 | Utonal | ^/,9no5 | 1-9/8-9/7 |
| 29 | 0-4-12 | 1-6/5-7/4 | Keenanismic | ^m,v\7 | |
| 30 | 0-5-12 | 1-3/2-7/4 | Otonal | v\m7no3 | |
| 31 | 0-7-12 | 1-7/6-7/4 | Utonal | v\m7no5 | |
| 32 | 0-8-12 | 1-16/11-7/4 | Keenanismic | ^m(v\b5) | 1-6/5-11/8 |
| 33 | 0-10-12 | 1-9/8-7/4 | Otonal | v\m7sus2 | |
| 34 | 0-11-12 | 1-7/5-7/4 | Utonal | v\7(\b5)no3 | |
| 35 | 0-1-13 | 1-5/4-12/11 | Keenanismic | ||
| 36 | 0-2-13 | 1-14/9-12/11 | Swetismic | 1-9/7-7/5 | |
| 37 | 0-4-13 | 1-6/5-12/11 | Utonal | ||
| 38 | 0-5-13 | 1-3/2-12/11 | Utonal | ||
| 39 | 0-8-13 | 1-16/11-12/11 | Otonal | ||
| 40 | 0-9-13 | 1-20/11-12/11 | Otonal | ||
| 41 | 0-11-13 | 1-7/5-12/11 | Swetismic | ||
| 42 | 0-12-13 | 1-7/4-12/11 | Keenanismic | ||
| 43 | 0-5-18 | 1-3/2-18/11 | Utonal | ||
| 44 | 0-7-18 | 1-7/6-18/11 | Swetismic | ||
| 45 | 0-8-18 | 1-16/11-18/11 | Otonal | ||
| 46 | 0-9-18 | 1-9/5-18/11 | Utonal | ||
| 47 | 0-10-18 | 1-9/8-18/11 | Utonal | ||
| 48 | 0-11-18 | 1-7/5-18/11 | Swetismic | ||
| 49 | 0-13-18 | 1-12/11-18/11 | Otonal | ||
| 50 | 0-2-20 | 1-14/9-14/11 | Utonal | ||
| 51 | 0-7-20 | 1-7/6-14/11 | Utonal | ||
| 52 | 0-8-20 | 1-16/11-14/11 | Otonal | ||
| 53 | 0-9-20 | 1-20/11-14/11 | Otonal | ||
| 54 | 0-10-20 | 1-9/8-14/11 | Pentacircle | ||
| 55 | 0-11-20 | 1-7/5-14/11 | Utonal | ||
| 56 | 0-12-20 | 1-7/4-14/11 | Utonal | ||
| 57 | 0-13-20 | 1-12/11-14/11 | Otonal | ||
| 58 | 0-18-20 | 1-18/11-14/11 | Otonal |
Tetrads
| # | Chord | Transversal | Type | name | comments |
|---|---|---|---|---|---|
| 1 | 0-1-2-9 | 1-5/4-14/9-9/5 | magic | v^7(vv#5) | |
| 2 | 0-2-4-9 | 1-14/9-6/5-9/5 | sensamagic | ^m7(vv#5) | |
| 3 | 0-1-5-9 | 1-5/4-3/2-9/5 | ptolemismic | v^7 | |
| 4 | 0-4-5-9 | 1-6/5-3/2-9/5 | ambitonal | ^m7 | or 1-5/4-3/2-5/3 = v6 |
| 5 | 0-2-7-9 | 1-14/9-7/6-9/5 | sensamagic | ^/,vv#9 | 1-9/7-3/2-7/3 |
| 6 | 0-5-7-9 | 1-3/2-7/6-9/5 | sensamagic | v\m^7 | |
| 7 | 0-1-8-9 | 1-5/4-16/11-9/5 | supermagic | v^7(^^b5) | |
| 8 | 0-4-8-9 | 1-6/5-16/11-9/5 | ptolemismic | ^m7(^^b5) | |
| 9 | 0-7-8-9 | 1-7/6-16/11-9/5 | magic | v\m,^7(^^b5) | |
| 10 | 0-1-2-10 | 1-5/4-14/9-9/8 | apollo | v,9(vv#5) | |
| 11 | 0-1-5-10 | 1-5/4-3/2-9/8 | otonal | v,9 | |
| 12 | 0-1-8-10 | 1-5/4-16/11-9/8 | sensamagic11 | v,9(^^b5) | |
| 13 | 0-1-9-10 | 1-5/4-9/5-9/8 | ptolemismic | v^7,9no5 | or v9(^7)no5 |
| 14 | 0-2-9-10 | 1-14/9-9/5-9/8 | sensamagic11 | ^9(vv#5)no3 | or ^7(vv#5)sus2 |
| 15 | 0-5-9-10 | 1-3/2-9/5-9/8 | utonal | ^9no3 | or ^7sus2 or 2,^7 |
| 16 | 0-8-9-10 | 1-16/11-9/5-9/8 | apollo | ||
| 17 | 0-1-2-11 | 1-5/4-14/9-7/5 | marvel | ||
| 18 | 0-2-4-11 | 1-14/9-6/5-7/5 | sensamagic | ||
| 19 | 0-2-7-11 | 1-14/9-7/6-7/5 | utonal | ||
| 20 | 0-1-9-11 | 1-5/4-9/5-7/5 | apollo | ||
| 21 | 0-2-9-11 | 1-14/9-9/5-7/5 | sensamagic | ||
| 22 | 0-4-9-11 | 1-6/5-9/5-7/5 | otonal | ^m7(\b5) | |
| 23 | 0-7-9-11 | 1-7/6-9/5-7/5 | sensamagic | ||
| 24 | 0-1-10-11 | 1-5/4-9/8-7/5 | marvel | ||
| 25 | 0-2-10-11 | 1-14/9-9/8-7/5 | apollo | ||
| 26 | 0-9-10-11 | 1-9/5-9/8-7/5 | marvel | ||
| 27 | 0-1-2-12 | 1-5/4-14/9-7/4 | marvel | ||
| 28 | 0-2-4-12 | 1-14/9-6/5-7/4 | sensamagic11 | ||
| 29 | 0-1-5-12 | 1-5/4-3/2-7/4 | otonal | v,v\7 | |
| 30 | 0-4-5-12 | 1-6/5-3/2-7/4 | keenanismic | ^mv\7 | |
| 31 | 0-2-7-12 | 1-14/9-7/6-7/4 | utonal | v\m7(vv#5) | |
| 32 | 0-5-7-12 | 1-3/2-7/6-7/4 | ambitonal | v\m7 | |
| 33 | 0-1-8-12 | 1-5/4-16/11-7/4 | keenanismic | ||
| 34 | 0-4-8-12 | 1-6/5-16/11-7/4 | supermagic | ||
| 35 | 0-7-8-12 | 1-7/6-16/11-7/4 | keenanismic | v\m7(^^b5) | |
| 36 | 0-1-10-12 | 1-5/4-9/8-7/4 | otonal | ||
| 37 | 0-2-10-12 | 1-14/9-9/8-7/4 | pentacircle | ||
| 38 | 0-5-10-12 | 1-3/2-9/8-7/4 | otonal | v\7sus2 | or 2,v\7 or v\9no3 |
| 39 | 0-8-10-12 | 1-16/11-9/8-7/4 | sensamagic11 | ||
| 40 | 0-1-11-12 | 1-5/4-7/5-7/4 | marvel | ||
| 41 | 0-2-11-12 | 1-14/9-7/5-7/4 | utonal | ||
| 42 | 0-4-11-12 | 1-6/5-7/5-7/4 | keenanismic | ||
| 43 | 0-7-11-12 | 1-7/6-7/5-7/4 | utonal | ||
| 44 | 0-10-11-12 | 1-9/8-7/5-7/4 | marvel | ||
| 45 | 0-1-2-13 | 1-5/4-14/9-12/11 | unimarvel | ||
| 46 | 0-2-4-13 | 1-14/9-6/5-12/11 | octarod | ||
| 47 | 0-1-5-13 | 1-5/4-3/2-12/11 | keenanismic | ||
| 48 | 0-4-5-13 | 1-6/5-3/2-12/11 | utonal | ||
| 49 | 0-1-8-13 | 1-5/4-16/11-12/11 | keenanismic | ||
| 50 | 0-4-8-13 | 1-6/5-16/11-12/11 | ptolemismic | ||
| 51 | 0-1-9-13 | 1-5/4-9/5-12/11 | supermagic | ||
| 52 | 0-2-9-13 | 1-14/9-9/5-12/11 | octarod | ||
| 53 | 0-4-9-13 | 1-6/5-9/5-12/11 | ptolemismic | ||
| 54 | 0-5-9-13 | 1-3/2-9/5-12/11 | ptolemismic | ||
| 55 | 0-8-9-13 | 1-16/11-20/11-12/11 | otonal | ||
| 56 | 0-1-11-13 | 1-5/4-7/5-12/11 | unimarvel | ||
| 57 | 0-2-11-13 | 1-14/9-7/5-12/11 | swetismic | ||
| 58 | 0-4-11-13 | 1-6/5-7/5-12/11 | octarod | ||
| 59 | 0-9-11-13 | 1-9/5-7/5-12/11 | octarod | ||
| 60 | 0-1-12-13 | 1-5/4-7/4-12/11 | keenanismic | ||
| 61 | 0-2-12-13 | 1-14/9-7/4-12/11 | unimarvel | ||
| 62 | 0-4-12-13 | 1-6/5-7/4-12/11 | supermagic | ||
| 63 | 0-5-12-13 | 1-3/2-7/4-12/11 | keenanismic | ||
| 64 | 0-8-12-13 | 1-16/11-7/4-12/11 | keenanismic | ||
| 65 | 0-11-12-13 | 1-7/5-7/4-12/11 | unimarvel | ||
| 66 | 0-5-7-18 | 1-3/2-7/6-18/11 | swetismic | ||
| 67 | 0-7-8-18 | 1-7/6-16/11-18/11 | unimarvel | ||
| 68 | 0-5-9-18 | 1-3/2-9/5-18/11 | utonal | ||
| 69 | 0-7-9-18 | 1-7/6-9/5-18/11 | octarod | ||
| 70 | 0-8-9-18 | 1-16/11-20/11-18/11 | otonal | ||
| 71 | 0-5-10-18 | 1-3/2-9/8-18/11 | utonal | ||
| 72 | 0-8-10-18 | 1-16/11-9/8-18/11 | pentacircle | ||
| 73 | 0-9-10-18 | 1-9/5-9/8-18/11 | utonal | ||
| 74 | 0-7-11-18 | 1-7/6-7/5-18/11 | swetismic | ||
| 75 | 0-9-11-18 | 1-9/5-7/5-18/11 | octarod | ||
| 76 | 0-10-11-18 | 1-9/8-7/5-18/11 | unimarvel | ||
| 77 | 0-5-13-18 | 1-3/2-12/11-18/11 | ambitonal | ||
| 78 | 0-8-13-18 | 1-16/11-12/11-18/11 | otonal | ||
| 79 | 0-9-13-18 | 1-20/11-12/11-18/11 | otonal | ||
| 80 | 0-11-13-18 | 1-7/5-12/11-18/11 | swetismic | ||
| 81 | 0-2-7-20 | 1-14/9-7/6-14/11 | utonal | ||
| 82 | 0-7-8-20 | 1-7/6-16/11-14/11 | keenanismic | ||
| 83 | 0-2-9-20 | 1-14/9-9/5-14/11 | octarod | ||
| 84 | 0-7-9-20 | 1-7/6-9/5-14/11 | octarod | ||
| 85 | 0-8-9-20 | 1-16/11-20/11-14/11 | otonal | ||
| 86 | 0-2-10-20 | 1-14/9-9/8-14/11 | pentacircle | ||
| 87 | 0-8-10-20 | 1-16/11-9/8-14/11 | pentacircle | ||
| 88 | 0-9-10-20 | 1-9/5-9/8-14/11 | apollo | ||
| 89 | 0-2-11-20 | 1-14/9-7/5-14/11 | utonal | ||
| 90 | 0-7-11-20 | 1-7/6-7/5-14/11 | utonal | ||
| 91 | 0-9-11-20 | 1-9/5-7/5-14/11 | ptolemismic | ||
| 92 | 0-10-11-20 | 1-9/8-7/5-14/11 | apollo | ||
| 93 | 0-2-12-20 | 1-14/9-7/4-14/11 | utonal | ||
| 94 | 0-7-12-20 | 1-7/6-7/4-14/11 | utonal | ||
| 95 | 0-8-12-20 | 1-16/11-7/4-14/11 | keenanismic | ||
| 96 | 0-10-12-20 | 1-9/8-7/4-14/11 | pentacircle | ||
| 97 | 0-11-12-20 | 1-7/5-7/4-14/11 | utonal | ||
| 98 | 0-2-13-20 | 1-14/9-12/11-14/11 | swetismic | ||
| 99 | 0-8-13-20 | 1-16/11-12/11-14/11 | otonal | ||
| 100 | 0-9-13-20 | 1-20/11-12/11-14/11 | otonal | ||
| 101 | 0-11-13-20 | 1-7/5-12/11-14/11 | octarod | ||
| 102 | 0-12-13-20 | 1-7/4-12/11-14/11 | keenanismic | ||
| 103 | 0-7-18-20 | 1-7/6-18/11-14/11 | swetismic | ||
| 104 | 0-8-18-20 | 1-16/11-18/11-14/11 | otonal | ||
| 105 | 0-9-18-20 | 1-20/11-18/11-14/11 | otonal | ||
| 106 | 0-10-18-20 | 1-9/8-18/11-14/11 | pentacircle | ||
| 107 | 0-11-18-20 | 1-7/5-18/11-14/11 | octarod | ||
| 108 | 0-13-18-20 | 1-12/11-18/11-14/11 | otonal |
Pentads
| # | Chord | Transversal | Type |
|---|---|---|---|
| 1 | 0-1-2-9-10 | 1-5/4-14/9-9/5-9/8 | magic |
| 2 | 0-1-5-9-10 | 1-5/4-3/2-9/5-9/8 | ptolemismic |
| 3 | 0-1-8-9-10 | 1-5/4-16/11-9/5-9/8 | magic |
| 4 | 0-1-2-9-11 | 1-5/4-14/9-9/5-7/5 | magic |
| 5 | 0-2-4-9-11 | 1-14/9-6/5-9/5-7/5 | sensamagic |
| 6 | 0-2-7-9-11 | 1-14/9-7/6-9/5-7/5 | sensamagic |
| 7 | 0-1-2-10-11 | 1-5/4-14/9-9/8-7/5 | apollo |
| 8 | 0-1-9-10-11 | 1-5/4-9/5-9/8-7/5 | apollo |
| 9 | 0-2-9-10-11 | 1-14/9-9/5-9/8-7/5 | magic |
| 10 | 0-1-2-10-12 | 1-5/4-14/9-9/8-7/4 | apollo |
| 11 | 0-1-5-10-12 | 1-5/4-3/2-9/8-7/4 | otonal |
| 12 | 0-1-8-10-12 | 1-5/4-16/11-9/8-7/4 | sensamagic11 |
| 13 | 0-1-2-11-12 | 1-5/4-14/9-7/5-7/4 | marvel |
| 14 | 0-2-4-11-12 | 1-14/9-6/5-7/5-7/4 | sensamagic11 |
| 15 | 0-2-7-11-12 | 1-14/9-7/6-7/5-7/4 | utonal |
| 16 | 0-1-10-11-12 | 1-5/4-9/8-7/5-7/4 | marvel |
| 17 | 0-2-10-11-12 | 1-14/9-9/8-7/5-7/4 | apollo |
| 18 | 0-1-2-9-13 | 1-5/4-14/9-9/5-12/11 | magic |
| 19 | 0-2-4-9-13 | 1-14/9-6/5-9/5-12/11 | octarod |
| 20 | 0-1-5-9-13 | 1-5/4-3/2-9/5-12/11 | supermagic |
| 21 | 0-4-5-9-13 | 1-6/5-3/2-9/5-12/11 | ptolemismic |
| 22 | 0-1-8-9-13 | 1-5/4-16/11-9/5-12/11 | supermagic |
| 23 | 0-4-8-9-13 | 1-6/5-16/11-9/5-12/11 | ptolemismic |
| 24 | 0-1-2-11-13 | 1-5/4-14/9-7/5-12/11 | unimarvel |
| 25 | 0-2-4-11-13 | 1-14/9-6/5-7/5-12/11 | octarod |
| 26 | 0-1-9-11-13 | 1-5/4-9/5-7/5-12/11 | magic |
| 27 | 0-2-9-11-13 | 1-14/9-9/5-7/5-12/11 | octarod |
| 28 | 0-4-9-11-13 | 1-6/5-9/5-7/5-12/11 | octarod |
| 29 | 0-1-2-12-13 | 1-5/4-14/9-7/4-12/11 | unimarvel |
| 30 | 0-2-4-12-13 | 1-14/9-6/5-7/4-12/11 | magic |
| 31 | 0-1-5-12-13 | 1-5/4-3/2-7/4-12/11 | keenanismic |
| 32 | 0-4-5-12-13 | 1-6/5-3/2-7/4-12/11 | supermagic |
| 33 | 0-1-8-12-13 | 1-5/4-16/11-7/4-12/11 | keenanismic |
| 34 | 0-4-8-12-13 | 1-6/5-16/11-7/4-12/11 | supermagic |
| 35 | 0-1-11-12-13 | 1-5/4-7/5-7/4-12/11 | unimarvel |
| 36 | 0-2-11-12-13 | 1-14/9-7/5-7/4-12/11 | unimarvel |
| 37 | 0-4-11-12-13 | 1-6/5-7/5-7/4-12/11 | magic |
| 38 | 0-5-7-9-18 | 1-3/2-7/6-9/5-18/11 | octarod |
| 39 | 0-7-8-9-18 | 1-7/6-16/11-9/5-18/11 | magic |
| 40 | 0-5-9-10-18 | 1-3/2-9/5-9/8-18/11 | utonal |
| 41 | 0-8-9-10-18 | 1-16/11-9/5-9/8-18/11 | apollo |
| 42 | 0-7-9-11-18 | 1-7/6-9/5-7/5-18/11 | octarod |
| 43 | 0-9-10-11-18 | 1-9/5-9/8-7/5-18/11 | magic |
| 44 | 0-5-9-13-18 | 1-3/2-9/5-12/11-18/11 | ptolemismic |
| 45 | 0-8-9-13-18 | 1-16/11-20/11-12/11-18/11 | otonal |
| 46 | 0-9-11-13-18 | 1-9/5-7/5-12/11-18/11 | octarod |
| 47 | 0-2-7-9-20 | 1-14/9-7/6-9/5-14/11 | octarod |
| 48 | 0-7-8-9-20 | 1-7/6-16/11-9/5-14/11 | magic |
| 49 | 0-2-9-10-20 | 1-14/9-9/5-9/8-14/11 | magic |
| 50 | 0-8-9-10-20 | 1-16/11-9/5-9/8-14/11 | apollo |
| 51 | 0-2-7-11-20 | 1-14/9-7/6-7/5-14/11 | utonal |
| 52 | 0-2-9-11-20 | 1-14/9-9/5-7/5-14/11 | octarod |
| 53 | 0-7-9-11-20 | 1-7/6-9/5-7/5-14/11 | octarod |
| 54 | 0-2-10-11-20 | 1-14/9-9/8-7/5-14/11 | apollo |
| 55 | 0-9-10-11-20 | 1-9/5-9/8-7/5-14/11 | apollo |
| 56 | 0-2-7-12-20 | 1-14/9-7/6-7/4-14/11 | utonal |
| 57 | 0-7-8-12-20 | 1-7/6-16/11-7/4-14/11 | keenanismic |
| 58 | 0-2-10-12-20 | 1-14/9-9/8-7/4-14/11 | pentacircle |
| 59 | 0-8-10-12-20 | 1-16/11-9/8-7/4-14/11 | sensamagic11 |
| 60 | 0-2-11-12-20 | 1-14/9-7/5-7/4-14/11 | utonal |
| 61 | 0-7-11-12-20 | 1-7/6-7/5-7/4-14/11 | utonal |
| 62 | 0-10-11-12-20 | 1-9/8-7/5-7/4-14/11 | apollo |
| 63 | 0-2-9-13-20 | 1-14/9-9/5-12/11-14/11 | octarod |
| 64 | 0-8-9-13-20 | 1-16/11-20/11-12/11-14/11 | otonal |
| 65 | 0-2-11-13-20 | 1-14/9-7/5-12/11-14/11 | octarod |
| 66 | 0-9-11-13-20 | 1-9/5-7/5-12/11-14/11 | octarod |
| 67 | 0-2-12-13-20 | 1-14/9-7/4-12/11-14/11 | unimarvel |
| 68 | 0-8-12-13-20 | 1-16/11-7/4-12/11-14/11 | keenanismic |
| 69 | 0-11-12-13-20 | 1-7/5-7/4-12/11-14/11 | magic |
| 70 | 0-7-8-18-20 | 1-7/6-16/11-18/11-14/11 | unimarvel |
| 71 | 0-7-9-18-20 | 1-7/6-9/5-18/11-14/11 | octarod |
| 72 | 0-8-9-18-20 | 1-16/11-20/11-18/11-14/11 | otonal |
| 73 | 0-8-10-18-20 | 1-16/11-9/8-18/11-14/11 | pentacircle |
| 74 | 0-9-10-18-20 | 1-9/5-9/8-18/11-14/11 | apollo |
| 75 | 0-7-11-18-20 | 1-7/6-7/5-18/11-14/11 | octarod |
| 76 | 0-9-11-18-20 | 1-9/5-7/5-18/11-14/11 | octarod |
| 77 | 0-10-11-18-20 | 1-9/8-7/5-18/11-14/11 | magic |
| 78 | 0-8-13-18-20 | 1-16/11-12/11-18/11-14/11 | otonal |
| 79 | 0-9-13-18-20 | 1-20/11-12/11-18/11-14/11 | otonal |
| 80 | 0-11-13-18-20 | 1-7/5-12/11-18/11-14/11 | octarod |
Hexads
| # | Chord | Transversal | Type |
|---|---|---|---|
| 1 | 0-1-2-9-10-11 | 1-5/4-14/9-9/5-9/8-7/5 | magic |
| 2 | 0-1-2-10-11-12 | 1-5/4-14/9-9/8-7/5-7/4 | apollo |
| 3 | 0-1-2-9-11-13 | 1-5/4-14/9-9/5-7/5-12/11 | magic |
| 4 | 0-2-4-9-11-13 | 1-14/9-6/5-9/5-7/5-12/11 | octarod |
| 5 | 0-1-2-11-12-13 | 1-5/4-14/9-7/5-7/4-12/11 | unimarvel |
| 6 | 0-2-4-11-12-13 | 1-14/9-6/5-7/5-7/4-12/11 | magic |
| 7 | 0-2-7-9-11-20 | 1-14/9-7/6-9/5-7/5-14/11 | octarod |
| 8 | 0-2-9-10-11-20 | 1-14/9-9/5-9/8-7/5-14/11 | magic |
| 9 | 0-2-7-11-12-20 | 1-14/9-7/6-7/5-7/4-14/11 | utonal |
| 10 | 0-2-10-11-12-20 | 1-14/9-9/8-7/5-7/4-14/11 | apollo |
| 11 | 0-2-9-11-13-20 | 1-14/9-9/5-7/5-12/11-14/11 | octarod |
| 12 | 0-2-11-12-13-20 | 1-14/9-7/5-7/4-12/11-14/11 | magic |
| 13 | 0-7-8-9-18-20 | 1-7/6-16/11-9/5-18/11-14/11 | magic |
| 14 | 0-8-9-10-18-20 | 1-16/11-9/5-9/8-18/11-14/11 | apollo |
| 15 | 0-7-9-11-18-20 | 1-7/6-9/5-7/5-18/11-14/11 | octarod |
| 16 | 0-9-10-11-18-20 | 1-9/5-9/8-7/5-18/11-14/11 | magic |
| 17 | 0-8-9-13-18-20 | 1-16/11-20/11-12/11-18/11-14/11 | otonal |
| 18 | 0-9-11-13-18-20 | 1-9/5-7/5-12/11-18/11-14/11 | octarod |