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 arrows (ups and downs) as described on the pergens page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the list of pergens. One up is 19 generators, octave-reduced. The generator is vM3 = 380¢ + c/5, where c is the amount in cents the tempered fifth exceeds 700¢. The enharmonic interval is ^5dd2, thus ^5C = B##.
To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus /1 = −25G + 3G = m2 + ^^d8 = ^^d2. Thus a lift equals two ups minus a tempered pythagorean comma, so /C = ^^Dbb, \C = vvB#, ^^C = /B#, and vvC = \Dbb. When naming 7-limit chords, note that an up is ~81/80 and a lift is ~64/63.
The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore if the fifth is narrower than 19edo's, an up will be descending.
| Sharp | Up | Lift | How to convert the notation to an edo | |
|---|---|---|---|---|
| 19edo | 1\19 = 61¢ | 0\19 = 0¢ | 1\19 = 61¢ | Ignore the arrows, treat slashes as sharps/flats |
| 22edo | 3\22 = 164¢ | 1\22 = 55¢ | 0\22 = 0¢ | Ignore the slashes |
| 41edo | 4\41 = 117¢ | 1\41 = 29¢ | 1\41 = 29¢ | Treat slashes as arrows |
| 60edo | 5\60 = 100¢ | 1\60 = 20¢ | 2\60 = 40¢ | Treat slashes as double arrows |
| Rank-2 | 100¢ + 7c | 20¢ + 3.8c | 40¢ − 4.4c |
| 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 |
| Ratio | 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 \m6 |
^^d8 /M7 |
^m3 | P5 | vM7 | vvA2 \m3 |
^^d5 /A4 |
^m7 | M2 | vA4 ^\d5 |
vvA6 \m7 |
^^m2 /A1 |
| Note (in C) |
C | vE | vvG# \Ab |
^^Cb /B |
^Eb | G | vB | vvD# \Eb |
^^Gb /F# |
^Bb | D | vF# ^\Gb |
vvA# \Bb |
^^Db /C# |
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 | \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 | \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 | \mv7no5 | |
| 15 | 0-8-9 | 1-16/11-20/11 | Otonal | v(\b5) | 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 | \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,\7no5 | |
| 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\7 | |
| 30 | 0-5-12 | 1-3/2-7/4 | Otonal | \7no3 | |
| 31 | 0-7-12 | 1-7/6-7/4 | Utonal | \m7no5 | |
| 32 | 0-8-12 | 1-16/11-7/4 | Keenanismic | ^m(\b5) | 1-6/5-11/8 |
| 33 | 0-10-12 | 1-9/8-7/4 | Otonal | \7sus2 | |
| 34 | 0-11-12 | 1-7/5-7/4 | Utonal | \7(^\b5)no3 | |
| 35 | 0-1-13 | 1-5/4-12/11 | Keenanismic | ||
| 36 | 0-2-13 | 1-14/9-12/11 | Swetismic | /(^\b5) | 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 | 0-1-5-6 | 1-5/4-3/2-15/8 | Ambitonal | vM7 | |
| 2 | 0-1-2-9 | 1-5/4-14/9-9/5 | Magic | v^7(vv#5) | |
| 3 | 0-2-4-9 | 1-14/9-6/5-9/5 | Sensamagic | ^m7(vv#5) | |
| 4 | 0-1-5-9 | 1-5/4-3/2-9/5 | Ptolemismic | v^7 | |
| 5 | 0-4-5-9 | 1-6/5-3/2-9/5 | Ambitonal | ^m7 | or 1-5/4-3/2-5/3 = v6 |
| 6 | 0-2-7-9 | 1-14/9-7/6-9/5 | Sensamagic | /,vv#9 | 1-9/7-3/2-7/3 |
| 7 | 0-5-7-9 | 1-3/2-7/6-9/5 | Sensamagic | \m^7 | |
| 8 | 0-1-8-9 | 1-5/4-16/11-9/5 | Supermagic | v^7(^^b5) | |
| 9 | 0-4-8-9 | 1-6/5-16/11-9/5 | Ptolemismic | ^m7(^^b5) | |
| 10 | 0-7-8-9 | 1-7/6-16/11-9/5 | Magic | \m^7(^^b5) | |
| 11 | 0-1-2-10 | 1-5/4-14/9-9/8 | Apollo | v,9(vv#5) | |
| 12 | 0-1-5-10 | 1-5/4-3/2-9/8 | Otonal | v,9 | |
| 13 | 0-1-8-10 | 1-5/4-16/11-9/8 | Sensamagic11 | v,9(^^b5) | |
| 14 | 0-1-9-10 | 1-5/4-9/5-9/8 | Ptolemismic | v^7,9no5 | or v9(^7)no5 |
| 15 | 0-2-9-10 | 1-14/9-9/5-9/8 | Sensamagic11 | ^9(vv#5)no3 | or ^7(vv#5)sus2 |
| 16 | 0-5-9-10 | 1-3/2-9/5-9/8 | Utonal | ^9no3 | or ^7sus2 or 2,^7 |
| 17 | 0-8-9-10 | 1-16/11-9/5-9/8 | Apollo | ||
| 18 | 0-1-2-11 | 1-5/4-14/9-7/5 | Marvel | ||
| 19 | 0-2-4-11 | 1-14/9-6/5-7/5 | Sensamagic | ||
| 20 | 0-2-7-11 | 1-14/9-7/6-7/5 | Utonal | ||
| 21 | 0-1-9-11 | 1-5/4-9/5-7/5 | Apollo | ||
| 22 | 0-2-9-11 | 1-14/9-9/5-7/5 | Sensamagic | ||
| 23 | 0-4-9-11 | 1-6/5-9/5-7/5 | Otonal | ^m7(^\b5) | |
| 24 | 0-7-9-11 | 1-7/6-9/5-7/5 | Sensamagic | ||
| 25 | 0-1-10-11 | 1-5/4-9/8-7/5 | Marvel | ||
| 26 | 0-2-10-11 | 1-14/9-9/8-7/5 | Apollo | ||
| 27 | 0-9-10-11 | 1-9/5-9/8-7/5 | Marvel | ||
| 28 | 0-1-2-12 | 1-5/4-14/9-7/4 | Marvel | ||
| 29 | 0-2-4-12 | 1-14/9-6/5-7/4 | Sensamagic11 | ||
| 30 | 0-1-5-12 | 1-5/4-3/2-7/4 | Otonal | v,\7 | |
| 31 | 0-4-5-12 | 1-6/5-3/2-7/4 | Keenanismic | ^m\7 | |
| 32 | 0-2-7-12 | 1-14/9-7/6-7/4 | Utonal | \m7(vv#5) | |
| 33 | 0-5-7-12 | 1-3/2-7/6-7/4 | Ambitonal | \m7 | |
| 34 | 0-1-8-12 | 1-5/4-16/11-7/4 | Keenanismic | ||
| 35 | 0-4-8-12 | 1-6/5-16/11-7/4 | Supermagic | ||
| 36 | 0-7-8-12 | 1-7/6-16/11-7/4 | Keenanismic | \m7(^^b5) | |
| 37 | 0-7-11-12 | 1-7/6-7/5-7/4 | Otonal | \m7(^\b5) | or 1-6/5-3/2-12/7 = ^m/6 |
| 38 | 0-1-10-12 | 1-5/4-9/8-7/4 | Otonal | ||
| 39 | 0-2-10-12 | 1-14/9-9/8-7/4 | Pentacircle | ||
| 40 | 0-5-10-12 | 1-3/2-9/8-7/4 | Otonal | \7sus2 | or 2,\7 or \9no3 |
| 41 | 0-8-10-12 | 1-16/11-9/8-7/4 | Sensamagic11 | ||
| 42 | 0-1-11-12 | 1-5/4-7/5-7/4 | Marvel | ||
| 43 | 0-2-11-12 | 1-14/9-7/5-7/4 | Utonal | ||
| 44 | 0-4-11-12 | 1-6/5-7/5-7/4 | Keenanismic | ||
| 45 | 0-7-11-12 | 1-7/6-7/5-7/4 | Utonal | ||
| 46 | 0-10-11-12 | 1-9/8-7/5-7/4 | Marvel | ||
| 47 | 0-1-2-13 | 1-5/4-14/9-12/11 | Unimarvel | ||
| 48 | 0-2-4-13 | 1-14/9-6/5-12/11 | Octarod | ||
| 49 | 0-1-5-13 | 1-5/4-3/2-12/11 | Keenanismic | ||
| 50 | 0-4-5-13 | 1-6/5-3/2-12/11 | Utonal | ||
| 51 | 0-1-8-13 | 1-5/4-16/11-12/11 | Keenanismic | ||
| 52 | 0-4-8-13 | 1-6/5-16/11-12/11 | Ptolemismic | ||
| 53 | 0-1-9-13 | 1-5/4-9/5-12/11 | Supermagic | ||
| 54 | 0-2-9-13 | 1-14/9-9/5-12/11 | Octarod | ||
| 55 | 0-4-9-13 | 1-6/5-9/5-12/11 | Ptolemismic | ||
| 56 | 0-5-9-13 | 1-3/2-9/5-12/11 | Ptolemismic | ||
| 57 | 0-8-9-13 | 1-16/11-20/11-12/11 | Otonal | ||
| 58 | 0-1-11-13 | 1-5/4-7/5-12/11 | Unimarvel | ||
| 59 | 0-2-11-13 | 1-14/9-7/5-12/11 | Swetismic | ||
| 60 | 0-4-11-13 | 1-6/5-7/5-12/11 | Octarod | ||
| 61 | 0-9-11-13 | 1-9/5-7/5-12/11 | Octarod | ||
| 62 | 0-1-12-13 | 1-5/4-7/4-12/11 | Keenanismic | ||
| 63 | 0-2-12-13 | 1-14/9-7/4-12/11 | Unimarvel | ||
| 64 | 0-4-12-13 | 1-6/5-7/4-12/11 | Supermagic | ||
| 65 | 0-5-12-13 | 1-3/2-7/4-12/11 | Keenanismic | ||
| 66 | 0-8-12-13 | 1-16/11-7/4-12/11 | Keenanismic | ||
| 67 | 0-11-12-13 | 1-7/5-7/4-12/11 | Unimarvel | ||
| 68 | 0-5-7-18 | 1-3/2-7/6-18/11 | Swetismic | ||
| 69 | 0-7-8-18 | 1-7/6-16/11-18/11 | Unimarvel | ||
| 70 | 0-5-9-18 | 1-3/2-9/5-18/11 | Utonal | ||
| 71 | 0-7-9-18 | 1-7/6-9/5-18/11 | Octarod | ||
| 72 | 0-8-9-18 | 1-16/11-20/11-18/11 | Otonal | ||
| 73 | 0-5-10-18 | 1-3/2-9/8-18/11 | Utonal | ||
| 74 | 0-8-10-18 | 1-16/11-9/8-18/11 | Pentacircle | ||
| 75 | 0-9-10-18 | 1-9/5-9/8-18/11 | Utonal | ||
| 76 | 0-7-11-18 | 1-7/6-7/5-18/11 | Swetismic | ||
| 77 | 0-9-11-18 | 1-9/5-7/5-18/11 | Octarod | ||
| 78 | 0-10-11-18 | 1-9/8-7/5-18/11 | Unimarvel | ||
| 79 | 0-5-13-18 | 1-3/2-12/11-18/11 | Ambitonal | ||
| 80 | 0-8-13-18 | 1-16/11-12/11-18/11 | Otonal | ||
| 81 | 0-9-13-18 | 1-20/11-12/11-18/11 | Otonal | ||
| 82 | 0-11-13-18 | 1-7/5-12/11-18/11 | Swetismic | ||
| 83 | 0-2-7-20 | 1-14/9-7/6-14/11 | Utonal | ||
| 84 | 0-7-8-20 | 1-7/6-16/11-14/11 | Keenanismic | ||
| 85 | 0-2-9-20 | 1-14/9-9/5-14/11 | Octarod | ||
| 86 | 0-7-9-20 | 1-7/6-9/5-14/11 | Octarod | ||
| 87 | 0-8-9-20 | 1-16/11-20/11-14/11 | Otonal | ||
| 88 | 0-2-10-20 | 1-14/9-9/8-14/11 | Pentacircle | ||
| 89 | 0-8-10-20 | 1-16/11-9/8-14/11 | Pentacircle | ||
| 90 | 0-9-10-20 | 1-9/5-9/8-14/11 | Apollo | ||
| 91 | 0-2-11-20 | 1-14/9-7/5-14/11 | Utonal | ||
| 92 | 0-7-11-20 | 1-7/6-7/5-14/11 | Utonal | ||
| 93 | 0-9-11-20 | 1-9/5-7/5-14/11 | Ptolemismic | ||
| 94 | 0-10-11-20 | 1-9/8-7/5-14/11 | Apollo | ||
| 95 | 0-2-12-20 | 1-14/9-7/4-14/11 | Utonal | ||
| 96 | 0-7-12-20 | 1-7/6-7/4-14/11 | Utonal | ||
| 97 | 0-8-12-20 | 1-16/11-7/4-14/11 | Keenanismic | ||
| 98 | 0-10-12-20 | 1-9/8-7/4-14/11 | Pentacircle | ||
| 99 | 0-11-12-20 | 1-7/5-7/4-14/11 | Utonal | ||
| 100 | 0-2-13-20 | 1-14/9-12/11-14/11 | Swetismic | ||
| 101 | 0-8-13-20 | 1-16/11-12/11-14/11 | Otonal | ||
| 102 | 0-9-13-20 | 1-20/11-12/11-14/11 | Otonal | ||
| 103 | 0-11-13-20 | 1-7/5-12/11-14/11 | Octarod | ||
| 104 | 0-12-13-20 | 1-7/4-12/11-14/11 | Keenanismic | ||
| 105 | 0-7-18-20 | 1-7/6-18/11-14/11 | Swetismic | ||
| 106 | 0-8-18-20 | 1-16/11-18/11-14/11 | Otonal | ||
| 107 | 0-9-18-20 | 1-20/11-18/11-14/11 | Otonal | ||
| 108 | 0-10-18-20 | 1-9/8-18/11-14/11 | Pentacircle | ||
| 109 | 0-11-18-20 | 1-7/5-18/11-14/11 | Octarod | ||
| 110 | 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 |