Chords of magic

Below are listed the 11-odd-limit 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 keemic. 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.

Kite Giedraitis has named the chords using arrows (ups and downs), as described in Kite's thoughts on pergens. The pergen is (P8, P12/5) fifth-of-a-twelfth, #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 unison is ^⁵dd2, thus ^⁵C = Bx. 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. 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.

Cents values of magic accidentals in various tunings

	Sharp	Up	Lift	How to convert the notation to the 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	N/a

In magic, 5/4 = vM3, 7/4 = \m7 and 11/8 = vvA4. Thus an up is ~81/80 and a lift is ~64/63. This may not be true for other (P8, P12/5) temperaments. Therefore, the ratios in the following table are specific to magic, but the chord names apply to any (P8, P12/5) temperament.

Magic's genchain

Genspan	0	1	2	3	4	5	6	7	8	9	10	11	12	13	…	18	…	20
Cents (41edo)	0	380	761	1141	322	702	1083	263	644	1024	205	585	966	146	…	849	…	410
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	…	18/11	…	14/11
Interval	P1	vM3	vvA5 \m6	^^d8 /M7	^m3	P5	vM7	vvA2 \m3	^^d5 /A4	^m7	M2	vA4 ^\d5	vvA6 \m7	^^m2 /A1	…	^^m6 /A5	…	M3
Note (in C)	C	vE	vvG# \Ab	^^Cb /B	^Eb	G	vB	vvD# \Eb	^^Gb /F#	^Bb	D	vF# ^\Gb	vvA# \Bb	^^Db /C#	…	^^Ab /G#	…	E

Todo: complete table

Triads

#	Generators	Transversal	Type	Comments	Kite's name
1	0–1–2	1–5/4–14/9	Marvel		Cv(vv#5)
2	0–2–4	1–14/9–6/5	Sensamagic		C^m(vv#5)
3	0–1–5	1–5/4–3/2	Otonal	4:5:6	Cv
4	0–4–5	1–6/5–3/2	Utonal	1/(6:5:4)	C^m
5	0–2–7	1–14/9–7/6	Utonal	1/(9:7:6)	C/
6	0–5–7	1–3/2–7/6	Otonal	6:7:9	C\m
7	0–1–8	1–5/4–16/11	Keenanismic		Cv(^^b5)
8	0–4–8	1–6/5–16/11	Ptolemismic		C^m(^^b5)
9	0–7–8	1–7/6–16/11	Keenanismic		C\m(^^b5)
10	0–1–9	1–5/4–20/11	Utonal		Cv^7no5
11	0–2–9	1–14/9–9/5	Sensamagic		C^m7(vv#5)no3
12	0–4–9	1–6/5–9/5	Otonal	6:9:10	C^m7no5 or Cv6no3
13	0–5–9	1–3/2–9/5	Utonal	1/(9:6:5)	C^m7no3
14	0–7–9	1–7/6–9/5	Sensamagic		C\mv7no5
15	0–8–9	1–16/11–20/11	Otonal	1–5/4–11/8	Cv(\b5)
16	0–1–10	1–5/4–9/8	Otonal		Cv,9no5
17	0–2–10	1–14/9–9/8	Pentacircle		C2(vv#5)
18	0–5–10	1–3/2–9/8	Ambitonal	6:8:9, 8:9:12	C2
19	0–8–10	1–16/11–9/8	Pentacircle		C2(^^b5)
20	0–9–10	1–9/5–9/8	Utonal		C^9no35 or C^7sus2no5
21	0–1–11	1–5/4–7/5	Marvel		Cv(^\b5)
22	0–2–11	1–14/9–7/5	Utonal	1–9/7–9/5	C/,^7no5
23	0–4–11	1–6/5–7/5	Otonal	5:6:7	C^m(^\b5)
24	0–7–11	1–7/6–7/5	Utonal	1/(7:6:5)	C\m(^\b5)
25	0–9–11	1–9/5–7/5	Otonal	1–9/7–10/7	C/(^b5)
26	0–10–11	1–9/8–7/5	Marvel	1–5/4–16/9	Cv,7no5
27	0–1–12	1–5/4–7/4	Otonal	4:5:7	Cv,\7no5
28	0–2–12	1–14/9–7/4	Utonal	1–9/8–9/7	C/,9no5
29	0–4–12	1–6/5–7/4	Keenanismic		C^m\7
30	0–5–12	1–3/2–7/4	Otonal	4:6:7	C\7no3
31	0–7–12	1–7/6–7/4	Utonal	1/(12:8:7)	C\m7no5
32	0–8–12	1–16/11–7/4	Keenanismic	1–6/5–11/8	C^m(\b5)
33	0–10–12	1–9/8–7/4	Otonal		C\7sus2
34	0–11–12	1–7/5–7/4	Utonal	1/(10:8:7)	C\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	C/(^\b5)
37	0–4–13	1–6/5–12/11	Utonal
38	0–5–13	1–3/2–12/11	Utonal		C^^b2
39	0–8–13	1–16/11–12/11	Otonal	1–11/8–3/2	Cvv#4
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

#	Generators	Transversal	Type	Comments	Kite's name
1	0–1–2–9	1–5/4–14/9–9/5	Magic		Cv^7(vv#5)
2	0–2–4–9	1–14/9–6/5–9/5	Sensamagic		C^m7(vv#5)
3	0–1–5–9	1–5/4–3/2–9/5	Ptolemismic		Cv^7
4	0–4–5–9	1–6/5–3/2–9/5	Ambitonal	10:12:15:18, 12:15:18:20 9-odd-limit ASS	C^m7 or Cv6
5	0–2–7–9	1–14/9–7/6–9/5	Sensamagic	1–9/7–3/2–7/3	C/,vv#9
6	0–5–7–9	1–3/2–7/6–9/5	Sensamagic		C\m^7
7	0–1–8–9	1–5/4–16/11–9/5	Keemic		Cv^7(^^b5)
8	0–4–8–9	1–6/5–16/11–9/5	Ptolemismic		C^m7(^^b5)
9	0–7–8–9	1–7/6–16/11–9/5	Magic		C\m^7(^^b5)
10	0–1–2–10	1–5/4–14/9–9/8	Apollo		Cv,9(vv#5)
11	0–1–5–10	1–5/4–3/2–9/8	Otonal	4:5:6:9	Cv,9
12	0–1–8–10	1–5/4–16/11–9/8	Sensamagic11		Cv,9(^^b5)
13	0–1–9–10	1–5/4–9/5–9/8	Ptolemismic		Cv^7,9no5 or Cv9(^7)no5
14	0–2–9–10	1–14/9–9/5–9/8	Sensamagic11		C^9(vv#5)no3 or C^7(vv#5)sus2
15	0–5–9–10	1–3/2–9/5–9/8	Utonal	1/(9:6:5:4)	C^9no3 or C^7sus2 or C2,^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	1/(9:7:6:5)
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	6:7:9:10	C^m7(^\b5) or C\mv6
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	4:5:6:7	Cv,\7
30	0–4–5–12	1–6/5–3/2–7/4	Keenanismic		C^m\7
31	0–2–7–12	1–14/9–7/6–7/4	Utonal		C\m7(vv#5)
32	0–5–7–12	1–3/2–7/6–7/4	Ambitonal	12:14:18:21, 14:18:21:24 9-odd-limit ASS	C\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	Keemic
35	0–7–8–12	1–7/6–16/11–7/4	Keenanismic		C\m7(^^b5)
36	0–1–10–12	1–5/4–9/8–7/4	Otonal	4:5:7:9
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	4:6:7:9	C2\7 or C\7sus2 or C\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	1/(9:7:5:4)
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	1/(12:10:8:7)	C\m7(^\b5) or C^m/6
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	Keemic
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	Keemic
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

#	Generators	Transversal	Type	Comments	Kite's name
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		Cv9(^7)
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	4:5:6:7:9	Cv9(\7)
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	1/(24:20:16:14:9)	C/9(^7)
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	Keemic
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	Keemic
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	Keemic
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	Keemic
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	1/(24:20:16:11:9)
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	4:5:6:9:11
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	1/(24:20:14:11:9)
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	1/(24:16:14:11:9)
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	1/(20:16:14:11:9)
61	0–7–11–12–20	1–7/6–7/5–7/4–14/11	Utonal	1/(24:20:16:14:11)
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	4:5:6:7:11
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	4:5:7:9:11
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	4:6:7:9:11
79	0–9–13–18–20	1–20/11–12/11–18/11–14/11	Otonal	5:6:7:9:11
80	0–11–13–18–20	1–7/5–12/11–18/11–14/11	Octarod

Hexads

#	Generators	Transversal	Type	Comment
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	1/(24:20:16:14:11:9)
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	4:5:6:7:9:11
18	0–9–11–13–18–20	1–9/5–7/5–12/11–18/11–14/11	Octarod