Template:Interval table/doc

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Revision as of 03:52, 2 October 2024 by BudjarnLambeth (talk | contribs) (Provided a range of edo sizes as examples)
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Parameters

additonal
Additional rows and columns that can be added to the table. Columns are separated by semicolons.
max_error
Not currently working. Changes the maximum error cutoff for approximate ratios in cents.

Examples

{{Interval table|12edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 100 15/14, 16/15, 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 D♯, E♭
2 200 9/8, 10/9, 17/15, 19/17, 21/19 E
3 300 6/5, 19/16, 20/17 F
4 400 5/4, 14/11, 19/15, 23/18 F♯, G♭
5 500 4/3, 23/17 G
6 600 7/5, 10/7, 17/12, 23/16 G♯, A♭
7 700 3/2 A
8 800 8/5, 11/7, 19/12 A♯, B♭
9 900 5/3, 17/10 B
10 1000 9/5, 16/9, 23/13 C
11 1100 15/8, 17/9, 19/10, 21/11, 23/12 C♯, D♭
12 1200 2/1 D 
{{Interval table|13edo|additional=
[[26edo]] names; Fox-Raven<br>Notation (J = 360Hz)
C; J
Cx/Dbb; J#/Kb
D; K
Dx/Ebb; L
E; L#/Mb
Ex/Fb; M
F#; M#/Nb
Gb; N
G#; O
Ab; O#/Pb
A#; P
Bb; Q
B#/Cbb; Q#/Jb
C; J
}}

Result:

Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 7\13) 		Ups and downs notation
(Dual sharp fifth 8\13) 		26edo names Fox-Raven
Notation (J = 360Hz)
0 0 1/1 D D C J
1 92.3 16/15, 17/16, 20/19, 21/20, 22/21, 23/22 E ^D, vF Cx/Dbb J#/Kb
2 184.6 11/10, 19/17, 21/19 ^E, F♭ F D K
3 276.9 13/11, 19/16, 20/17, 22/19 vE♯, ^F♭ E Dx/Ebb L
4 369.2 5/4, 16/13, 21/17 E♯, vF ^E, vG E L#/Mb
5 461.5 13/10, 17/13, 21/16, 22/17 F G Ex/Fb M
6 553.8 11/8, 15/11, 19/14 G ^G, vvA F# M#/Nb
7 646.2 16/11, 19/13, 22/15, 23/16 A ^^G, vA Gb N
8 738.5 17/11, 20/13, 23/15 B A G# O
9 830.8 8/5, 13/8, 21/13 ^B, C♭ ^A, vC Ab O#/Pb
10 923.1 17/10, 19/11, 22/13 vB♯, ^C♭ C A# P
11 1015.4 20/11 B♯, vC B Bb Q
12 1107.7 15/8, 19/10, 21/11, 23/12 C ^B, vD B#/Cbb Q#/Jb
13 1200 2/1 D D C J 
{{Interval table|13edt}}

Result:

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 146.3 100 11/10, 12/11, 13/12, 14/13, 23/21
2 292.6 200 6/5, 7/6, 13/11
3 438.9 300 9/7, 13/10, 14/11, 23/18
4 585.2 400 7/5, 18/13
5 731.5 500 20/13, 23/15
6 877.8 600 5/3, 18/11, 23/14
7 1024.1 700 9/5, 11/6, 20/11
8 1170.4 800
9 1316.7 900 13/6, 15/7, 19/9
10 1463 1000 7/3, 23/10
11 1609.3 1100 5/2, 18/7, 23/9
12 1755.7 1200 11/4
13 1902 1300 3/1 
{{Interval table|15edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 80 19/18, 20/19, 21/20, 22/21, 23/22 ^D, ^E♭, ^F♭
2 160 11/10, 12/11, 13/12, 21/19, 23/21 vD♯, vE, vF
3 240 8/7, 15/13, 22/19, 23/20 E, F
4 320 6/5, 17/14, 23/19 ^E, ^F, ^G♭
5 400 5/4, 14/11, 19/15 vE♯, vF♯, vG
6 480 4/3, 21/16 G
7 560 11/8, 18/13 ^G, ^A♭
8 640 13/9, 16/11, 19/13, 23/16 vG♯, vA
9 720 3/2, 23/15 A
10 800 8/5, 11/7, 19/12 ^A, ^B♭, ^C♭
11 880 5/3, 23/14 vA♯, vB, vC
12 960 7/4, 19/11 B, C
13 1040 11/6, 20/11 ^B, ^C, ^D♭
14 1120 19/10, 21/11, 23/12 vB♯, vC♯, vD
15 1200 2/1 D 
{{Interval table|30edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 17\30) 		Ups and downs notation
(Dual sharp fifth 18\30)
0 0 1/1 D D
1 40 D♯, E♭♭♭ ^D, ^E♭, ^F♭
2 80 21/20, 22/21, 23/22, 24/23, 25/24 D𝄪, E♭♭ ^^D, ^^E♭, ^^F♭
3 120 14/13 D♯𝄪, E♭ ^3D, v3E, v3F
4 160 11/10, 12/11, 23/21 E vvD♯, vvE, vvF
5 200 E♯, F♭♭♭♭ vD♯, vE, vF
6 240 8/7, 23/20 E𝄪, F♭♭♭ E, F
7 280 13/11, 20/17 E♯𝄪, F♭♭ ^E, ^F, ^G♭
8 320 6/5 E𝄪𝄪, F♭ ^^E, ^^F, ^^G♭
9 360 16/13, 21/17, 26/21 F ^3E, ^3F, v3G
10 400 F♯, G♭♭♭ vvE♯, vvF♯, vvG
11 440 22/17 F𝄪, G♭♭ vE♯, vF♯, vG
12 480 21/16 F♯𝄪, G♭ G
13 520 19/14, 23/17 G ^G, ^A♭
14 560 11/8, 25/18 G♯, A♭♭♭ ^^G, ^^A♭
15 600 17/12, 24/17 G𝄪, A♭♭ ^3G, v3A
16 640 16/11 G♯𝄪, A♭ vvG♯, vvA
17 680 A vG♯, vA
18 720 A♯, B♭♭♭ A
19 760 17/11 A𝄪, B♭♭ ^A, ^B♭, ^C♭
20 800 A♯𝄪, B♭ ^^A, ^^B♭, ^^C♭
21 840 13/8, 21/13 B ^3A, v3B, v3C
22 880 5/3 B♯, C♭♭♭♭ vvA♯, vvB, vvC
23 920 17/10, 22/13 B𝄪, C♭♭♭ vA♯, vB, vC
24 960 7/4 B♯𝄪, C♭♭ B, C
25 1000 B𝄪𝄪, C♭ ^B, ^C, ^D♭
26 1040 11/6, 20/11 C ^^B, ^^C, ^^D♭
27 1080 13/7 C♯, D♭♭♭ ^3B, ^3C, v3D
28 1120 21/11, 23/12 C𝄪, D♭♭ vvB♯, vvC♯, vvD
29 1160 C♯𝄪, D♭ vB♯, vC♯, vD
30 1200 2/1 D D 
{{Interval table|60edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 20 ^D, ^E♭♭
2 40 ^^D, ^^E♭♭
3 60 28/27, 29/28, 30/29, 31/30 vvD♯, vvE♭
4 80 21/20 vD♯, vE♭
5 100 18/17 D♯, E♭
6 120 15/14, 29/27 ^D♯, ^E♭
7 140 13/12, 25/23 ^^D♯, ^^E♭
8 160 23/21, 34/31 vvD𝄪, vvE
9 180 10/9, 31/28 vD𝄪, vE
10 200 9/8, 28/25 E
11 220 17/15 ^E, ^F♭
12 240 23/20, 31/27 ^^E, ^^F♭
13 260 29/25 vvE♯, vvF
14 280 20/17, 27/23 vE♯, vF
15 300 19/16, 25/21, 31/26 F
16 320 6/5 ^F, ^G♭♭
17 340 17/14, 28/23 ^^F, ^^G♭♭
18 360 16/13 vvF♯, vvG♭
19 380 vF♯, vG♭
20 400 24/19, 29/23, 34/27 F♯, G♭
21 420 23/18 ^F♯, ^G♭
22 440 31/24 ^^F♯, ^^G♭
23 460 17/13, 30/23 vvF𝄪, vvG
24 480 vF𝄪, vG
25 500 4/3 G
26 520 23/17, 27/20, 31/23 ^G, ^A♭♭
27 540 26/19 ^^G, ^^A♭♭
28 560 18/13, 29/21 vvG♯, vvA♭
29 580 7/5 vG♯, vA♭
30 600 17/12, 24/17 G♯, A♭
31 620 10/7 ^G♯, ^A♭
32 640 13/9, 29/20 ^^G♯, ^^A♭
33 660 19/13 vvG𝄪, vvA
34 680 34/23 vG𝄪, vA
35 700 3/2 A
36 720 ^A, ^B♭♭
37 740 23/15, 26/17 ^^A, ^^B♭♭
38 760 31/20 vvA♯, vvB♭
39 780 vA♯, vB♭
40 800 19/12, 27/17 A♯, B♭
41 820 ^A♯, ^B♭
42 840 13/8 ^^A♯, ^^B♭
43 860 23/14, 28/17 vvA𝄪, vvB
44 880 5/3 vA𝄪, vB
45 900 32/19 B
46 920 17/10 ^B, ^C♭
47 940 31/18 ^^B, ^^C♭
48 960 33/19 vvB♯, vvC
49 980 30/17 vB♯, vC
50 1000 16/9, 25/14 C
51 1020 9/5 ^C, ^D♭♭
52 1040 31/17 ^^C, ^^D♭♭
53 1060 24/13 vvC♯, vvD♭
54 1080 28/15 vC♯, vD♭
55 1100 17/9 C♯, D♭
56 1120 ^C♯, ^D♭
57 1140 27/14, 29/15 ^^C♯, ^^D♭
58 1160 vvC𝄪, vvD
59 1180 vC𝄪, vD
60 1200 2/1 D 
{{Interval table|120edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 10 ^D, ^E♭♭
2 20 ^^D, ^^E♭♭
3 30 ^3D, ^3E♭♭
4 40 42/41, 43/42, 44/43, 45/44, 46/45 ^4D, ^4E♭♭
5 50 34/33 ^5D, v5E♭
6 60 29/28, 30/29 v4D♯, v4E♭
7 70 v3D♯, v3E♭
8 80 22/21, 45/43 vvD♯, vvE♭
9 90 20/19, 39/37 vD♯, vE♭
10 100 18/17 D♯, E♭
11 110 16/15, 49/46 ^D♯, ^E♭
12 120 15/14 ^^D♯, ^^E♭
13 130 14/13, 41/38 ^3D♯, ^3E♭
14 140 13/12 ^4D♯, ^4E♭
15 150 12/11 ^5D♯, v5E
16 160 45/41 v4D𝄪, v4E
17 170 32/29, 43/39 v3D𝄪, v3E
18 180 vvD𝄪, vvE
19 190 29/26, 48/43 vD𝄪, vE
20 200 37/33, 46/41 E
21 210 35/31, 44/39 ^E, ^F♭
22 220 42/37 ^^E, ^^F♭
23 230 8/7 ^3E, ^3F♭
24 240 23/20 ^4E, ^4F♭
25 250 37/32 ^5E, v5F
26 260 43/37 v4E♯, v4F
27 270 v3E♯, v3F
28 280 47/40 vvE♯, vvF
29 290 13/11 vE♯, vF
30 300 44/37 F
31 310 49/41 ^F, ^G♭♭
32 320 ^^F, ^^G♭♭
33 330 23/19 ^3F, ^3G♭♭
34 340 28/23, 45/37 ^4F, ^4G♭♭
35 350 49/40 ^5F, v5G♭
36 360 16/13 v4F♯, v4G♭
37 370 26/21 v3F♯, v3G♭
38 380 vvF♯, vvG♭
39 390 vF♯, vG♭
40 400 29/23, 34/27 F♯, G♭
41 410 19/15 ^F♯, ^G♭
42 420 37/29 ^^F♯, ^^G♭
43 430 41/32 ^3F♯, ^3G♭
44 440 40/31, 49/38 ^4F♯, ^4G♭
45 450 48/37 ^5F♯, v5G
46 460 30/23, 43/33 v4F𝄪, v4G
47 470 21/16 v3F𝄪, v3G
48 480 29/22 vvF𝄪, vvG
49 490 vF𝄪, vG
50 500 4/3 G
51 510 43/32, 47/35 ^G, ^A♭♭
52 520 ^^G, ^^A♭♭
53 530 19/14 ^3G, ^3A♭♭
54 540 41/30 ^4G, ^4A♭♭
55 550 11/8 ^5G, v5A♭
56 560 29/21 v4G♯, v4A♭
57 570 32/23 v3G♯, v3A♭
58 580 vvG♯, vvA♭
59 590 45/32 vG♯, vA♭
60 600 41/29 G♯, A♭
61 610 37/26 ^G♯, ^A♭
62 620 ^^G♯, ^^A♭
63 630 23/16 ^3G♯, ^3A♭
64 640 42/29 ^4G♯, ^4A♭
65 650 16/11 ^5G♯, v5A
66 660 41/28 v4G𝄪, v4A
67 670 28/19 v3G𝄪, v3A
68 680 43/29 vvG𝄪, vvA
69 690 vG𝄪, vA
70 700 3/2 A
71 710 ^A, ^B♭♭
72 720 44/29, 47/31 ^^A, ^^B♭♭
73 730 32/21 ^3A, ^3B♭♭
74 740 23/15 ^4A, ^4B♭♭
75 750 37/24 ^5A, v5B♭
76 760 31/20, 45/29 v4A♯, v4B♭
77 770 v3A♯, v3B♭
78 780 vvA♯, vvB♭
79 790 30/19, 41/26 vA♯, vB♭
80 800 27/17, 46/29 A♯, B♭
81 810 ^A♯, ^B♭
82 820 45/28 ^^A♯, ^^B♭
83 830 21/13 ^3A♯, ^3B♭
84 840 13/8 ^4A♯, ^4B♭
85 850 49/30 ^5A♯, v5B
86 860 23/14 v4A𝄪, v4B
87 870 38/23, 43/26 v3A𝄪, v3B
88 880 vvA𝄪, vvB
89 890 vA𝄪, vB
90 900 37/22 B
91 910 22/13, 49/29 ^B, ^C♭
92 920 ^^B, ^^C♭
93 930 ^3B, ^3C♭
94 940 ^4B, ^4C♭
95 950 45/26 ^5B, v5C
96 960 40/23 v4B♯, v4C
97 970 7/4 v3B♯, v3C
98 980 37/21 vvB♯, vvC
99 990 39/22 vB♯, vC
100 1000 41/23 C
101 1010 43/24 ^C, ^D♭♭
102 1020 ^^C, ^^D♭♭
103 1030 29/16 ^3C, ^3D♭♭
104 1040 ^4C, ^4D♭♭
105 1050 11/6 ^5C, v5D♭
106 1060 24/13 v4C♯, v4D♭
107 1070 13/7 v3C♯, v3D♭
108 1080 28/15 vvC♯, vvD♭
109 1090 15/8 vC♯, vD♭
110 1100 17/9 C♯, D♭
111 1110 19/10 ^C♯, ^D♭
112 1120 21/11 ^^C♯, ^^D♭
113 1130 ^3C♯, ^3D♭
114 1140 29/15 ^4C♯, ^4D♭
115 1150 33/17 ^5C♯, v5D
116 1160 41/21, 43/22, 45/23 v4C𝄪, v4D
117 1170 v3C𝄪, v3D
118 1180 vvC𝄪, vvD
119 1190 vC𝄪, vD
120 1200 2/1 D

See also

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