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Template:Interval table

Revision as of 00:39, 6 July 2023 by CompactStar (talk | contribs)
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

The interval table template automatically generates a table of intervals for an equal pitch division system. Like most of the manual interval tables on this wiki, it includes the step number, cents, approximate JI ratios (based on the patent val mapping), and, for EDOs, ups and downs notation (based on Template:Ups and downs note name).

Parameters

Paramater Description
additonal Additional rows and columns that can be added to the table. Columns are separated by semicolons.

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|19edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 63.2 23/22, 24/23 D♯, E♭♭
2 126.3 13/12, 14/13, 15/14, 16/15 D𝄪, E♭
3 189.5 9/8, 10/9, 19/17 E
4 252.6 7/6, 15/13, 22/19, 23/20 E♯, F♭
5 315.8 6/5, 23/19 F
6 378.9 5/4 F♯, G♭♭
7 442.1 9/7, 13/10, 22/17 F𝄪, G♭
8 505.3 4/3 G
9 568.4 7/5, 18/13 G♯, A♭♭
10 631.6 10/7, 13/9, 23/16 G𝄪, A♭
11 694.7 3/2 A
12 757.9 14/9, 17/11, 20/13 A♯, B♭♭
13 821.1 8/5, 21/13 A𝄪, B♭
14 884.2 5/3 B
15 947.4 12/7, 19/11 B♯, C♭
16 1010.5 9/5, 16/9 C
17 1073.7 13/7, 15/8, 24/13 C♯, D♭♭
18 1136.8 23/12 C𝄪, D♭
19 1200 2/1 D 


{{Interval table|159edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 7.5 ^D, ^4E♭♭
2 15.1 ^^D, ^5E♭♭
3 22.6 ^3D, ^6E♭♭
4 30.2 56/55, 57/56, 58/57 ^4D, ^7E♭♭
5 37.7 45/44, 46/45, 47/46, 48/47 ^5D, v7E♭
6 45.3 38/37, 39/38 ^6D, v6E♭
7 52.8 33/32, 34/33 ^7D, v5E♭
8 60.4 29/28 v7D♯, v4E♭
9 67.9 26/25 v6D♯, v3E♭
10 75.5 47/45 v5D♯, vvE♭
11 83 43/41 v4D♯, vE♭
12 90.6 39/37, 58/55 v3D♯, E♭
13 98.1 18/17, 55/52 vvD♯, ^E♭
14 105.7 17/16 vD♯, ^^E♭
15 113.2 47/44 D♯, ^3E♭
16 120.8 15/14 ^D♯, ^4E♭
17 128.3 14/13 ^^D♯, ^5E♭
18 135.8 40/37 ^3D♯, ^6E♭
19 143.4 25/23, 38/35 ^4D♯, ^7E♭
20 150.9 12/11 ^5D♯, v7E
21 158.5 23/21, 34/31, 57/52 ^6D♯, v6E
22 166 11/10 ^7D♯, v5E
23 173.6 21/19, 52/47 v7D𝄪, v4E
24 181.1 10/9 v6D𝄪, v3E
25 188.7 29/26, 39/35 v5D𝄪, vvE
26 196.2 28/25 v4D𝄪, vE
27 203.8 9/8 E
28 211.3 26/23 ^E, ^4F♭
29 218.9 42/37 ^^E, ^5F♭
30 226.4 41/36, 57/50 ^3E, ^6F♭
31 234 ^4E, ^7F♭
32 241.5 23/20, 54/47 ^5E, v7F
33 249.1 15/13, 52/45 ^6E, v6F
34 256.6 29/25, 51/44 ^7E, v5F
35 264.2 v7E♯, v4F
36 271.7 48/41, 55/47 v6E♯, v3F
37 279.2 47/40 v5E♯, vvF
38 286.8 46/39 v4E♯, vF
39 294.3 32/27, 51/43 F
40 301.9 25/21, 56/47 ^F, ^4G♭♭
41 309.4 55/46 ^^F, ^5G♭♭
42 317 6/5 ^3F, ^6G♭♭
43 324.5 35/29, 41/34 ^4F, ^7G♭♭
44 332.1 23/19, 40/33 ^5F, v7G♭
45 339.6 28/23, 45/37 ^6F, v6G♭
46 347.2 11/9 ^7F, v5G♭
47 354.7 27/22 v7F♯, v4G♭
48 362.3 37/30 v6F♯, v3G♭
49 369.8 26/21, 57/46 v5F♯, vvG♭
50 377.4 46/37, 51/41, 56/45 v4F♯, vG♭
51 384.9 5/4 v3F♯, G♭
52 392.5 vvF♯, ^G♭
53 400 29/23, 34/27 vF♯, ^^G♭
54 407.5 43/34 F♯, ^3G♭
55 415.1 47/37 ^F♯, ^4G♭
56 422.6 37/29 ^^F♯, ^5G♭
57 430.2 41/32, 50/39 ^3F♯, ^6G♭
58 437.7 ^4F♯, ^7G♭
59 445.3 22/17 ^5F♯, v7G
60 452.8 13/10 ^6F♯, v6G
61 460.4 30/23, 47/36 ^7F♯, v5G
62 467.9 38/29, 55/42 v7F𝄪, v4G
63 475.5 25/19, 54/41 v6F𝄪, v3G
64 483 37/28, 41/31 v5F𝄪, vvG
65 490.6 v4F𝄪, vG
66 498.1 4/3 G
67 505.7 ^G, ^4A♭♭
68 513.2 35/26, 39/29 ^^G, ^5A♭♭
69 520.8 27/20, 50/37 ^3G, ^6A♭♭
70 528.3 19/14 ^4G, ^7A♭♭
71 535.8 15/11 ^5G, v7A♭
72 543.4 26/19 ^6G, v6A♭
73 550.9 11/8 ^7G, v5A♭
74 558.5 29/21 v7G♯, v4A♭
75 566 43/31 v6G♯, v3A♭
76 573.6 39/28, 46/33 v5G♯, vvA♭
77 581.1 7/5 v4G♯, vA♭
78 588.7 52/37 v3G♯, A♭
79 596.2 24/17, 55/39 vvG♯, ^A♭
80 603.8 17/12 vG♯, ^^A♭
81 611.3 37/26, 47/33 G♯, ^3A♭
82 618.9 10/7 ^G♯, ^4A♭
83 626.4 33/23, 56/39 ^^G♯, ^5A♭
84 634 ^3G♯, ^6A♭
85 641.5 42/29, 55/38 ^4G♯, ^7A♭
86 649.1 16/11 ^5G♯, v7A
87 656.6 19/13 ^6G♯, v6A
88 664.2 22/15, 47/32 ^7G♯, v5A
89 671.7 28/19 v7G𝄪, v4A
90 679.2 37/25, 40/27 v6G𝄪, v3A
91 686.8 52/35, 55/37, 58/39 v5G𝄪, vvA
92 694.3 v4G𝄪, vA
93 701.9 3/2 A
94 709.4 ^A, ^4B♭♭
95 717 56/37 ^^A, ^5B♭♭
96 724.5 38/25, 41/27 ^3A, ^6B♭♭
97 732.1 29/19 ^4A, ^7B♭♭
98 739.6 23/15 ^5A, v7B♭
99 747.2 20/13, 57/37 ^6A, v6B♭
100 754.7 17/11 ^7A, v5B♭
101 762.3 v7A♯, v4B♭
102 769.8 39/25 v6A♯, v3B♭
103 777.4 47/30, 58/37 v5A♯, vvB♭
104 784.9 v4A♯, vB♭
105 792.5 v3A♯, B♭
106 800 27/17, 46/29 vvA♯, ^B♭
107 807.5 51/32 vA♯, ^^B♭
108 815.1 8/5 A♯, ^3B♭
109 822.6 37/23, 45/28 ^A♯, ^4B♭
110 830.2 21/13 ^^A♯, ^5B♭
111 837.7 ^3A♯, ^6B♭
112 845.3 44/27, 57/35 ^4A♯, ^7B♭
113 852.8 18/11 ^5A♯, v7B
114 860.4 23/14 ^6A♯, v6B
115 867.9 33/20, 38/23 ^7A♯, v5B
116 875.5 58/35 v7A𝄪, v4B
117 883 5/3 v6A𝄪, v3B
118 890.6 v5A𝄪, vvB
119 898.1 42/25, 47/28 v4A𝄪, vB
120 905.7 27/16 B
121 913.2 39/23 ^B, ^4C♭
122 920.8 ^^B, ^5C♭
123 928.3 41/24 ^3B, ^6C♭
124 935.8 ^4B, ^7C♭
125 943.4 50/29 ^5B, v7C
126 950.9 26/15, 45/26 ^6B, v6C
127 958.5 40/23, 47/27 ^7B, v5C
128 966 v7B♯, v4C
129 973.6 v6B♯, v3C
130 981.1 37/21 v5B♯, vvC
131 988.7 23/13 v4B♯, vC
132 996.2 16/9 C
133 1003.8 25/14 ^C, ^4D♭♭
134 1011.3 52/29 ^^C, ^5D♭♭
135 1018.9 9/5 ^3C, ^6D♭♭
136 1026.4 38/21, 47/26 ^4C, ^7D♭♭
137 1034 20/11 ^5C, v7D♭
138 1041.5 31/17, 42/23 ^6C, v6D♭
139 1049.1 11/6 ^7C, v5D♭
140 1056.6 35/19, 46/25 v7C♯, v4D♭
141 1064.2 37/20 v6C♯, v3D♭
142 1071.7 13/7 v5C♯, vvD♭
143 1079.2 28/15 v4C♯, vD♭
144 1086.8 v3C♯, D♭
145 1094.3 32/17 vvC♯, ^D♭
146 1101.9 17/9 vC♯, ^^D♭
147 1109.4 55/29 C♯, ^3D♭
148 1117 ^C♯, ^4D♭
149 1124.5 ^^C♯, ^5D♭
150 1132.1 25/13 ^3C♯, ^6D♭
151 1139.6 56/29 ^4C♯, ^7D♭
152 1147.2 33/17 ^5C♯, v7D
153 1154.7 37/19 ^6C♯, v6D
154 1162.3 45/23, 47/24 ^7C♯, v5D
155 1169.8 55/28, 57/29 v7C𝄪, v4D
156 1177.4 v6C𝄪, v3D
157 1184.9 v5C𝄪, vvD
158 1192.5 v4C𝄪, vD
159 1200 2/1 D 


{{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


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