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Template:Interval table

Revision as of 03:02, 5 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 commas and rows 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|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|54edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 31\54) 		Ups and downs notation
(Dual sharp fifth 32\54)
0 0 1/1 D D
1 22.2 D♯, E♭♭♭♭♭♭♭ ^D, vE♭
2 44.4 D𝄪, E♭♭♭♭♭♭ ^^D, E♭
3 66.7 D♯𝄪, E♭♭♭♭♭ ^3D, ^E♭
4 88.9 20/19 D𝄪𝄪, E♭♭♭♭ ^4D, ^^E♭
5 111.1 16/15, 33/31 D♯𝄪𝄪, E♭♭♭ v3D♯, ^3E♭
6 133.3 14/13 D𝄪𝄪𝄪, E♭♭ vvD♯, v4E
7 155.6 12/11 D♯𝄪𝄪𝄪, E♭ vD♯, v3E
8 177.8 31/28 E D♯, vvE
9 200 E♯, F♭♭♭♭♭♭ ^D♯, vE
10 222.2 E𝄪, F♭♭♭♭♭ E
11 244.4 15/13, 23/20 E♯𝄪, F♭♭♭♭ ^E, vF
12 266.7 7/6 E𝄪𝄪, F♭♭♭ F
13 288.9 13/11, 33/28 E♯𝄪𝄪, F♭♭ ^F, vG♭
14 311.1 E𝄪𝄪𝄪, F♭ ^^F, G♭
15 333.3 17/14, 23/19 F ^3F, ^G♭
16 355.6 16/13 F♯, G♭♭♭♭♭♭♭ ^4F, ^^G♭
17 377.8 F𝄪, G♭♭♭♭♭♭ v3F♯, ^3G♭
18 400 29/23 F♯𝄪, G♭♭♭♭♭ vvF♯, v4G
19 422.2 14/11 F𝄪𝄪, G♭♭♭♭ vF♯, v3G
20 444.4 22/17, 31/24 F♯𝄪𝄪, G♭♭♭ F♯, vvG
21 466.7 17/13 F𝄪𝄪𝄪, G♭♭ ^F♯, vG
22 488.9 F♯𝄪𝄪𝄪, G♭ G
23 511.1 G ^G, vA♭
24 533.3 15/11 G♯, A♭♭♭♭♭♭♭ ^^G, A♭
25 555.6 11/8 G𝄪, A♭♭♭♭♭♭ ^3G, ^A♭
26 577.8 G♯𝄪, A♭♭♭♭♭ ^4G, ^^A♭
27 600 17/12, 24/17 G𝄪𝄪, A♭♭♭♭ v3G♯, ^3A♭
28 622.2 G♯𝄪𝄪, A♭♭♭ vvG♯, v4A
29 644.4 16/11, 29/20 G𝄪𝄪𝄪, A♭♭ vG♯, v3A
30 666.7 22/15 G♯𝄪𝄪𝄪, A♭ G♯, vvA
31 688.9 A ^G♯, vA
32 711.1 A♯, B♭♭♭♭♭♭♭ A
33 733.3 26/17, 29/19 A𝄪, B♭♭♭♭♭♭ ^A, vB♭
34 755.6 17/11 A♯𝄪, B♭♭♭♭♭ ^^A, B♭
35 777.8 11/7 A𝄪𝄪, B♭♭♭♭ ^3A, ^B♭
36 800 A♯𝄪𝄪, B♭♭♭ ^4A, ^^B♭
37 822.2 A𝄪𝄪𝄪, B♭♭ v3A♯, ^3B♭
38 844.4 13/8 A♯𝄪𝄪𝄪, B♭ vvA♯, v4B
39 866.7 28/17 B vA♯, v3B
40 888.9 B♯, C♭♭♭♭♭♭ A♯, vvB
41 911.1 22/13 B𝄪, C♭♭♭♭♭ ^A♯, vB
42 933.3 12/7 B♯𝄪, C♭♭♭♭ B
43 955.6 26/15 B𝄪𝄪, C♭♭♭ ^B, vC
44 977.8 B♯𝄪𝄪, C♭♭ C
45 1000 B𝄪𝄪𝄪, C♭ ^C, vD♭
46 1022.2 C ^^C, D♭
47 1044.4 11/6, 31/17 C♯, D♭♭♭♭♭♭♭ ^3C, ^D♭
48 1066.7 13/7 C𝄪, D♭♭♭♭♭♭ ^4C, ^^D♭
49 1088.9 15/8 C♯𝄪, D♭♭♭♭♭ v3C♯, ^3D♭
50 1111.1 19/10 C𝄪𝄪, D♭♭♭♭ vvC♯, v4D
51 1133.3 C♯𝄪𝄪, D♭♭♭ vC♯, v3D
52 1155.6 C𝄪𝄪𝄪, D♭♭ C♯, vvD
53 1177.8 C♯𝄪𝄪𝄪, D♭ ^C♯, vD
54 1200 2/1 D D 


{{Interval table|13edt|additional=Hekts; 0; 100; 200; 300; 400; 500; 600; 700; 800; 900; 1000; 1100; 1200; 1300}}

Result:

Steps Cents Hekts Approximate ratios Hekts 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
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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