Template:Interval table: Difference between revisions

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I might add a relative error threshold
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<includeonly>{{#invoke:Interval_table|interval_table|tuning={{{1|{{PAGENAME}}}}}|additional={{{additional|}}} }}</includeonly><noinclude>
<includeonly>{{#invoke:Interval_table|interval_table|tuning={{{1|{{PAGENAME}}}}}|additional={{{additional|}}} }}</includeonly><noinclude>
The '''interval table''' template automatically generates a table of intervals for an [[EPD|equal pitch division]] system. Like most of the manual interval tables on this wiki, it includes the step number, [[cent]]s, approximate [[JI]] [[ratio]]s (based on the [[patent val]] [[mapping]] and discarding [[inconsistent]] approximations), and, for [[edo]]s, [[ups and downs notation]] (based on [[Template: Ups and downs note name]]).
The '''interval table''' template automatically generates a table of intervals for an [[EPD|equal pitch division]] system. Like most of the manual interval tables on this wiki, it includes the step number, [[cent]]s, approximate [[JI]] [[ratio]]s (based on the [[patent val]] [[mapping]] and discarding those which are [[inconsistent]]), and, for [[edo]]s, [[ups and downs notation]] (based on [[Template: Ups and downs note name]]).


== Parameters ==
== Parameters ==
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| additonal
| additonal
| Additional rows and columns that can be added to the table. Columns are separated by semicolons.
| Additional rows and columns that can be added to the table. Columns are separated by semicolons.
|-
| threshold
| Allows to change the relative error threshold from 50% (0.5 would be the default 50%).
|}
|}


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Result:
Result:
{{Interval table|12edo}}
{{Interval table|12edo}}
<pre>{{Interval table|12edo|threshold=0.2}}</pre>
Result:
{{Interval table|12edo|threshold=0.2}}


<pre>{{Interval table|13edo|additional=
<pre>{{Interval table|13edo|additional=

Revision as of 00:52, 4 March 2024

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 discarding those which are inconsistent), 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.
threshold Allows to change the relative error threshold from 50% (0.5 would be the default 50%).

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|12edo|threshold=0.2}}

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|71edo}}

Result:

Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 41\71) 		Ups and downs notation
(Dual sharp fifth 42\71)
0 0 1/1 D D
1 16.9 ^D, vE♭♭♭ ^D, vvE♭
2 33.8 vD♯, E♭♭♭ ^^D, vE♭
3 50.7 35/34 D♯, ^E♭♭♭ ^3D, E♭
4 67.6 25/24, 26/25 ^D♯, vE♭♭ ^4D, ^E♭
5 84.5 21/20 vD𝄪, E♭♭ ^5D, ^^E♭
6 101.4 17/16 D𝄪, ^E♭♭ v4D♯, ^3E♭
7 118.3 31/29 ^D𝄪, vE♭ v3D♯, ^4E♭
8 135.2 13/12 vD♯𝄪, E♭ vvD♯, v5E
9 152.1 12/11, 35/32 D♯𝄪, ^E♭ vD♯, v4E
10 169 32/29 ^D♯𝄪, vE D♯, v3E
11 185.9 29/26 E ^D♯, vvE
12 202.8 ^E, vF♭♭ ^^D♯, vE
13 219.7 25/22 vE♯, F♭♭ E
14 236.6 E♯, ^F♭♭ ^E, vvF
15 253.5 22/19, 29/25, 37/32 ^E♯, vF♭ ^^E, vF
16 270.4 vE𝄪, F♭ F
17 287.3 13/11 E𝄪, ^F♭ ^F, vvG♭
18 304.2 25/21, 31/26, 37/31 ^E𝄪, vF ^^F, vG♭
19 321.1 F ^3F, G♭
20 338 17/14, 28/23 ^F, vG♭♭♭ ^4F, ^G♭
21 354.9 vF♯, G♭♭♭ ^5F, ^^G♭
22 371.8 26/21, 31/25 F♯, ^G♭♭♭ v4F♯, ^3G♭
23 388.7 5/4 ^F♯, vG♭♭ v3F♯, ^4G♭
24 405.6 19/15, 24/19 vF𝄪, G♭♭ vvF♯, v5G
25 422.5 37/29 F𝄪, ^G♭♭ vF♯, v4G
26 439.4 31/24 ^F𝄪, vG♭ F♯, v3G
27 456.3 13/10 vF♯𝄪, G♭ ^F♯, vvG
28 473.2 21/16, 25/19 F♯𝄪, ^G♭ ^^F♯, vG
29 490.1 ^F♯𝄪, vG G
30 507 G ^G, vvA♭
31 523.9 23/17 ^G, vA♭♭♭ ^^G, vA♭
32 540.8 26/19 vG♯, A♭♭♭ ^3G, A♭
33 557.7 29/21 G♯, ^A♭♭♭ ^4G, ^A♭
34 574.6 32/23 ^G♯, vA♭♭ ^5G, ^^A♭
35 591.5 31/22 vG𝄪, A♭♭ v4G♯, ^3A♭
36 608.5 37/26 G𝄪, ^A♭♭ v3G♯, ^4A♭
37 625.4 23/16 ^G𝄪, vA♭ vvG♯, v5A
38 642.3 29/20 vG♯𝄪, A♭ vG♯, v4A
39 659.2 19/13 G♯𝄪, ^A♭ G♯, v3A
40 676.1 31/21, 34/23, 37/25 ^G♯𝄪, vA ^G♯, vvA
41 693 A ^^G♯, vA
42 709.9 ^A, vB♭♭♭ A
43 726.8 32/21, 35/23 vA♯, B♭♭♭ ^A, vvB♭
44 743.7 20/13 A♯, ^B♭♭♭ ^^A, vB♭
45 760.6 31/20 ^A♯, vB♭♭ ^3A, B♭
46 777.5 vA𝄪, B♭♭ ^4A, ^B♭
47 794.4 19/12, 30/19 A𝄪, ^B♭♭ ^5A, ^^B♭
48 811.3 8/5 ^A𝄪, vB♭ v4A♯, ^3B♭
49 828.2 21/13 vA♯𝄪, B♭ v3A♯, ^4B♭
50 845.1 31/19 A♯𝄪, ^B♭ vvA♯, v5B
51 862 23/14, 28/17 ^A♯𝄪, vB vA♯, v4B
52 878.9 B A♯, v3B
53 895.8 ^B, vC♭♭ ^A♯, vvB
54 912.7 22/13 vB♯, C♭♭ ^^A♯, vB
55 929.6 B♯, ^C♭♭ B
56 946.5 19/11 ^B♯, vC♭ ^B, vvC
57 963.4 vB𝄪, C♭ ^^B, vC
58 980.3 37/21 B𝄪, ^C♭ C
59 997.2 ^B𝄪, vC ^C, vvD♭
60 1014.1 C ^^C, vD♭
61 1031 29/16 ^C, vD♭♭♭ ^3C, D♭
62 1047.9 11/6 vC♯, D♭♭♭ ^4C, ^D♭
63 1064.8 24/13, 37/20 C♯, ^D♭♭♭ ^5C, ^^D♭
64 1081.7 ^C♯, vD♭♭ v4C♯, ^3D♭
65 1098.6 32/17 vC𝄪, D♭♭ v3C♯, ^4D♭
66 1115.5 C𝄪, ^D♭♭ vvC♯, v5D
67 1132.4 25/13 ^C𝄪, vD♭ vC♯, v4D
68 1149.3 vC♯𝄪, D♭ C♯, v3D
69 1166.2 C♯𝄪, ^D♭ ^C♯, vvD
70 1183.1 ^C♯𝄪, vD ^^C♯, vD
71 1200 2/1 D 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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