Template:Interval table

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.
max_error	Changes the maximum error cutoff for approximate ratios in cents. The default is 35 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|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