Template:Q-odd-limit intervals/doc

This template generates a table for JI approximation qualities in an edo.

Usage

Use one unnamed argument for the edo number.

Use a second unnamed argument for the odd limit. The default is 15. The maximum is 27 since prime numbers beyond 23 are not stored.

The title is by default "[Limit]-odd-limit intervals by patent val mapping". You can enter your custom title by title = [your title].

Examples

You type

{{15-odd-limit|19}}

You get The following tables show how 15-odd-limit intervals are represented in 19edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 19edo (direct approximation, even if inconsistent)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
5/3, 6/5	0.148	0.2
13/7, 14/13	1.982	3.1
15/13, 26/15	4.891	7.7
13/9, 18/13	5.039	8.0
15/14, 28/15	6.873	10.9
9/7, 14/9	7.021	11.1
9/5, 10/9	7.070	11.2
3/2, 4/3	7.218	11.4
5/4, 8/5	7.366	11.7
13/10, 20/13	12.109	19.2
13/12, 24/13	12.257	19.4
7/5, 10/7	14.091	22.3
7/6, 12/7	14.239	22.5
9/8, 16/9	14.436	22.9
15/8, 16/15	14.585	23.1
11/8, 16/11	17.103	27.1
13/8, 16/13	19.475	30.8
7/4, 8/7	21.457	34.0
11/6, 12/11	24.321	38.5
11/10, 20/11	24.469	38.7
11/7, 14/11	24.597	38.9
13/11, 22/13	26.580	42.1
15/11, 22/15	31.470	49.8
11/9, 18/11	31.539	49.9

15-odd-limit intervals in 19edo (patent val mapping)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
5/3, 6/5	0.148	0.2
13/7, 14/13	1.982	3.1
15/13, 26/15	4.891	7.7
13/9, 18/13	5.039	8.0
15/14, 28/15	6.873	10.9
9/7, 14/9	7.021	11.1
9/5, 10/9	7.070	11.2
3/2, 4/3	7.218	11.4
5/4, 8/5	7.366	11.7
13/10, 20/13	12.109	19.2
13/12, 24/13	12.257	19.4
7/5, 10/7	14.091	22.3
7/6, 12/7	14.239	22.5
9/8, 16/9	14.436	22.9
15/8, 16/15	14.585	23.1
11/8, 16/11	17.103	27.1
13/8, 16/13	19.475	30.8
7/4, 8/7	21.457	34.0
11/6, 12/11	24.321	38.5
11/10, 20/11	24.469	38.7
11/9, 18/11	31.539	49.9
15/11, 22/15	31.688	50.2
13/11, 22/13	36.578	57.9
11/7, 14/11	38.561	61.1