Template:Q-odd-limit intervals/doc

From Xenharmonic Wiki
Jump to navigation Jump to search
This template is implemented by the Lua module Module:Q-odd-limit intervals.
This template invokes the following functions: q_odd_limit_intervals from Q-odd-limit intervals.

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, since low-complexity just intonation typically involves just the first 16 harmonics of the harmonic series. Currently, this template stores prime numbers up to 31 and supports odd limits up to 35.

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 

{{Q-odd-limit intervals|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

See also

Retrieved from "https://en.xen.wiki/index.php?title=Template:Q-odd-limit_intervals/doc&oldid=143963"