Template:Q-odd-limit intervals/doc
- 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.
A note can be added below the header by passing note= followed by the text to be displayed.
Pass header=none to get rid of the description.
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.
| 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 |
| 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 |