Template:Q-odd-limit intervals
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- 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 with the approximations of intervals for a given edo and odd limit.
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 61 and supports odd limits up to 65.
Pass header=none to get rid of the description.
To list only direct approximations, pass apx=direct. To list only val-based approximations, pass apx=val, and the header will be suffixed with (approximated with val). Otherwise, both approximations will be provided.
If apx is set to direct, the header will be suffixed with (approximated directly). If apx is set to val, the header will be suffixed with (approximated with val). Pass tag=none to remove this.
A note can be added below the header by passing note= followed by the text to be displayed.
The title is "[Limit]-odd-limit intervals by patent val mapping", but you can enter a 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 |