Template:Q-odd-limit intervals/doc: Difference between revisions
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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. | 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. | ||
Pass <code>header=none</code> to get rid of the description. | |||
To list only direct approximations, pass <code>apx=direct</code>. Otherwise, approximations will be based on the specified [[val]]. | |||
A note can be added below the header by passing <code>note=</code> followed by the text to be displayed. | A note can be added below the header by passing <code>note=</code> followed by the text to be displayed. | ||
The title is by default "[Limit]-odd-limit intervals by patent val mapping". You can enter your custom title by <code>title = [your title]</code>. | The title is by default "[Limit]-odd-limit intervals by patent val mapping". You can enter your custom title by <code>title = [your title]</code>. | ||
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You get | You get | ||
{{Q-odd-limit intervals|19}} | : {{Q-odd-limit intervals|19}} | ||
=== See also === | === See also === | ||
* {{modlink}} | * {{modlink}} | ||
Revision as of 13:55, 24 May 2024
- 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.
Pass header=none to get rid of the description.
To list only direct approximations, pass apx=direct. Otherwise, approximations will be based on the specified val.
A note can be added below the header by passing note= followed by the text to be displayed.
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 |