Template:Q-odd-limit intervals/doc: Difference between revisions
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{{ | {{Q-odd-limit intervals|19}} | ||
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{{ | {{Q-odd-limit intervals|19}} | ||
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Revision as of 13:08, 15 May 2024
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.
| 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 |