13ed5/2: Difference between revisions
Jump to navigation
Jump to search
CompactStar (talk | contribs) No edit summary |
CompactStar (talk | contribs) No edit summary |
||
| Line 32: | Line 32: | ||
|3 | |3 | ||
|366.072 | |366.072 | ||
|[[5/4]], [[49/40]] | |[[5/4]], [[16/13]], [[49/40]] | ||
|D#, Eb | |D#, Eb | ||
|- | |- | ||
| Line 47: | Line 47: | ||
|6 | |6 | ||
|732.144 | |732.144 | ||
|[[25/16]], [[49/32]] | |[[20/13]], [[25/16]], [[49/32]] | ||
|F#, Gb | |F#, Gb | ||
|- | |- | ||
|7 | |7 | ||
|854.168 | |854.168 | ||
|[[8/5]] | |[[8/5]], [[13/8]] | ||
|G | |G | ||
|- | |- | ||
| Line 86: | Line 86: | ||
|} | |} | ||
<nowiki>*</nowiki> Based on treating 13ed5/2 as a | <nowiki>*</nowiki> Based on treating 13ed5/2 as a 5/2.5.7.13 subgroup temperament | ||
Revision as of 00:44, 25 June 2023
| ← 12ed5/2 | 13ed5/2 | 14ed5/2 → |
(semiconvergent)
13ed5/2 is the equal division of the 5/2 interval into 13 parts of 122.024 cents each. It roughly corresponds to 10edo.
Theory
Like 10edo, 13ed5/2 tempers out 50/49 in the no-threes 7-limit, supporting 5/2-equivalent jubilic temperament with a generator of ~7/5.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +20.2 | +50.4 | +40.5 | +20.2 | -51.4 | +47.8 | +60.7 | -21.2 | +40.5 | -2.5 | -31.1 |
| Relative (%) | +16.6 | +41.3 | +33.2 | +16.6 | -42.1 | +39.2 | +49.8 | -17.3 | +33.2 | -2.0 | -25.5 | |
| Steps (reduced) |
10 (10) |
16 (3) |
20 (7) |
23 (10) |
25 (12) |
28 (2) |
30 (4) |
31 (5) |
33 (7) |
34 (8) |
35 (9) | |
Intervals
| # | Cents | Approximate ratios* | Jubilic[8] notation |
|---|---|---|---|
| 0 | 0.000 | 1/1 | C |
| 1 | 122.024 | 35/32 | C#, Db |
| 2 | 244.048 | 8/7, 28/25 | D |
| 3 | 366.072 | 5/4, 16/13, 49/40 | D#, Eb |
| 4 | 488.096 | 32/25, 64/49 | E |
| 5 | 610.120 | 7/5, 10/7 | F |
| 6 | 732.144 | 20/13, 25/16, 49/32 | F#, Gb |
| 7 | 854.168 | 8/5, 13/8 | G |
| 8 | 976.192 | 7/4, 25/14 | H |
| 9 | 1098.216 | 64/35 | H#, Ab |
| 10 | 1220.240 | 2/1, 49/25 | A |
| 11 | 1342.264 | 35/16 | A#, Bb |
| 12 | 1464.288 | 16/7 | B |
| 13 | 1586.312 | 5/2 | C |
* Based on treating 13ed5/2 as a 5/2.5.7.13 subgroup temperament