2730edo: Difference between revisions
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{{Infobox ET}} | |||
{{ | {{ED intro}} | ||
2730edo is consistent | 2730edo is [[consistent]] to the [[21-odd-limit]]. | ||
In the 5-limit, it tunes the 13th-octave temperament [[aluminium]] and [[raider]]. In the 7-limit, it tunes 30th-octave [[zinc]] and 21st-octave [[akjayland]]. It is a tuning for the 35th-octave [[bromine]] temperament in the [[17-limit]] and the 91st-octave [[protactinium]] temperament in the | In the 5-limit, it tunes the 13th-octave temperament [[aluminium]] and [[raider]]. In the 7-limit, it tunes 30th-octave [[zinc]] and 21st-octave [[akjayland]]. It is a tuning for the 35th-octave [[bromine]] temperament in the [[17-limit]] and the 91st-octave [[protactinium]] temperament in the 7-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2730}} | |||
{{ | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 2730 factors into {{factorization|2730}}, 2730edo has subset edos {{EDOs| 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, and 1365 }}. Its abundancy index is around 1.95. | |||
2730edo has subset edos {{EDOs| | |||
Latest revision as of 05:42, 21 February 2025
| ← 2729edo | 2730edo | 2731edo → |
2730 equal divisions of the octave (abbreviated 2730edo or 2730ed2), also called 2730-tone equal temperament (2730tet) or 2730 equal temperament (2730et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2730 equal parts of about 0.44 ¢ each. Each step represents a frequency ratio of 21/2730, or the 2730th root of 2.
2730edo is consistent to the 21-odd-limit.
In the 5-limit, it tunes the 13th-octave temperament aluminium and raider. In the 7-limit, it tunes 30th-octave zinc and 21st-octave akjayland. It is a tuning for the 35th-octave bromine temperament in the 17-limit and the 91st-octave protactinium temperament in the 7-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.023 | +0.060 | -0.035 | -0.109 | -0.088 | +0.100 | +0.069 | -0.142 | -0.127 | +0.019 |
| Relative (%) | +0.0 | +5.2 | +13.6 | -7.9 | -24.8 | -20.0 | +22.6 | +15.8 | -32.4 | -28.8 | +4.4 | |
| Steps (reduced) |
2730 (0) |
4327 (1597) |
6339 (879) |
7664 (2204) |
9444 (1254) |
10102 (1912) |
11159 (239) |
11597 (677) |
12349 (1429) |
13262 (2342) |
13525 (2605) | |
Subsets and supersets
Since 2730 factors into 2 × 3 × 5 × 7 × 13, 2730edo has subset edos 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, and 1365. Its abundancy index is around 1.95.