2730edo

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Revision as of 14:45, 19 March 2024 by Eliora (talk | contribs) (simplify)
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← 2729edo 2730edo 2731edo →
Prime factorization 2 × 3 × 5 × 7 × 13
Step size 0.43956 ¢ 
Fifth 1597\2730 (701.978 ¢)
Semitones (A1:m2) 259:205 (113.8 ¢ : 90.11 ¢)
Consistency limit 21
Distinct consistency limit 21

Template:EDO intro

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

Approximation of prime harmonics in 2730edo
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.