1547edo

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1547 equal divisions of the octave (1547edo), or 1547-tone equal temperament (1547tet), 1547 equal temperament (1547et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1547 equal parts of about 0.776 ¢ each.

Theory

Approximation of prime harmonics in 1547edo
Harmonic 2 3 5 7 11 13 17 19 23 29
Error absolute (¢) +0.000 +0.049 -0.018 +0.017 +0.201 +0.326 -0.237 +0.354 +0.039 -0.230
relative (%) +0 +6 -2 +2 +26 +42 -31 +46 +5 -30
Steps
(reduced)
1547
(0)
2452
(905)
3592
(498)
4343
(1249)
5352
(711)
5725
(1084)
6323
(135)
6572
(384)
6998
(810)
7515
(1327)

1547edo is excellent in the 7-limit.

In the 5-limit, it supports gross.

In the 7-limit, it supports semidimi and brahmagupta.

In the 17-limit, it supports 91th-octave temperament protactinium.

1547's divisors are 1, 7, 13, 17, 91, 119, 221.

Regular temperament properties

Rank-2 temperaments by generator

Table of rank-2 temperaments by generator
Periods
per octave
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
1 118\1547 91.532 [9 -32 18> Gross
1 579\1547 449.127 35/27 Semidimi
7 670\1547
(7\1547)
519.715
(5.429)
27/20
(325/324)
Brahmagupta
91 905\1547
(4\1547)
702.003
(3.103)
3/2
(?)
Protactinium