547edo

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← 546edo547edo548edo →
Prime factorization 547 (prime)
Step size 2.19378¢
Fifth 320\547 (702.011¢)
Semitones (A1:m2) 52:41 (114.1¢ : 89.95¢)
Consistency limit 9
Distinct consistency limit 9

547 equal divisions of the octave (abbreviated 547edo), or 547-tone equal temperament (547tet), 547 equal temperament (547et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 547 equal parts of about 2.19 ¢ each. Each step of 547edo represents a frequency ratio of 21/547, or the 547th root of 2.

Theory

547edo is a strong 5-limit system, tuning fortune, gammic, and vavoom temperaments. Past the 5-limit, good subgroups of choice include 2.3.5.13.17.31, or 2.3.5.77.29/23.

Prime harmonics

Approximation of prime harmonics in 547edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.056 -0.208 +0.827 -0.678 -0.308 +0.346 +0.842 -0.852 -0.692 +0.120
relative (%) +0 +3 -9 +38 -31 -14 +16 +38 -39 -32 +5
Steps
(reduced)
547
(0)
867
(320)
1270
(176)
1536
(442)
1892
(251)
2024
(383)
2236
(48)
2324
(136)
2474
(286)
2657
(469)
2710
(522)

Subsets and supersets

547edo is the 101st prime edo. 1641edo, which divides edostep in 3, corrects the mapping for the 11-limit.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [867 -547 [547 867]] -0.0177 0.0177 0.81
2.3.5 [39 -29 3, [-29 -11 20 [547 867 1270]] +0.0180 0.0525 2.39
2.3.5.7 4375/4374, 4096000/4084101, 23066015625/23018340352 [547 867 1270 1536]] -0.0601 0.1428 6.51

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 16\547 35.10 1990656/1953125 Gammic
1 51\547 111.88 16/15 Vavoom
1 101\547 221.57 8388608/7381125 Fortune
1 105\547 230.35 8/7 Gamera
1 258\547 566.00 104/75 Tricot

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Francium