# 547edo

 ← 546edo 547edo 548edo →
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 547ed2), also called 547-tone equal temperament (547tet) or 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 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 (%) +0.0 +2.6 -9.5 +37.7 -30.9 -14.1 +15.8 +38.4 -38.8 -31.6 +5.5
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

Francium