547edo
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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
| ← 546edo | 547edo | 548edo → |
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
| 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
| 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