User:Francium/2447edo
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Prime factorization
2447 (prime)
Step size
0.490396 ¢
Fifth
1431\2447 (701.757 ¢)
Semitones (A1:m2)
229:186 (112.3 ¢ : 91.21 ¢)
Dual sharp fifth
1432\2447 (702.248 ¢)
Dual flat fifth
1431\2447 (701.757 ¢)
Dual major 2nd
416\2447 (204.005 ¢)
Consistency limit
3
Distinct consistency limit
3
| ← 2446edo | 2447edo | 2448edo → |
2447 equal divisions of the octave (abbreviated 2447edo or 2447ed2), also called 2447-tone equal temperament (2447tet) or 2447 equal temperament (2447et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2447 equal parts of about 0.49 ¢ each. Each step represents a frequency ratio of 21/2447, or the 2447th root of 2.
Theory
2447edo is inconsistent to the 5-limit and the error of its harmonic 3 is very high. It is strong in the 2.9.15.21.13.17.23.31 subgroup, tempering out 256000/255879, 11662/11661, 213003/212992, 352625/352512, 22816/22815, 469625/469476 and 492128/492075.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.198 | +0.119 | +0.197 | +0.095 | -0.112 | +0.012 | -0.079 | -0.011 | +0.158 | -0.000 | -0.077 |
| Relative (%) | -40.3 | +24.2 | +40.3 | +19.4 | -22.9 | +2.4 | -16.1 | -2.2 | +32.1 | -0.1 | -15.6 | |
| Steps (reduced) |
3878 (1431) |
5682 (788) |
6870 (1976) |
7757 (416) |
8465 (1124) |
9055 (1714) |
9560 (2219) |
10002 (214) |
10395 (607) |
10748 (960) |
11069 (1281) | |
Subsets and supersets
2447edo is the 363rd prime edo. 4894edo, which doubles it, gives a good correction to its harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [7757 -2447⟩ | [⟨2447 7757]] | −0.0150 | 0.0150 | 3.06 |
| 2.9.5 | [93 -33 5⟩, [82 32 -79⟩ | [⟨2447 7757 5682]] | −0.0270 | 0.0210 | 4.28 |
| 2.9.5.7 | 184528125/184473632, 2567836929097728/2564544677734375, 54975581388800000/54927178684361361 | [⟨2447 7757 5682 6870]] | −0.0378 | 0.0261 | 5.32 |