3643edo
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Prime factorization
3643 (prime)
Step size
0.329399¢
Fifth
2131\3643 (701.949¢)
Semitones (A1:m2)
345:274 (113.6¢ : 90.26¢)
Consistency limit
15
Distinct consistency limit
15
| ← 3642edo | 3643edo | 3644edo → |
3643 equal divisions of the octave (abbreviated 3643edo or 3643ed2), also called 3643-tone equal temperament (3643tet) or 3643 equal temperament (3643et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3643 equal parts of about 0.329 ¢ each. Each step represents a frequency ratio of 21/3643, or the 3643rd root of 2.
Theory
3643edo is consistent to the 15-odd-limit, tempering out 123201/123200, 6656/6655, 1016064/1015625, 655473/655360 and 2250423/2249728 in the 13-limit. It supports 9177/9176 in the 2.3.7.19.23.31.37 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.006 | +0.071 | -0.064 | +0.096 | +0.098 | +0.123 | -0.066 | -0.111 | +0.124 | -0.045 |
| Relative (%) | +0.0 | -1.8 | +21.6 | -19.4 | +29.1 | +29.8 | +37.3 | -20.0 | -33.6 | +37.5 | -13.7 | |
| Steps (reduced) |
3643 (0) |
5774 (2131) |
8459 (1173) |
10227 (2941) |
12603 (1674) |
13481 (2552) |
14891 (319) |
15475 (903) |
16479 (1907) |
17698 (3126) |
18048 (3476) | |
Subsets and supersets
3643edo is the 510th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-5774 3643⟩ | [⟨3643 5774]] | +0.0019 | 0.0019 | 0.58 |
| 2.3.5 | [22 33 -32⟩, [199 -86 -27⟩ | [⟨3643 5774 8459]] | -0.0089 | 0.0154 | 4.68 |
| 2.3.5.7 | [-9 5 -8 7⟩, [3 -24 3 10⟩, [43 -1 -13 -4⟩ | [⟨3643 5774 8459 10227]] | -0.0010 | 0.0192 | 5.83 |
| 2.3.5.7.11 | 117649/117612, 50014503/50000000, 520224768/519921875, 234365481/234256000 | [⟨3643 5774 8459 10227 12603]] | -0.0063 | 0.0202 | 6.13 |
| 2.3.5.7.11.13 | 123201/123200, 6656/6655, 1016064/1015625, 655473/655360, 2250423/2249728 | [⟨3643 5774 8459 10227 12603 13481]] | -0.0097 | 0.0199 | 6.04 |
| 2.3.5.7.11.13.17 | 12376/12375, 14400/14399, 123201/123200, 1796256/1795625, 637637/637500, 2100875/2100384 | [⟨3643 5774 8459 10227 12603 13481 14891]] | -0.0126 | 0.0197 | 5.98 |