User:Francium/2239edo: Difference between revisions
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Prime factorization
2239 (prime)
Step size
0.535954 ¢
Fifth
1310\2239 (702.099 ¢)
Semitones (A1:m2)
214:167 (114.7 ¢ : 89.5 ¢)
Consistency limit
7
Distinct consistency limit
7
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Latest revision as of 14:43, 1 August 2025
| ← 2238edo | 2239edo | 2240edo → |
2239 equal divisions of the octave (abbreviated 2239edo or 2239ed2), also called 2239-tone equal temperament (2239tet) or 2239 equal temperament (2239et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2239 equal parts of about 0.536 ¢ each. Each step represents a frequency ratio of 21/2239, or the 2239th root of 2.
Theory
2239edo is consistent to the 7-limit, tempering out 4375/4374, 3955078125/3954653486 and [67 -22 -9 -4⟩. As an equal temperament, it supports olympic.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.144 | +0.109 | +0.178 | -0.248 | +0.178 | -0.152 | +0.253 | +0.091 | -0.059 | -0.214 | -0.137 |
| Relative (%) | +26.9 | +20.3 | +33.2 | -46.2 | +33.3 | -28.5 | +47.2 | +17.1 | -11.0 | -39.9 | -25.5 | |
| Steps (reduced) |
3549 (1310) |
5199 (721) |
6286 (1808) |
7097 (380) |
7746 (1029) |
8285 (1568) |
8748 (2031) |
9152 (196) |
9511 (555) |
9834 (878) |
10128 (1172) | |
Subsets and supersets
2239edo is the 333rd prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [3549 -2239⟩ | [⟨2239 3549]] | −0.0455 | 0.0455 | 8.49 |
| 2.3.5 | [63 -50 7⟩, [75 23 -48⟩ | [⟨2239 3549 5199]] | −0.0459 | 0.0371 | 6.92 |
| 2.3.5.7 | 4375/4374, 3955078125/3954653486, [67 -22 -9 -4⟩ | [⟨2239 3549 5199 6286]] | −0.0503 | 0.0330 | 6.16 |
| 2.3.5.7.11 | 4375/4374, 131072/130977, 3294225/3294172, 246071287/246037500 | [⟨2239 3549 5199 6286 7746]] | −0.0506 | 0.0296 | 5.52 |