1019edo
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Prime factorization
1019 (prime)
Step size
1.17763¢
Fifth
596\1019 (701.865¢)
Semitones (A1:m2)
96:77 (113.1¢ : 90.68¢)
Consistency limit
17
Distinct consistency limit
17
| ← 1018edo | 1019edo | 1020edo → |
1019 equal divisions of the octave (abbreviated 1019edo or 1019ed2), also called 1019-tone equal temperament (1019tet) or 1019 equal temperament (1019et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1019 equal parts of about 1.18 ¢ each. Each step represents a frequency ratio of 21/1019, or the 1019th root of 2.
Theory
1019edo is consistent to the 17-odd-limit. As an equal temperament, it tempers out 3025/3024 and 1771561/1771470 in the 11-limit; 1716/1715 and 4096/4095 in the 13-limit; and 1275/1274, 2500/2499 and 3536379/3536000 in the 17-limit. Using the 2.3.5.11.17.29.43 subgroup, it tempers out 17545/17544.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.090 | -0.053 | +0.360 | -0.189 | +0.297 | -0.147 | +0.426 | +0.577 | -0.333 | -0.384 |
| Relative (%) | +0.0 | -7.7 | -4.5 | +30.5 | -16.1 | +25.2 | -12.5 | +36.2 | +49.0 | -28.3 | -32.6 | |
| Steps (reduced) |
1019 (0) |
1615 (596) |
2366 (328) |
2861 (823) |
3525 (468) |
3771 (714) |
4165 (89) |
4329 (253) |
4610 (534) |
4950 (874) |
5048 (972) | |
Subsets and supersets
1019edo is the 171st prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1615 1019⟩ | [⟨1019 1615]] | +0.0285 | 0.0285 | 2.42 |
| 2.3.5 | [-31 43 -16⟩, [-68 18 17⟩ | [⟨1019 1615 2366]] | +0.0266 | 0.0235 | 2.00 |
| 2.3.5.7 | 703125/702464, 14348907/14336000, 283115520/282475249 | [⟨1019 1615 2366 2861]] | -0.0121 | 0.0700 | 5.94 |
| 2.3.5.7.11 | 3025/3024, 180224/180075, 759375/758912, 14348907/14336000 | [⟨1019 1615 2366 2861 3525]] | +0.0013 | 0.0681 | 5.78 |
| 2.3.5.7.11.13 | 1716/1715, 3025/3024, 4096/4095, 216513/216320, 540000/539539 | [⟨1019 1615 2366 2861 3525 3771]] | -0.0123 | 0.0692 | 5.88 |
| 2.3.5.7.11.13.17 | 1275/1274, 1716/1715, 2500/2499, 3025/3024, 4096/4095, 3536379/3536000 | [⟨1019 1615 2366 2861 3525 3771 4165]] | -0.0054 | 0.0662 | 5.62 |