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

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

Approximation of prime harmonics in 1019edo
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