# 803edo

 ← 802edo 803edo 804edo →
Prime factorization 11 × 73
Step size 1.4944¢
Fifth 470\803 (702.366¢)
Semitones (A1:m2) 78:59 (116.6¢ : 88.17¢)
Consistency limit 5
Distinct consistency limit 5

803 equal divisions of the octave (abbreviated 803edo or 803ed2), also called 803-tone equal temperament (803tet) or 803 equal temperament (803et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 803 equal parts of about 1.49 ¢ each. Each step represents a frequency ratio of 21/803, or the 803rd root of 2.

803edo is only consistent to the 5-odd-limit, and if harmonic 5 is used, the equal temperament tends very sharp. It is most notable for tempering out the escapade comma, providing the optimal patent val for the escapade temperament in the 5-limit.

The 803bd val is a tuning for swetneus and the 803c val tempers out the maja comma in the 5-limit, tuning the maja temperament. In the higher limits, it is a strong 2.11.13/9.17/15.19.21 system.

### Odd harmonics

Approximation of odd harmonics in 803edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.411 +0.735 -0.457 -0.672 +0.114 -0.677 -0.348 -0.348 -0.128 -0.046 -0.628
Relative (%) +27.5 +49.2 -30.6 -45.0 +7.6 -45.3 -23.3 -23.3 -8.6 -3.1 -42.0
Steps
(reduced)
1273
(470)
1865
(259)
2254
(648)
2545
(136)
2778
(369)
2971
(562)
3137
(728)
3282
(70)
3411
(199)
3527
(315)
3632
(420)

### Subsets and supersets

Since 803 factors into 11 × 73, 803edo contains 11edo and 73edo as subsets.