803edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 802edo803edo804edo →
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.