803edo
| ← 802edo | 803edo | 804edo → |
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
| 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.