80edn
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80 equal divisions of the natave (80edn, 80ede) is a tuning that divides the natave, e/1 into steps of 21.640 cents each, a size close to 81/80, the syntonic comma. The step size arises from the limit definition of the number e.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -9.78 | +2.40 | +5.30 | +7.08 | +3.64 | -4.24 | +7.42 | +9.63 | +3.47 | -8.30 |
| relative (%) | -45 | +11 | +24 | +33 | +17 | -20 | +34 | +44 | +16 | -38 | |
| Steps (reduced) |
55 (55) |
88 (8) |
129 (49) |
156 (76) |
192 (32) |
205 (45) |
227 (67) |
236 (76) |
251 (11) |
269 (29) | |
80edo is good at 3.5.11.13.23 subgroup. In the 2.3.5.11.13 on the minor octave it shares the mapping with the 55bcceeeff val in 55edo, and tempers out 100/99, 256/243, 624/605, 704/675.