729edt
729 equal divisions of the tritave, 729edt, is the tuning system that divides the 3/1 interval into steps of 2.60899 cents each.
| ← 728edt | 729edt | 730edt → |
729edt is closely related to 460edo, with the difference of 3/1 instead of 2/1 being just, and it actually beats it slightly in consistency limit, being consistent in the 22-integer limit, while 460edo is consistent only to 21-odd-limit. Overall, 729edt performs exceptionally in 2.3.5.13.17 subgroup, while 460edo only has this good of an error on the 19th harmonic.
729edt tempers out the [-81 28 -54⟩ comma which sets 27 intervals of 25/24 equal to the tritave.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.14 | +0.00 | +0.09 | -0.62 | -0.41 | -0.02 | -0.05 | +0.46 | +1.04 | -1.09 |
| Relative (%) | +5.2 | +0.0 | +3.4 | -23.7 | -15.8 | -0.9 | -2.0 | +17.5 | +39.8 | -41.8 | |
| Steps (reduced) |
460 (460) |
729 (0) |
1068 (339) |
1291 (562) |
1591 (133) |
1702 (244) |
1880 (422) |
1954 (496) |
2081 (623) |
2234 (47) | |