719edo
| ← 718edo | 719edo | 720edo → |
719 equal divisions of the octave (abbreviated 719edo or 719ed2), also called 719-tone equal temperament (719tet) or 719 equal temperament (719et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 719 equal parts of about 1.67 ¢ each. Each step represents a frequency ratio of 21/719, or the 719th root of 2.
Theory
719edo is only consistent to the 3-odd-limit and the error of its harmonic 3 is quite large. Its harmonics 5 and 7 are also about halfway its steps. It can be used in the 2.9.15.21.11.17.19.23.29 subgroup, tempering out 1701/1700, 3025/3024, 2376/2375, 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000. It supports marfifths.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.688 | -0.778 | -0.815 | -0.294 | -0.553 | +0.641 | -0.091 | +0.191 | -0.434 | -0.127 | -0.736 |
| Relative (%) | +41.2 | -46.6 | -48.8 | -17.6 | -33.1 | +38.4 | -5.4 | +11.4 | -26.0 | -7.6 | -44.1 | |
| Steps (reduced) |
1140 (421) |
1669 (231) |
2018 (580) |
2279 (122) |
2487 (330) |
2661 (504) |
2809 (652) |
2939 (63) |
3054 (178) |
3158 (282) |
3252 (376) | |
Subsets and supersets
719edo is the 128th prime EDO. 1438edo, which doubles it, gives a good correction to the harmonics 3, 5 and 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-2279 719⟩ | [⟨719 2279]] | 0.0464 | 0.0464 | 2.78 |