2024edo
| ← 2023edo | 2024edo | 2025edo → |
2024 equal divisions of the octave (2024edo), or 2024-tone equal temperament (2024tet), 2024 equal temperament (2024et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2024 equal parts of about 0.593 ¢ each.
Theory
2024edo is enfactored in the 13-limit, with the same tuning as 1012edo, which is also a zeta EDO. Beyond that, it does make for a reasonable 17- an 19-limit system.
It has two suitable mappings for 5th harmonic, one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the wizma, 420175/419904 in the 7-limit, as well as 3025/3024, 4225/4224 and 10648/10647 in the 13-limit.
Likewise, 2024edo can be conceptualized as a 2.3.25 subgroup temperament, where sharp and flat mappings of 5/4 make together a dual 25/1. In the 2.3.25.7 subgroup, it tempers out the ragisma, 4375/4374. In the 2.3.25.7.11, it tempers out 117649/117612.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.021 | +0.248 | -0.051 | +0.065 | +0.184 | -0.015 | +0.115 | +0.184 | +0.265 | -0.174 |
| relative (%) | +0 | +4 | +42 | -9 | +11 | +31 | -2 | +19 | +31 | +45 | -29 | |
| Steps (reduced) |
2024 (0) |
3208 (1184) |
4700 (652) |
5682 (1634) |
7002 (930) |
7490 (1418) |
8273 (177) |
8598 (502) |
9156 (1060) |
9833 (1737) |
10027 (1931) | |