11358058edo
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It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
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Although its step size is far beyond the human melodic just-noticeable difference, it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-OPSL, where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller edo, meaning it is very likely a zeta peak edo.
While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000000 | -0.0000012 | +0.0000028 | -0.0000033 | +0.0000030 | +0.0000059 | -0.0000025 | -0.0000082 | -0.0000067 | +0.0000100 | -0.0000039 | -0.0000502 | -0.0000429 |
| Relative (%) | +0.0 | -1.1 | +2.6 | -3.1 | +2.8 | +5.6 | -2.4 | -7.7 | -6.3 | +9.4 | -3.7 | -47.5 | -40.6 | |
| Steps (reduced) |
11358058 (0) |
18002096 (6644038) |
26372594 (3656478) |
31886100 (9169984) |
39292425 (5218251) |
42029809 (7955635) |
46425640 (993408) |
48248207 (2815975) |
51378879 (5946647) |
55177230 (9744998) |
56270049 (10837817) |
59169273 (2378983) |
60851386 (4061096) | |