11358058edo

From Xenharmonic Wiki
Jump to navigation Jump to search

This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, unnecessarily complex or chosen arbitrarily.

Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations or conceptual frameworks.

← 11358057edo11358058edo11358059edo →
Prime factorization 2 × 5679029
Step size 0.000105652¢
Fifth 6644038\11358058 (701.955¢) (→3322019\5679029)
Semitones (A1:m2) 1076034:853984 (113.7¢ : 90.23¢)
Consistency limit 35
Distinct consistency limit 35

11358058edo, or 11358058 equal divisions of the octave, is an equal tuning system with a step size of only about 0.00010565 cents, far beyond the human melodic just-noticeable difference. It has been noted for its highly accurate approximation of the 31-limit.

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

Approximation of prime harmonics in 11358058edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000000 -0.0000012 +0.0000028 -0.0000033 +0.0000030 +0.0000059 -0.0000025 -0.0000082 -0.0000067 +0.0000100 -0.0000039
relative (%) +0 -1 +3 -3 +3 +6 -2 -8 -6 +9 -4
Steps
(reduced)
11358058
(0)
18002096
(6644038)
26372594
(3656478)
31886100
(9169984)
39292425
(5218251)
42029809
(7955635)
46425640
(993408)
48248207
(2815975)
51378879
(5946647)
55177230
(9744998)
56270049
(10837817)