102557edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 102556edo102557edo102558edo →
Prime factorization 73 × 13 × 23
Step size 0.0117008¢ 
Fifth 59992\102557 (701.955¢)
Semitones (A1:m2) 9716:7711 (113.7¢ : 90.22¢)
Consistency limit 39
Distinct consistency limit 39
Special properties

102557 equal divisions of the octave (abbreviated 102557edo or 102557ed2), also called 102557-tone equal temperament (102557tet) or 102557 equal temperament (102557et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 102557 equal parts of about 0.0117 ¢ each. Each step represents a frequency ratio of 21/102557, or the 102557th root of 2.

It is notable for being a high-limit system and is the first non-trivial EDO to be consistent in the 32-odd-prime-sum-limit.


Approximation of prime harmonics in 102557edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) +0.00000 +0.00001 +0.00024 +0.00118 +0.00084 +0.00004 +0.00086 +0.00349 +0.00066 +0.00050 +0.00572 +0.00107 -0.00539
Relative (%) +0.0 +0.1 +2.0 +10.1 +7.1 +0.4 +7.3 +29.8 +5.6 +4.3 +48.9 +9.1 -46.1
Steps
(reduced)
102557
(0)
162549
(59992)
238130
(33016)
287914
(82800)
354789
(47118)
379506
(71835)
419198
(8970)
435655
(25427)
463923
(53695)
498220
(87992)
508088
(97860)
534266
(21481)
549454
(36669)