4973edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 4972edo4973edo4974edo →
Prime factorization 4973 (prime)
Step size 0.241303¢
Fifth 2909\4973 (701.951¢)
Semitones (A1:m2) 471:374 (113.7¢ : 90.25¢)
Consistency limit 11
Distinct consistency limit 11
Special properties

4973 equal divisions of the octave (abbreviated 4973edo), or 4973-tone equal temperament (4973tet), 4973 equal temperament (4973et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4973 equal parts of about 0.241 ¢ each. Each step of 4973edo represents a frequency ratio of 21/4973, or the 4973rd root of 2. It is a very strong 7-limit system: it tempers out the unnoticeable comma [1 -15 -18 23 and supports a number of very high accuracy 7-limit rank-3 temperaments. In the 5-limit it supports whoosh, the 441 & 730 temperament. It is a zeta peak integer edo.

Prime harmonics

Approximation of prime harmonics in 4973edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 -0.0045 +0.0124 +0.0058 +0.0595 -0.0692 +0.0114 +0.0136 +0.0788 +0.0629 -0.0527
relative (%) +0 -2 +5 +2 +25 -29 +5 +6 +33 +26 -22
Steps
(reduced)
4973
(0)
7882
(2909)
11547
(1601)
13961
(4015)
17204
(2285)
18402
(3483)
20327
(435)
21125
(1233)
22496
(2604)
24159
(4267)
24637
(4745)