3178edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 3177edo3178edo3179edo →
Prime factorization 2 × 7 × 227
Step size 0.377596¢ 
Fifth 1859\3178 (701.951¢)
Semitones (A1:m2) 301:239 (113.7¢ : 90.25¢)
Consistency limit 27
Distinct consistency limit 27

3178 equal divisions of the octave (abbreviated 3178edo or 3178ed2), also called 3178-tone equal temperament (3178tet) or 3178 equal temperament (3178et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3178 equal parts of about 0.378 ¢ each. Each step represents a frequency ratio of 21/3178, or the 3178th root of 2.

This edo is quite accurate in the 23-limit and has an exceptional approximation of harmonic 13. However, like most edos of this size, it is rather impractical to use. It tempers out several of the smaller 23-limit superparticular commas, including 28561/28560, 28900/28899, 43264/43263, and 43681/43680.

Prime harmonics

Approximation of prime harmonics in 3178edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.004 -0.033 +0.085 -0.028 +0.001 +0.016 +0.033 +0.045 +0.127 -0.165
Relative (%) +0.0 -1.1 -8.7 +22.6 -7.4 +0.3 +4.3 +8.6 +12.0 +33.6 -43.6
Steps
(reduced)
3178
(0)
5037
(1859)
7379
(1023)
8922
(2566)
10994
(1460)
11760
(2226)
12990
(278)
13500
(788)
14376
(1664)
15439
(2727)
15744
(3032)