# 1506edo

 ← 1505edo 1506edo 1507edo →
Prime factorization 2 × 3 × 251
Step size 0.796813¢
Fifth 881\1506 (701.992¢)
Semitones (A1:m2) 143:113 (113.9¢ : 90.04¢)
Consistency limit 17
Distinct consistency limit 17

1506 equal divisions of the octave (abbreviated 1506edo or 1506ed2), also called 1506-tone equal temperament (1506tet) or 1506 equal temperament (1506et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1506 equal parts of about 0.797 ¢ each. Each step represents a frequency ratio of 21/1506, or the 1506th root of 2.

1506edo is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit relative error, and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.

### Prime harmonics

Approximation of prime harmonics in 1506edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.037 +0.140 +0.098 +0.076 +0.110 +0.224 -0.302 -0.386 -0.095 -0.016
Relative (%) +0.0 +4.6 +17.6 +12.3 +9.6 +13.8 +28.1 -37.9 -48.4 -11.9 -2.0
Steps
(reduced)
1506
(0)
2387
(881)
3497
(485)
4228
(1216)
5210
(692)
5573
(1055)
6156
(132)
6397
(373)
6812
(788)
7316
(1292)
7461
(1437)

### Subsets and supersets

Since 1506 factors into 2 × 3 × 251, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.