1525edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 1524edo1525edo1526edo →
Prime factorization 52 × 61
Step size 0.786885¢ 
Fifth 892\1525 (701.902¢)
Semitones (A1:m2) 144:115 (113.3¢ : 90.49¢)
Consistency limit 9
Distinct consistency limit 9

1525 equal divisions of the octave (abbreviated 1525edo or 1525ed2), also called 1525-tone equal temperament (1525tet) or 1525 equal temperament (1525et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1525 equal parts of about 0.787 ¢ each. Each step represents a frequency ratio of 21/1525, or the 1525th root of 2.

1525edo is consistent to the 9-odd-limit, though its approcimation for 7 is worse than for the 5-limit. In higher limits, it is a good 2.3.5.7.13.19.31 system, and an excellent 2.3.5.19 system with an optional addition of 29/23.

In the 5-limit, it tempers out the dipromethia, mapping 2048/2025 into 1\61 as well as the astro comma, [91 -12 -31 and the 25th-octave manganese comma, [211 50 -125. In the 7-limit, it tunes osiris, and in the 2.5.7.11.13 subgroup, french decimal.

Prime harmonics

Approximation of prime harmonics in 1525edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.053 +0.047 -0.170 +0.289 -0.134 -0.300 -0.070 -0.340 -0.331 -0.118
Relative (%) +0.0 -6.8 +6.0 -21.6 +36.7 -17.1 -38.1 -8.9 -43.2 -42.1 -14.9
Steps
(reduced)
1525
(0)
2417
(892)
3541
(491)
4281
(1231)
5276
(701)
5643
(1068)
6233
(133)
6478
(378)
6898
(798)
7408
(1308)
7555
(1455)

Subsets and supersets

Since 1525 factors as 52 × 61, 1525edo has subset edos 1, 5, 25, 61, 305.