1395edo

 ← 1394edo 1395edo 1396edo →
Prime factorization 32 × 5 × 31
Step size 0.860215¢
Fifth 816\1395 (701.935¢) (→272\465)
Semitones (A1:m2) 132:105 (113.5¢ : 90.32¢)
Consistency limit 21
Distinct consistency limit 21
Special properties

1395 equal divisions of the octave (abbreviated 1395edo or 1395ed2), also called 1395-tone equal temperament (1395tet) or 1395 equal temperament (1395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1395 equal parts of about 0.86 ¢ each. Each step represents a frequency ratio of 21/1395, or the 1395th root of 2.

1395edo is a strong higher-limit system, being a zeta peak, peak integer, integral and gap edo. The patent val is the first one after 311 with a lower 37-limit relative error, though it is only consistent through the 21-odd-limit, due to harmonic 23 being all of 0.3 cents flat. A comma basis for the 19-limit is {2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

Prime harmonics

Approximation of prime harmonics in 1395edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.000 -0.020 -0.077 -0.224 +0.080 -0.098 -0.009 +0.121 -0.317 +0.100 -0.089 -0.161 +0.185 +0.310 +0.300
Relative (%) +0.0 -2.3 -9.0 -26.0 +9.3 -11.3 -1.1 +14.1 -36.9 +11.7 -10.4 -18.7 +21.5 +36.1 +34.9
Steps
(reduced)
1395
(0)
2211
(816)
3239
(449)
3916
(1126)
4826
(641)
5162
(977)
5702
(122)
5926
(346)
6310
(730)
6777
(1197)
6911
(1331)
7267
(292)
7474
(499)
7570
(595)
7749
(774)

Subsets and supersets

Since 1395 factors into 32 × 5 × 31, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.