2544edo

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← 2543edo 2544edo 2545edo →
Prime factorization 24 × 3 × 53
Step size 0.471698¢ 
Fifth 1488\2544 (701.887¢) (→31\53)
Semitones (A1:m2) 240:192 (113.2¢ : 90.57¢)
Consistency limit 15
Distinct consistency limit 15

2544 equal divisions of the octave (abbreviated 2544edo or 2544ed2), also called 2544-tone equal temperament (2544tet) or 2544 equal temperament (2544et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2544 equal parts of about 0.472 ¢ each. Each step represents a frequency ratio of 21/2544, or the 2544th root of 2.

2544edo is consistent in the 15-odd-limit and is a satisfactory 2.3.5.7.11.13.23 subgroup (add-23 13-limit) system in addition to that.

Being a strong higher-limit system with many notable divisors, it tempers out the Mercator comma, as well as the landscape comma, supporting the 7-limit aemilic temperament, 159 & 954. It also suppors the 70/69-48-commatic temperament, dividing the octave into 48 parts and using 70/69 as a chroma.

Prime harmonics

Approximation of prime harmonics in 2544edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.068 +0.007 +0.042 +0.097 +0.038 +0.233 +0.128 +0.028 +0.140 -0.224
Relative (%) +0.0 -14.5 +1.5 +8.9 +20.6 +8.1 +49.5 +27.2 +5.8 +29.6 -47.5
Steps
(reduced)
2544
(0)
4032
(1488)
5907
(819)
7142
(2054)
8801
(1169)
9414
(1782)
10399
(223)
10807
(631)
11508
(1332)
12359
(2183)
12603
(2427)

Subsets and supersets

Since 2544edo factors as 24 × 3 × 53, it has subset edos 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 53, 106, 159, 212, 318, 424, 636, 848, 1272.