2547047edo

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Prime factorization 1583 × 1609
Step size 0.000471134¢ 
Fifth 1489927\2547047 (701.955¢)
Semitones (A1:m2) 241301:191506 (113.7¢ : 90.22¢)
Consistency limit 41
Distinct consistency limit 41

2547047 equal divisions of the octave (abbreviated 2547047edo or 2547047ed2), also called 2547047-tone equal temperament (2547047tet) or 2547047 equal temperament (2547047et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2547047 equal parts of about 0.000471 ¢ each. Each step represents a frequency ratio of 21/2547047, or the 2547047th root of 2.

Despite being less practical than many smaller EDOs, it is a strong higher-limit system, especially in the 35-odd-limit and 36-OPSL. An interesting quirk, though, is that all prime harmonics up to 41 are tuned sharp except for 19 which is only slightly flat. Also, the only two prime factors of the number of notes per octave appear to be unusually close together.


Approximation of prime harmonics in 2547047edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000008 +0.000006 +0.000032 +0.000035 +0.000055 +0.000015 -0.000014 +0.000043 +0.000038 +0.000071
Relative (%) +0.0 +1.7 +1.2 +6.8 +7.4 +11.7 +3.3 -2.9 +9.1 +8.0 +15.0
Steps
(reduced)
2547047
(0)
4036974
(1489927)
5914060
(819966)
7150465
(2056371)
8811335
(1170194)
9425194
(1784053)
10410960
(222772)
10819671
(631483)
11521725
(1333537)
12373506
(2185318)
12618571
(2430383)
Approximation of prime harmonics in 2547047edo (continued)
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) +0.000204 +0.000113 -0.000172 +0.000061 +0.000184 -0.000156 +0.000121 -0.000129 +0.000023 -0.000034 +0.000074
Relative (%) +43.3 +23.9 -36.5 +12.9 +39.0 -33.1 +25.7 -27.4 +4.9 -7.3 +15.7
Steps
(reduced)
13268723
(533488)
13645937
(910702)
13820951
(1085716)
14147799
(1412564)
14589283
(1854048)
14983368
(2248133)
15105867
(2370632)
15450614
(168332)
15663695
(381413)
15765774
(483492)
16056026
(773744)