2547047edo

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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 2^1/2547047, 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)