2901533edo

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← 2901532edo2901533edo2901534edo →
Prime factorization 433 × 6701
Step size 0.000413574¢
Fifth 1697288\2901533 (701.955¢)
Semitones (A1:m2) 274884:218159 (113.7¢ : 90.22¢)
Consistency limit 131
Distinct consistency limit 131

2901533 equal divisions of the octave (abbreviated 2901533edo), or 2901533-tone equal temperament (2901533tet), 2901533 equal temperament (2901533et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2901533 equal parts of about 0.000414 ¢ each. Each step of 2901533edo represents a frequency ratio of 21/2901533, or the 2901533rd root of 2. Except for 8 barely-inconsistent interval pairs, it is consistent in the 137-prime-limited no-247's 255-odd-limit (a total of 4067 interval pairs), with primes 151, 157, 163, 173, 181, 197 and 211 being includeable to that odd limit for a tiny penalty of only 3 more barely-inconsistent interval pairs (and for a total of 4830). Including odd 247 adds 8 more inconsistent interval pairs and 90 more consistent interval pairs for a total of 4928 interval pairs (of which 19 interval pairs are inconsistent). Because of its unusual consistency at its size range, it could be a candidate for "miracle edo" (not miracle, the temperament) after 311edo, although this is not entirely certain or clear because a deep exhaustive search of comprehensive odd-limit performance has not been done up until this point, but it is at least significant that it holds a significant amount of records for odd limit consistency as detailed on the page for minimal consistent EDOs.

Theory

Approximation of prime harmonics in 2901533edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error absolute (¢) +0.000000 +0.000000 +0.000004 +0.000021 -0.000001 +0.000018 -0.000132 +0.000057 -0.000121 -0.000071 -0.000034 +0.000061 +0.000025
relative (%) +0 +0 +1 +5 -0 +4 -32 +14 -29 -17 -8 +15 +6
Steps
(reduced)
2901533
(0)
4598821
(1697288)
6737151
(934085)
8145633
(2342567)
10037655
(1333056)
10736948
(2032349)
11859908
(253776)
12325502
(719370)
13125264
(1519132)
14095592
(2489460)
14374764
(2768632)
15115401
(607736)
15545114
(1037449)
Approximation of prime harmonics in 2901533edo (continued)
Harmonic 43 47 53 59 61 67 71 73 79 83 89 97
Error absolute (¢) -0.000104 +0.000060 -0.000091 +0.000027 -0.000041 +0.000014 -0.000086 -0.000092 +0.000056 -0.000118 -0.000103 +0.000038
relative (%) -25 +15 -22 +7 -10 +3 -21 -22 +13 -29 -25 +9
Steps
(reduced)
15744486
(1236821)
16116823
(1609158)
16619750
(2112085)
17068683
(2561018)
17208230
(2700565)
17600958
(191760)
17843694
(434496)
17959980
(550782)
18290628
(881430)
18497387
(1088189)
18789554
(1380356)
19149865
(1740667)