5407372813edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 5407372812edo5407372813edo5407372814edo →
Prime factorization 5407372813 (prime)
Step size 2.21919e-07¢ 
Fifth 3163110323\5407372813 (701.955¢)
Semitones (A1:m2) 512281009:406566824 (113.7¢ : 90.22¢)
Consistency limit 155
Distinct consistency limit 155

5407372813 equal divisions of the octave (abbreviated 5407372813edo or 5407372813ed2), also called 5407372813-tone equal temperament (5407372813tet) or 5407372813 equal temperament (5407372813et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5407372813 equal parts of about 2.22e-07 ¢ each. Each step represents a frequency ratio of 21/5407372813, or the 5407372813th root of 2.

5407372813edo is consistent in the 155-odd-limit and thus has been used in Scale Workshop to quickly decide the constant structure property for JI scales.

Prime harmonics

Approximation of prime harmonics in 5407372813edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0000000000 -0.0000000053 -0.0000000077 +0.0000000053 -0.0000000115 -0.0000000048 +0.0000000167 +0.0000000467 -0.0000000230
Relative (%) +0.0 -2.4 -3.5 +2.4 -5.2 -2.2 +7.5 +21.0 -10.4
Steps
(reduced)
5407372813
(0)
8570483136
(3163110323)
12555530854
(1740785228)
15180414682
(4365669056)
18706436483
(2484318044)
20009657128
(3787538689)
22102435442
(472944190)
22970127748
(1340636496)
24460585939
(2831094687)
Approximation of prime harmonics in 5407372813edo (continued)
Harmonic 29 31 37 41 43 47 53 59 61
Error Absolute (¢) -0.0000000274 -0.0000000113 +0.0000000237 -0.0000000012 +0.0000000630 +0.0000000101 -0.0000000070 +0.0000000660 -0.0000000403
Relative (%) -12.4 -5.1 +10.7 -0.5 +28.4 +4.5 -3.2 +29.7 -18.2
Steps
(reduced)
26268914359
(4639423107)
26789186439
(5159695187)
28169456500
(1132592435)
28970281054
(1933416989)
29341836511
(2304972446)
30035732744
(2998868679)
30973001341
(3936137276)
31809644094
(4772780029)
32069707840
(5032843775)
Approximation of prime harmonics in 5407372813edo (continued)
Harmonic 67 71 73 79 83 89 97 101 103
Error Absolute (¢) +0.0000000634 +0.0000000367 +0.0000000161 +0.0000000431 +0.0000000292 +0.0000000349 -0.0000000027 -0.0000000081 +0.0000000442
Relative (%) +28.5 +16.5 +7.2 +19.4 +13.2 +15.7 -1.2 -3.6 +19.9
Steps
(reduced)
32801605770
(357368892)
33253975381
(809738503)
33470689037
(1026452159)
34086892637
(1642655759)
34472214903
(2027978025)
35016704899
(2572468021)
35688189271
(3243952393)
36003431755
(3559194877)
36156401165
(3712164287)
Approximation of prime harmonics in 5407372813edo (continued)
Harmonic 107 109 113 127 131 137 139 149 151
Error Absolute (¢) -0.0000000006 -0.0000000381 -0.0000000352 +0.0000000264 +0.0000000350 -0.0000000449 +0.0000000013 -0.0000000028 +0.0000000185
Relative (%) -0.3 -17.2 -15.8 +11.9 +15.8 -20.3 +0.6 -1.3 +8.3
Steps
(reduced)
36453625302
(4009388424)
36598095911
(4153859033)
36879250301
(4435013423)
37790423574
(5346186696)
38032340321
(180730630)
38381705711
(530096020)
38494768414
(643158723)
39036735590
(1185125899)
39140752997
(1289143306)