5407372813edo

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5407372813edo

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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

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.

Theory

Approximation of prime harmonics in 5407372813edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47	53	59	61	67	71
Error	Absolute (¢)	+0.0000000000	-0.0000000053	-0.0000000077	+0.0000000053	-0.0000000115	-0.0000000048	+0.0000000167	+0.0000000467	-0.0000000230	-0.0000000274	-0.0000000113	+0.0000000237	-0.0000000012	+0.0000000630	+0.0000000101	-0.0000000070	+0.0000000660	-0.0000000403	+0.0000000634	+0.0000000367
	Relative (%)	+0.0	-2.4	-3.5	+2.4	-5.2	-2.2	+7.5	+21.0	-10.4	-12.4	-5.1	+10.7	-0.5	+28.4	+4.5	-3.2	+29.7	-18.2	+28.5	+16.5
Steps (reduced)		5407372813 (0)	8570483136 (3163110323)	12555530854 (1740785228)	15180414682 (4365669056)	18706436483 (2484318044)	20009657128 (3787538689)	22102435442 (472944190)	22970127748 (1340636496)	24460585939 (2831094687)	26268914359 (4639423107)	26789186439 (5159695187)	28169456500 (1132592435)	28970281054 (1933416989)	29341836511 (2304972446)	30035732744 (2998868679)	30973001341 (3936137276)	31809644094 (4772780029)	32069707840 (5032843775)	32801605770 (357368892)	33253975381 (809738503)

Approximation of prime harmonics in 5407372813edo (continued)

Harmonic		73	79	83	89	97	101	103	107	109	113	127	131	137	139	149	151	157	163	167	173
Error	Absolute (¢)	+0.0000000161	+0.0000000431	+0.0000000292	+0.0000000349	-0.0000000027	-0.0000000081	+0.0000000442	-0.0000000006	-0.0000000381	-0.0000000352	+0.0000000264	+0.0000000350	-0.0000000449	+0.0000000013	-0.0000000028	+0.0000000185	+0.0000000661	-0.0000000703	-0.0000000789	+0.0000000255
	Relative (%)	+7.2	+19.4	+13.2	+15.7	-1.2	-3.6	+19.9	-0.3	-17.2	-15.8	+11.9	+15.8	-20.3	+0.6	-1.3	+8.3	+29.8	-31.7	-35.6	+11.5
Steps (reduced)		33470689037 (1026452159)	34086892637 (1642655759)	34472214903 (2027978025)	35016704899 (2572468021)	35688189271 (3243952393)	36003431755 (3559194877)	36156401165 (3712164287)	36453625302 (4009388424)	36598095911 (4153859033)	36879250301 (4435013423)	37790423574 (5346186696)	38032340321 (180730630)	38381705711 (530096020)	38494768414 (643158723)	39036735590 (1185125899)	39140752997 (1289143306)	39444733919 (1593124228)	39737312831 (1885703140)	39926441850 (2074832159)	40201806553 (2350196862)