463edo

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463edo

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Prime factorization	463 (prime)
Step size	2.59179 ¢
Fifth	271\463 (702.376 ¢)
Semitones (A1:m2)	45:34 (116.6 ¢ : 88.12 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

463et tempers out 184528125/184473632, 4096000/4084101, 703125/702464, 67108864/66976875, 95703125/95551488, 359661568/358722675 and 420175/419904 in the 7-limit; 161280/161051, 25165824/25109315, 820125/819896, 29296875/29218112, 1019215872/1019046875, 4000/3993, 759375/758912, 117649/117612, 2359296/2358125, 6250/6237, 369140625/369098752, 200704/200475, 283115520/282475249, 825000/823543, 180224/180075, 537109375/536870912, 19712/19683, 3025/3024, 199297406/199290375, 1362944/1361367, 532400/531441, 3294225/3294172 and 1771561/1771470 in the 11-limit. It supports amity, trinity and undesemi.

Prime harmonics

Approximation of prime harmonics in 463edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.42	-0.14	+0.50	+0.73	-0.79	-1.28	+0.54	-1.06	-0.64	+0.54
	Relative (%)	+0.0	+16.2	-5.3	+19.5	+28.3	-30.4	-49.5	+21.0	-40.9	-24.5	+20.7
Steps (reduced)		463 (0)	734 (271)	1075 (149)	1300 (374)	1602 (213)	1713 (324)	1892 (40)	1967 (115)	2094 (242)	2249 (397)	2294 (442)

Subsets and supersets

463edo is the 90th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[734 -463⟩	⟨463 734]	-0.1328	0.1327	5.12
2.3.5	[9 -13 5⟩, [91 -12 -31⟩	⟨463 734 1075]	-0.0689	0.1411	5.44
2.3.5.7	420175/419904, 703125/702464, 1600000/1594323	⟨463 734 1075 1300]	-0.0966	0.1313	5.07
2.3.5.7.11	3025/3024, 6250/6237, 19712/19683, 180224/180075	⟨463 734 1075 1300 1602]	-0.1197	0.1262	4.87
2.3.5.7.11.13	3025/3024, 1716/1715, 4096/4095, 676/675, 6250/6237	⟨463 734 1075 1300 1602 1713]	-0.0643	0.1691	6.52
2.3.5.7.11.13.17	442/441, 595/594, 1275/1274, 2601/2600, 3025/3024, 32955/32912, 45500/45441	⟨463 734 1075 1300 1602 1713 1892]	-0.0103	0.2051	7.91

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	131\463	339.52	243/200	Amity
1	198\463	513.17	168/125, 121/90	Trinity
1	31\463	80.35	22/21	Undesemi