User:Francium/647edo

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647edo

648edo →

Prime factorization	647 (prime)
Step size	1.85471 ¢
Fifth	378\647 (701.082 ¢)
Semitones (A1:m2)	58:51 (107.6 ¢ : 94.59 ¢)
Dual sharp fifth	379\647 (702.937 ¢)
Dual flat fifth	378\647 (701.082 ¢)
Dual major 2nd	110\647 (204.019 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

647edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. It tends heavily flat in the first few harmonics. Using the patent val it tempers out 2401/2400, 7381125/7340032 and 1224440064/1220703125 in the 7-limit; 8019/8000, 2401/2400, 46656/46585 and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.5.7.11.13 subgroup might be worth considering.

Odd harmonics

Approximation of odd harmonics in 647edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.873	-0.533	-0.665	+0.109	-0.468	-0.342	+0.448	+0.763	-0.759	+0.316	+0.474
	Relative (%)	-47.1	-28.7	-35.9	+5.9	-25.2	-18.4	+24.2	+41.2	-40.9	+17.1	+25.5
Steps (reduced)		1025 (378)	1502 (208)	1816 (522)	2051 (110)	2238 (297)	2394 (453)	2528 (587)	2645 (57)	2748 (160)	2842 (254)	2927 (339)

Subsets and supersets

647edo is the 118th prime EDO. 1294edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[2051 -647⟩	[⟨647 2051]]	-0.0171	0.0171	0.92
2.9.5	[-50 -4 27⟩, [63 -25 7⟩	[⟨647 2051 1502]]	+0.0651	0.1172	6.32
2.9.5.7	703125/702464, 3500000000/3486784401, 4202539929/4194304000	[⟨647 2051 1502 1816]]	+0.1081	0.1258	6.78
2.9.5.7.11	496125/495616, 1684375/1679616, 151263/151250, 40960000/40920957	[⟨647 2051 1502 1816 2238]]	+0.1135	0.1131	6.10
2.9.5.7.11.13	4459/4455, 35750/35721, 47432/47385, 60025/59904, 1146880/1146717	[⟨647 2051 1502 1816 2238 2394]]	+0.1100	0.1035	5.58