640edo

← 639edo

640edo

641edo →

Prime factorization	27 × 5
Step size	1.875¢
Fifth	374\640 (701.25¢) (→187\320)
Semitones (A1:m2)	58:50 (108.8¢ : 93.75¢)
Dual sharp fifth	375\640 (703.125¢) (→75\128)
Dual flat fifth	374\640 (701.25¢) (→187\320)
Dual major 2nd	109\640 (204.375¢)
Consistency limit	5
Distinct consistency limit	5

640 equal divisions of the octave (abbreviated 640edo or 640ed2), also called 640-tone equal temperament (640tet) or 640 equal temperament (640et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 640 equal parts of about 1.88 ¢ each. Each step represents a frequency ratio of 2^1/640, or the 640th root of 2.

640edo is enfactored in the 5-limit, tempering out the vishnuzma, [23 6 -14⟩, with the same tuning as 320edo. In the 7-limit it tempers out 19683/19600 and [16 2 -1 -6⟩ and in the 11-limit it tempers out 540/539, 8019/8000 and [14 -1 -2 -4 1⟩. It provides the optimal patent val for the rank-3 albus temperament tempering out 540/539 and 8019/8000, and hemipental, the 255 & 385 temperament.

Odd harmonics

Approximation of odd harmonics in 640edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.705	-0.064	+0.549	+0.465	-0.068	-0.528	-0.769	+0.045	+0.612	-0.156	-0.149
	Relative (%)	-37.6	-3.4	+29.3	+24.8	-3.6	-28.1	-41.0	+2.4	+32.6	-8.3	-8.0
Steps (reduced)		1014 (374)	1486 (206)	1797 (517)	2029 (109)	2214 (294)	2368 (448)	2500 (580)	2616 (56)	2719 (159)	2811 (251)	2895 (335)

Subsets and supersets

Since 640 factors into 2⁷ × 5, 640edo has subset edos 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320.