622edo

← 621edo

622edo

623edo →

Prime factorization	2 × 311
Step size	1.92926 ¢
Fifth	364\622 (702.251 ¢) (→ 182\311)
Semitones (A1:m2)	60:46 (115.8 ¢ : 88.75 ¢)
Consistency limit	7
Distinct consistency limit	7

622 equal divisions of the octave (abbreviated 622edo or 622ed2), also called 622-tone equal temperament (622tet) or 622 equal temperament (622et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 622 equal parts of about 1.93 ¢ each. Each step represents a frequency ratio of 2^1/622, or the 622nd root of 2.

622edo is enfactored in the 41-limit, having the same tuning as the highly notable 311edo. In that regard, 622edo is a compound of two 311edos that don't intersect, and provides barely anything new apart from most characteristics of what it doubles.

622edo has potential as an add-43 system, correcting 311edo's mapping for 43, which is the first harmonic not represented consistently by 311edo. Some 43-limit commas it tempers out are 1849/1848, 1850/1849, 50000/49923, 59168/59049, 300125/299538, 6837602/6834375, 1048576/1048383.

Prime harmonics

Approximation of prime harmonics in 622edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41
Error	Absolute (¢)	+0.000	+0.296	-0.462	-0.337	+0.451	+0.630	-0.775	-0.407	+0.665	+0.648	+0.945	-0.540	-0.767
	Relative (%)	+0.0	+15.3	-23.9	-17.5	+23.4	+32.6	-40.2	-21.1	+34.4	+33.6	+49.0	-28.0	-39.7
Steps (reduced)		622 (0)	986 (364)	1444 (200)	1746 (502)	2152 (286)	2302 (436)	2542 (54)	2642 (154)	2814 (326)	3022 (534)	3082 (594)	3240 (130)	3332 (222)

Approximation of prime harmonics in 622edo (continued)

Harmonic		43	47	53	59	61	67	71	73	79	83	89	97	101
Error	Absolute (¢)	-0.264	+0.088	+0.450	-0.008	+0.157	-0.207	-0.275	-0.137	+0.093	-0.530	+0.181	-0.281	-0.786
	Relative (%)	-13.7	+4.6	+23.3	-0.4	+8.1	-10.7	-14.3	-7.1	+4.8	-27.5	+9.4	-14.6	-40.8
Steps (reduced)		3375 (265)	3455 (345)	3563 (453)	3659 (549)	3689 (579)	3773 (41)	3825 (93)	3850 (118)	3921 (189)	3965 (233)	4028 (296)	4105 (373)	4141 (409)