669edo

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← 668edo669edo670edo →
Prime factorization 3 × 223
Step size 1.79372¢
Fifth 391\669 (701.345¢)
Semitones (A1:m2) 61:52 (109.4¢ : 93.27¢)
Dual sharp fifth 392\669 (703.139¢)
Dual flat fifth 391\669 (701.345¢)
Dual major 2nd 114\669 (204.484¢) (→38\223)
Consistency limit 7
Distinct consistency limit 7

669 equal divisions of the octave (669edo), or 669-tone equal temperament (669tet), 669 equal temperament (669et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 669 equal parts of about 1.79 ¢ each.

669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tuning for the sensipent temperament in the 5-limit.

669edo appears much more useful as a higher-limit system, with harmonics 37 through 53 all having an error of 20% or less, with a comma basis for the 2.37.41.43.47.53 subgroup being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}.

Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.

Harmonics

Approximation of odd harmonics in 669edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.610 -0.663 -0.216 +0.574 -0.645 +0.728 +0.521 +0.874 +0.245 -0.826 -0.472
relative (%) -34 -37 -12 +32 -36 +41 +29 +49 +14 -46 -26
Steps
(reduced)
1060
(391)
1553
(215)
1878
(540)
2121
(114)
2314
(307)
2476
(469)
2614
(607)
2735
(59)
2842
(166)
2938
(262)
3026
(350)