336edo

 ← 335edo 336edo 337edo →
Prime factorization 24 × 3 × 7
Step size 3.57143¢
Fifth 197\336 (703.571¢)
Semitones (A1:m2) 35:23 (125¢ : 82.14¢)
Dual sharp fifth 197\336 (703.571¢)
Dual flat fifth 196\336 (700¢) (→7\12)
Dual major 2nd 57\336 (203.571¢) (→19\112)
Consistency limit 3
Distinct consistency limit 3

336 equal divisions of the octave (abbreviated 336edo or 336ed2), also called 336-tone equal temperament (336tet) or 336 equal temperament (336et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 336 equal parts of about 3.57 ¢ each. Each step represents a frequency ratio of 21/336, or the 336th root of 2.

336edo has poor approximation for harmonic 3, therefore it naturally yields a 2.9 subgroup interpretation. In the 2.9.5.7 subgroup, it tempers out the schisma and the landscape comma.

Nonetheless, there are a number of mappings to be considered. Using the 336d val in the 7-limit, 336edo tempers out the octagar comma, 4000/3969, and 336def val tunes the slithy temperament in the 13-limit. 336cefg val is a tuning for the catamite temperament in the 19-limit. 336b val uses the 12edo mapping for 3/2 and tunes the 24th-octave rabic temperament.

Odd harmonics

Approximation of odd harmonics in 336edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.62 -0.60 -0.97 -0.34 -1.32 -1.24 +1.02 -1.38 -1.08 +0.65 +0.30
Relative (%) +45.3 -16.8 -27.1 -9.5 -36.9 -34.8 +28.5 -38.8 -30.4 +18.1 +8.3
Steps
(reduced)
533
(197)
780
(108)
943
(271)
1065
(57)
1162
(154)
1243
(235)
1313
(305)
1373
(29)
1427
(83)
1476
(132)
1520
(176)