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 2^1/336, 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)