297edo

← 296edo

297edo

298edo →

Prime factorization	33 × 11
Step size	4.0404 ¢
Fifth	174\297 (703.03 ¢) (→ 58\99)
Semitones (A1:m2)	30:21 (121.2 ¢ : 84.85 ¢)
Consistency limit	7
Distinct consistency limit	7

297 equal divisions of the octave (abbreviated 297edo or 297ed2), also called 297-tone equal temperament (297tet) or 297 equal temperament (297et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 297 equal parts of about 4.04 ¢ each. Each step represents a frequency ratio of 2^1/297, or the 297th root of 2.

Since 297 = 3 × 99, 297edo is enfactored in the 7-limit with the same tuning as 99edo. It is only consistent in the 7-odd-limit, unlike 99edo. In the 11-limit, the 297e val is the most reasonable, and it corrects 99edo's harmonic 11 somewhat closer to just, tempering out 4000/3993.

The 297cddee val is a tuning for the musneb temperament.

Odd harmonics

Approximation of odd harmonics in 297edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.08	+1.57	+0.87	-1.89	-1.82	-0.12	-1.40	+0.10	+1.48	+1.95	-2.01
	Relative (%)	+26.6	+38.7	+21.6	-46.8	-45.1	-3.1	-34.7	+2.4	+36.6	+48.2	-49.8
Steps (reduced)		471 (174)	690 (96)	834 (240)	941 (50)	1027 (136)	1099 (208)	1160 (269)	1214 (26)	1262 (74)	1305 (117)	1343 (155)

Subsets and supersets

Since 297 factors into 3³ × 11, 297edo has subset edos 3, 9, 11, 27, 33, and 99.