297edo

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← 296edo297edo298edo →
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 21/297, or the 297th root of 2.

297 = 3 × 99, and 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.