497edo

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← 496edo497edo498edo →
Prime factorization 7 × 71
Step size 2.41449¢
Fifth 291\497 (702.616¢)
Semitones (A1:m2) 49:36 (118.3¢ : 86.92¢)
Consistency limit 5
Distinct consistency limit 5

497 equal divisions of the octave (abbreviated 497edo), or 497-tone equal temperament (497tet), 497 equal temperament (497et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 497 equal parts of about 2.41 ¢ each. Each step of 497edo represents a frequency ratio of 21/497, or the 497th root of 2.

Theory

497et only is consistent to the 5-odd-limit. Using the patent val, the equal temperament tempers out 2100875/2097152, 48828125/48771072, 67108864/66976875, and 200120949/200000000 in the 7-limit; 5632/5625, 42875/42768, 43923/43904, 131072/130977, 151263/151250, 160083/160000, and 391314/390625 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 497edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.66 +0.00 -0.62 -1.09 -0.81 -0.29 +0.66 -1.13 -0.53 +0.04 -0.51
relative (%) +27 +0 -26 -45 -34 -12 +28 -47 -22 +2 -21
Steps
(reduced)
788
(291)
1154
(160)
1395
(401)
1575
(84)
1719
(228)
1839
(348)
1942
(451)
2031
(43)
2111
(123)
2183
(195)
2248
(260)

Subsets and supersets

497 factors into 7 × 41, with 7edo and 41edo as its subset edos. 1491edo, which triples it, gives a good correction to harmonics 3 and 7.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [788 -497 [497 788]] -0.2084 0.2084 8.63
2.3.5 [38 -2 -15, [12 -31 16 [497 788 1154]] -0.1396 0.1961 8.12

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 80\497 193.16 262144/234375 Luna

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct