247edo

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← 246edo247edo248edo →
Prime factorization 13 × 19
Step size 4.8583¢
Fifth 144\247 (699.595¢)
Semitones (A1:m2) 20:21 (97.17¢ : 102¢)
Dual sharp fifth 145\247 (704.453¢)
Dual flat fifth 144\247 (699.595¢)
Dual major 2nd 42\247 (204.049¢)
Consistency limit 3
Distinct consistency limit 3

247 equal divisions of the octave (abbreviated 247edo or 247ed2), also called 247-tone equal temperament (247tet) or 247 equal temperament (247et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 247 equal parts of about 4.858 ¢ each. Each step represents a frequency ratio of 21/247, or the 247th root of 2.

Prime harmonics 3, 5, 7, and 11 are all about halfway between 247edo's steps, so 247edo lacks consistency to the 5 and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of 12edo (700¢, compton fifth). Using the patent val, it tempers out 126/125, 243/242 and 1029/1024 in the 11-limit , so it supports the hemivalentino temperament (31 & 61e).

As every other step of the monstrous 494edo, 247edo can be used in the 2.9.15.21 subgroup.

Odd harmonics

Approximation of odd harmonics in 247edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error absolute (¢) -2.36 +2.35 -2.02 +0.14 -2.33 -0.04 -0.01 +1.93 -1.16 +0.47 -1.55 -0.16 -2.22 +0.38 +1.52
relative (%) -49 +48 -42 +3 -48 -1 -0 +40 -24 +10 -32 -3 -46 +8 +31
Steps
(reduced)
391
(144)
574
(80)
693
(199)
783
(42)
854
(113)
914
(173)
965
(224)
1010
(22)
1049
(61)
1085
(97)
1117
(129)
1147
(159)
1174
(186)
1200
(212)
1224
(236)

Subsets and supersets

Since 247 factors into 13 × 19, 247edo contains 13edo and 19edo as its subsets. 494edo, which doubles it, provides excellent correction to all the lower prime harmonics.