247edo

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The 247 equal divisions of the octave (247EDO), or the 247(-tone) equal temperament (247TET, 247ET) when viewed from a regular temperament perspective, is the equal division of the octave into 247 parts of 4.8583 cents each.

Theory

In 247EDO, 144 degree represents 3/2 (2.36¢ flat), 80 degree represents 5/4 (2.35¢ sharp), 199 degree represents 7/4 (2.02¢ flat), and 113 degree represents 11/8 (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of 12EDO (700¢, compton fifth). It tempers out 126/125, 243/242 and 1029/1024 in the 11-limit patent mapping, so it supports the hemivalentino temperament (31&61e).

Approximation of odd harmonics in 247 EDO
Odd 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)