276edo

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276 equal divisions of the octave (276edo), or 276-tone equal temperament (276tet), 276 equal temperament (276et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 276 equal parts of about 4.35 ¢ each.

Theory

Approximation of odd harmonics in 276edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) -1.96 +0.64 +0.74 +0.44 +0.86 -1.40 -1.31 -0.61 -1.86 -1.22
relative (%) -45 +15 +17 +10 +20 -32 -30 -14 -43 -28
Steps
(reduced)
437
(161)
641
(89)
775
(223)
875
(47)
955
(127)
1021
(193)
1078
(250)
1128
(24)
1172
(68)
1212
(108)

276edo's fifth is quite bad, but it corresponds to 12edo's fifth, which means 276edo tempers out the Pythagorean comma. It's sharp val fifth comes from 46edo.

It is a multiple of 12 and 23.

Patent val

The patent val of 276edo supports compton temperament, owing to the fact that it is a 12edo fifth.

In the 7-limit, 276edo supports grendel.

276b val

In the 5-limit, it supports hanson, but all the variants of it are contorted.

In the 7-limit, it supports quadritikleismic.

Music