276edo

← 275edo

276edo

277edo →

Prime factorization	22 × 3 × 23
Step size	4.34783¢
Fifth	161\276 (700¢) (→7\12)
Semitones (A1:m2)	23:23 (100¢ : 100¢)
Dual sharp fifth	162\276 (704.348¢) (→27\46)
Dual flat fifth	161\276 (700¢) (→7\12)
Dual major 2nd	47\276 (204.348¢)
Consistency limit	3
Distinct consistency limit	3

276 equal divisions of the octave (abbreviated 276edo or 276ed2), also called 276-tone equal temperament (276tet) or 276 equal temperament (276et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 276 equal parts of about 4.35 ¢ each. Each step represents a frequency ratio of 2^1/276, or the 276th root of 2.

Theory

276edo's fifth is quite bad, but it corresponds to 12edo's fifth, which means the patent val tempers out the Pythagorean comma. It thus supports compton, owing to the fact that it is a 12edo fifth. In the 7-limit, it supports grendel.

Its sharp fifth comes from 46edo, and the 276b val in the 5-limit supports hanson. In the 7-limit, it supports quadritikleismic.

Odd harmonics

Approximation of odd harmonics in 276edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.96	+0.64	+0.74	+0.44	+0.86	-1.40	-1.31	-0.61	-1.86	-1.22	+2.16
	Relative (%)	-45.0	+14.8	+17.0	+10.1	+19.7	-32.1	-30.2	-14.0	-42.8	-28.0	+49.7
Steps (reduced)		437 (161)	641 (89)	775 (223)	875 (47)	955 (127)	1021 (193)	1078 (250)	1128 (24)	1172 (68)	1212 (108)	1249 (145)

Subsets and supersets

Since 276 factors into 2² × 3 × 23, 276edo has subset edos 2, 3, 4, 6, 12, 23, 46, 69, 92, 138. 552edo, which doubles it, corrects its approximation of harmonic 3.

Intervals

See Table of 276edo intervals.

Music

Eliora, Sevish, and Evanescence

• What The Zoon (Mashup) (2021) – 12edo and 23edo polysystemic