296edo

The 296 equal temperament divides the octave into 296 equal parts of 4.054 cents each.

In the 5-limit, 296et not only tempers out the semicomma of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its optimal patent val, and tempers out the minortone comma, [-16 35 -17⟩. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out 4375/4374 and 16875/16807, supporting 7-limit octoid temperament. In the 11-limit, it tempers out 1375/1372, 6250/6237, 540/539, 4000/3993 and 3025/3024, and in the 13-limit 625/624, 729/728, 1575/1573, 1716/1715, 2080/2079, so that it also supports the 11- and 13-limit versions of octoid.

296 is divisible by 2, 4, 8, 37, 74 and 148.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-469 296⟩	[⟨296 469]]	+0.1904	0.1905	4.70
2.3.5	2109375/2097152, [-16 35 -17⟩	[⟨296 469 687]]	+0.2962	0.2158	5.32
2.3.5.7	4375/4374, 16875/16807, 2100875/2097152	[⟨296 469 687 831]]	+0.2138	0.2350	5.80
2.3.5.7.11	540/539, 1375/1372, 4000/3993, 2100875/2097152	[⟨296 469 687 831 1024]]	+0.1691	0.2284	5.63
2.3.5.7.11.13	540/539, 625/624, 729/728, 1375/1372, 15379/15360	[⟨296 469 687 831 1024 1095]]	+0.2012	0.2206	5.44