198edo

The 198 equal divisions of the octave (198edo), or the 198(-tone) equal temperament (198tet, 198et) when viewed from a regular temperament perspective, divides the octave into 198 parts of 6.061 cents each.

Theory

198edo is contorted in the 7-limit, with the same tuning as 99edo, but makes for a good 11- and 13-limit system. Like 99, it tempers out 2401/2400, 4375/4374, 3136/3125, 5120/5103 and 6144/6125 in the 7-limit; in the 11-limit it tempers 3025/3024, 9801/9800 and 14641/14580; and in the 13-limit 352/351, 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.

It is the optimal patent val for the rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as hemimist, and namaka. It is distinctly consistent through the 15-odd-limit. It factors into 2 × 3² × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.

Intervals

Main article: Table of 198edo intervals

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5.7.11	2401/2400, 3025/3024, 3136/3125, 4375/4374	[⟨198 314 460 556 685]]	-0.344	0.291	4.80
2.3.5.7.11.13	352/351, 676/675, 847/845, 1716/1715, 3025/3024	[⟨198 314 460 556 685 733]]	-0.372	0.273	4.50

Rank-2 temperaments

Note: temperaments supported by 99et are not included.

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
2	38\198	230.30	8/7	Hemigamera
2	40\198	242.42	121/105	Semiseptiquarter
2	47\198 (52\198)	315.15 (284.85)	6/5 (33/28)	Semiparakleismic
2	58\198 (41\198)	351.52 (248.48)	49/40 (15/13)	Semihemi
2	56\198 (43\198)	339.39 (260.61)	243/200 (64/55)	Hemiamity
2	74\198 (25\198)	448.48 (151.51)	35/27 (12/11)	Neusec
3	41\198 (25\198)	248.48 (151.51)	15/13 (12/11)	Hemimist
18	52\198 (3\198)	315.15 (18.18)	6/5 (99/98)	Hemiennealimmal
22	82\198 (1\198)	496.97 (6.06)	4/3 (385/384)	Icosidillic