398edo

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398edo

399edo →

Prime factorization	2 × 199
Step size	3.01508 ¢
Fifth	233\398 (702.513 ¢)
Semitones (A1:m2)	39:29 (117.6 ¢ : 87.44 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

398et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 1280000000/1275989841, 65625/65536, 102760448/102515625 and 200120949/200000000 in the 7-limit; 1073741824/1071794405, 100663296/100656875, 161280/161051, 35156250/35153041, 2097152/2096325, 4000/3993, 2734375/2725888, 496125/495616, 131072/130977, 6250/6237, 9765625/9732096, 4302592/4296875, 352947/352000, 422576/421875, 184877/184320, 3025/3024, 9453125/9437184 and 456533/455625 in the 11-limit. It supports quartonic, yarman, bisupermajor and semiquindromeda.

Prime harmonics

Approximation of prime harmonics in 398edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.56	-0.38	-0.99	+0.44	+0.68	+0.57	+0.98	-1.14	-1.44	+0.69
	Relative (%)	+0.0	+18.5	-12.7	-32.7	+14.6	+22.5	+19.0	+32.5	-37.8	-47.6	+23.0
Steps (reduced)		398 (0)	631 (233)	924 (128)	1117 (321)	1377 (183)	1473 (279)	1627 (35)	1691 (99)	1800 (208)	1933 (341)	1972 (380)

Subsets and supersets

398 factors into 2 × 199, with 2edo and 199edo as its subset edos.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[631 -398⟩	[⟨398 631]]	-0.1759	0.1759	5.83
2.3.5	390625000/387420489, [-53 10 16⟩	[⟨398 631 924]]	-0.0622	0.2157	7.15
2.3.5.7	10976/10935, 65625/65536, 1280000000/1275989841	[⟨398 631 924 1117]]	+0.0412	0.2588	8.58
2.3.5.7.11	3025/3024, 6250/6237, 10976/10935, 496125/495616	[⟨398 631 924 1117 1377]]	+0.0075	0.2411	8.00
2.3.5.7.11.13	2080/2079, 625/624, 3025/3024, 4096/4095, 10976/10935	[⟨398 631 924 1117 1377 1473]]	-0.0243	0.2313	7.67

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	5\398	15.08	126/125	Yarman
1	183\398	551.76	11/8	Emka / Emkay
2	54\398	162.81	11/10	Kwazy / Bisupermajor

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct