190edo

← 189edo

190edo

191edo →

Prime factorization	2 × 5 × 19
Step size	6.31579 ¢
Fifth	111\190 (701.053 ¢)
Semitones (A1:m2)	17:15 (107.4 ¢ : 94.74 ¢)
Consistency limit	15
Distinct consistency limit	15

The 190 equal divisions of the octave (190edo) or 190(-tone) equal temperament (190tet, 190et) when view from a regular temperament perspective, divides the octave into 190 equal parts of about 6.32 cents each.

Theory

190edo is interesting because of the utility of its approximations; it tempers out 1029/1024, 4375/4374, 385/384, 441/440, 3025/3024 and 9801/9800. It provides the optimal patent val for both the 7- and 11-limit versions of unidec, the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament portent, which tempers out 385/384 and 441/440, and gamelan, the rank-3 7-limit temperament which tempers out 1029/1024, as well as slendric, the 2.3.7 subgroup temperament featured in the #Music section. In the 13-limit, 190et tempers out 847/845, 625/624, 729/728, 1575/1573 and 1001/1000, and provides the optimal patent val for the ekadash temperament and the rank-3 portentous temperament.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-301 190⟩	[⟨190 301]]	+0.285	0.285	4.51
2.3.5	2109375/2097152, [-7 22 -12⟩	[⟨190 301 441]]	+0.341	0.246	3.89
2.3.5.7	1029/1024, 4375/4374, 235298/234375	[⟨190 301 441 533]]	+0.479	0.321	5.07
2.3.5.7.11	385/384, 441/440, 4375/4374, 234375/234256	[⟨190 301 441 533 657]]	+0.490	0.288	4.55
2.3.5.7.11.13	385/384, 441/440, 625/624, 729/728, 847/845	[⟨190 301 441 533 657 703]]	+0.432	0.293	4.63

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	37\190	233.68	8/7	Slendric
1	43\190	271.58	75/64	Orson / sabric
1	49\190	309.47	448/375	Triwell
1	71\190	448.42	35/27	Semidimfourth
1	83\190	524.21	65/48	Widefourth
2	28\190	176.84	195/176	Quatracot
2	29\190	183.16	10/9	Unidec / ekadash
2	59\190 (36\190)	372.63 (227.37)	26/21 (297/260)	Essence
2	71\190 (24\190)	448.42 (151.58)	35/27 (12/11)	Neusec
5	79\190 (3\190)	498.95 (18.95)	4/3 (81/80)	Pental
10	50\190 (7\190)	315.79 (45.79)	6/5 (40/39)	Deca
10	79\190 (3\190)	498.95 (18.95)	4/3 (81/80)	Decal
19	79\190 (1\190)	498.95 (6.32)	4/3 (225/224)	Enneadecal
38	79\190 (1\190)	498.95 (6.32)	4/3 (225/224)	Hemienneadecal

Scales

• Slendric5
• Slendric6
• Slendric11
• Slendric16

Music

• The 11th Slendric Fanfare
• 16 Slendric Virgins by Chris Vaisvil