119edo

← 118edo

119edo

120edo →

Prime factorization	7 × 17
Step size	10.084 ¢
Fifth	70\119 (705.882 ¢) (→ 10\17)
Semitones (A1:m2)	14:7 (141.2 ¢ : 70.59 ¢)
Dual sharp fifth	70\119 (705.882 ¢) (→ 10\17)
Dual flat fifth	69\119 (695.798 ¢)
Dual major 2nd	20\119 (201.681 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

119edo is inconsistent in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the optimal patent val for the 11-limit androboh and quasitemp temperaments. The patent val also tunes the 11-limit quadrawell temperament. 119c val tunes treecreeper, sensus, and senator as high as the 17-limit.

Odd harmonics

Approximation of odd harmonics in 119edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25	27	29	31	33	35	37	39	41
Error	Absolute (¢)	+3.93	-3.12	-0.76	-2.23	+3.30	-3.55	+0.81	-4.12	+5.01	+3.17	-3.06	+3.84	+1.70	-1.01	+4.54	-2.85	-3.88	+0.76	+0.37	+4.55
	Relative (%)	+38.9	-30.9	-7.5	-22.1	+32.8	-35.2	+8.0	-40.8	+49.7	+31.4	-30.4	+38.1	+16.8	-10.0	+45.1	-28.3	-38.5	+7.5	+3.7	+45.1
Steps (reduced)		189 (70)	276 (38)	334 (96)	377 (20)	412 (55)	440 (83)	465 (108)	486 (10)	506 (30)	523 (47)	538 (62)	553 (77)	566 (90)	578 (102)	590 (114)	600 (5)	610 (15)	620 (25)	629 (34)	638 (43)

Subsets and supersets

Since 119edo factors as 7 × 17, it contains 7edo and 17edo as a subset. Hence it supports circles of fifths of those respective equal temperaments.

Scales

• Approximation of 2/7 comma meantone: 19 19 19 12 19 19 19 19 12
• Approximation of half comma eventone: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2