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

119 equal divisions of the octave (abbreviated 119edo or 119ed2), also called 119-tone equal temperament (119tet) or 119 equal temperament (119et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 119 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of 2^1/119, or the 119th root of 2.

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
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
	relative (%)	+39	-31	-8	-22	+33	-35	+8	-41	+50	+31	-30	+38
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)

Approximation of odd harmonics in 119edo (continued)

Harmonic		27	29	31	33	35	37	39	41	43	45	47	49
Error	absolute (¢)	+1.70	-1.01	+4.54	-2.85	-3.88	+0.76	+0.37	+4.55	+2.77	+4.73	+0.04	-1.52
	relative (%)	+17	-10	+45	-28	-38	+8	+4	+45	+27	+47	+0	-15
Steps (reduced)		566 (90)	578 (102)	590 (114)	600 (5)	610 (15)	620 (25)	629 (34)	638 (43)	646 (51)	654 (59)	661 (66)	668 (73)

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