# 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 21/119, 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 (%) +38.9 -30.9 -7.5 -22.1 +32.8 -35.2 +8.0 -40.8 +49.7 +31.4 -30.4 +38.1
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)
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 (%) +16.8 -10.0 +45.1 -28.3 -38.5 +7.5 +3.7 +45.1 +27.4 +46.9 +0.4 -15.0
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