# 207edo

 ← 206edo 207edo 208edo →
Prime factorization 32 × 23
Step size 5.7971¢
Fifth 121\207 (701.449¢)
Semitones (A1:m2) 19:16 (110.1¢ : 92.75¢)
Consistency limit 7
Distinct consistency limit 7

207 equal divisions of the octave (abbreviated 207edo or 207ed2), also called 207-tone equal temperament (207tet) or 207 equal temperament (207et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 207 equal parts of about 5.8 ¢ each. Each step represents a frequency ratio of 21/207, or the 207th root of 2.

## Theory

207et tempers out 32805/32768 (schisma) in the 5-limit, 6144/6125 and 19683/19600 in the 7-limit, 441/440 and 43923/43904 in the 11-limit, and 351/350, 676/675, 729/728, 847/845, 1716/1715 in the 13-limit. It serves as a tuning in the 11- and 13-limit for the swetneus temperament. It is significantly more accurate on the 2.3.7.11.13 subgroup, a favorite of many people, and one which contains both 729/728 and 10648/10647, which it tempers out.

### Prime harmonics

Approximation of prime harmonics in 207edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.51 +2.09 -0.71 -0.59 +0.05 -0.61 -1.86 -2.19 +2.31 +2.79
Relative (%) +0.0 -8.7 +36.1 -12.2 -10.2 +0.9 -10.5 -32.1 -37.7 +39.8 +48.1
Steps
(reduced)
207
(0)
328
(121)
481
(67)
581
(167)
716
(95)
766
(145)
846
(18)
879
(51)
936
(108)
1006
(178)
1026
(198)

### Subsets and supersets

Since 207 factors into 32 × 23, 207edo has subset edos 3, 9, 23, and 69.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-328 207 [207 328]] +0.1595 0.1596 2.75
2.3.5 32805/32768, [2 31 -22 [207 328 481]] -0.1942 0.5166 8.91
2.3.5.7 6144/6125, 19683/19600, 50421/50000 [207 328 481 581]] -0.0825 0.4874 8.41
2.3.5.7.11 441/440, 3388/3375, 6144/6125, 19683/19600 [207 328 481 581 716]] -0.0317 0.4477 7.72
2.3.5.7.11.13 351/350, 441/440, 676/675, 847/845, 3584/3575 [207 328 481 581 716 766]] -0.0287 0.4087 7.05
2.3.5.7.11.13.17 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088 [207 328 481 581 716 766 846]] -0.0034 0.3834 6.61

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 25\207 144.93 49/45 Swetneus
1 43\207 249.28 15/13 Hemischis
1 86\207 498.55 4/3 Helmholtz

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