# 2edt

 ← 1edt 2edt 3edt →
Prime factorization 2 (prime)
Step size 950.978¢
Octave 1\2edt (950.978¢)
(convergent)
Consistency limit 2
Distinct consistency limit 1
Special properties

2 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 2edt or 2ed3), is a nonoctave tuning system that divides the interval of 3/1 into 2 equal parts of about 951 ¢ each. Each step represents a frequency ratio of 31/2, or the 2nd root of 3.

## Theory

As a temperament in the 3.5 subgroup, it tempers out 27/25, equating 5/3 with 9/5.

Since 26/15 is a convergent of sqrt(3), 26/15 (and its tritave complement 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)2 / (3/1) = 676/675, the island comma.

### Harmonics

Approximation of harmonics in 2edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) -249 +0 +453 +67 -249 +435 +204 +0 -182 -347 +453
relative (%) -26 +0 +48 +7 -26 +46 +21 +0 -19 -37 +48
Steps
(reduced)
1
(1)
2
(0)
3
(1)
3
(1)
3
(1)
4
(0)
4
(0)
4
(0)
4
(0)
4
(0)
5
(1)

## Relationship to octave temperaments

One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as monzismic.