2edt
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Prime factorization
2 (prime)
Step size
950.978¢
Octave
1\2edt (950.978¢)
(convergent)
Consistency limit
2
Distinct consistency limit
1
Special properties
| ← 1edt | 2edt | 3edt → |
(convergent)
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
| 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 (%) | -26.2 | +0.0 | +47.6 | +7.0 | -26.2 | +45.8 | +21.4 | +0.0 | -19.2 | -36.5 | +47.6 | |
| 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.