# 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 3^{1/2}, 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 | +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.