# 1419edo

Jump to navigation
Jump to search
Prime factorization
3 × 11 × 43
Step size
0.845666¢
Fifth
830\1419 (701.903¢)
Semitones (A1:m2)
134:107 (113.3¢ : 90.49¢)
Consistency limit
25
Distinct consistency limit
25

← 1418edo | 1419edo | 1420edo → |

**1419 equal divisions of the octave** (abbreviated **1419edo** or **1419ed2**), also called **1419-tone equal temperament** (**1419tet**) or **1419 equal temperament** (**1419et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1419 equal parts of about 0.846 ¢ each. Each step represents a frequency ratio of 2^{1/1419}, or the 1419th root of 2.

1419edo is consistent in the 25-odd-limit, and with excellent representation of 31/16 it is a strong no-29's 37-limit tuning. It is also an impressive system in even higher limits, with good tunings on harmonics 43, 47, and 53.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.000 | -0.052 | +0.156 | +0.307 | +0.056 | +0.064 | -0.093 | +0.161 | +0.055 | -0.402 | -0.004 |

Relative (%) | +0.0 | -6.2 | +18.4 | +36.3 | +6.7 | +7.6 | -11.0 | +19.1 | +6.6 | -47.5 | -0.5 | |

Steps (reduced) |
1419 (0) |
2249 (830) |
3295 (457) |
3984 (1146) |
4909 (652) |
5251 (994) |
5800 (124) |
6028 (352) |
6419 (743) |
6893 (1217) |
7030 (1354) |

### Subsets and supersets

Since 1419 factors into 3 × 11 × 43, 1419edo has subset edos 3, 11, 33, 43, 129, and 473.