# 3224edo

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Prime factorization
2
Step size
0.372208¢
Fifth
1886\3224 (701.985¢) (→943\1612)
Semitones (A1:m2)
306:242 (113.9¢ : 90.07¢)
Consistency limit
17
Distinct consistency limit
17

← 3223edo | 3224edo | 3225edo → |

^{3}× 13 × 31**3224 equal divisions of the octave** (abbreviated **3224edo** or **3224ed2**), also called **3224-tone equal temperament** (**3224tet**) or **3224 equal temperament** (**3224et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3224 equal parts of about 0.372 ¢ each. Each step represents a frequency ratio of 2^{1/3224}, or the 3224th root of 2.

3224edo is consistent in the 17-odd-limit and is a strong no-19s 29-limit tuning. It improves 1612edo's mapping of 7 and 11.

It tunes a number of rank-3 very high accuracy temperaments, tempering out [3 -24 3 10⟩, [0 -11 -7 12⟩, [-3 2 -17 14⟩.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | +0.030 | +0.039 | +0.033 | -0.077 | -0.081 | +0.007 | -0.118 | +0.013 | -0.049 | -0.122 |

Relative (%) | +0.0 | +8.1 | +10.4 | +8.8 | -20.8 | -21.8 | +2.0 | -31.8 | +3.6 | -13.1 | -32.9 | |

Steps (reduced) |
3224 (0) |
5110 (1886) |
7486 (1038) |
9051 (2603) |
11153 (1481) |
11930 (2258) |
13178 (282) |
13695 (799) |
14584 (1688) |
15662 (2766) |
15972 (3076) |