# 1905370edo

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Prime factorization
2 × 5 × 190537
Step size
0.000629799¢
Fifth
1114570\1905370 (701.955¢) (→111457\190537)
Semitones (A1:m2)
180510:143260 (113.7¢ : 90.22¢)
Consistency limit
17
Distinct consistency limit
17

← 1905369edo | 1905370edo | 1905371edo → |

**1905370 equal divisions of the octave** (abbreviated **1905370edo** or **1905370ed2**), also called **1905370-tone equal temperament** (**1905370tet**) or **1905370 equal temperament** (**1905370et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1905370 equal parts of about 0.00063 ¢ each. Each step represents a frequency ratio of 2^{1/1905370}, or the 1905370th root of 2.

## Theory

This EDO has a consistency limit of 17, but seems to be at its best in the 2.3.5.7.13.17 subgroup. It tempers out the Archangelic comma in the 3-limit.

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

Error | Absolute (¢) | +0.000000 | +0.000000 | -0.000084 | +0.000096 | -0.000141 | +0.000110 | -0.000047 | +0.000223 | -0.000154 | -0.000157 | -0.000015 |

Relative (%) | +0.0 | +0.0 | -13.4 | +15.2 | -22.3 | +17.4 | -7.4 | +35.4 | -24.4 | -24.9 | -2.4 | |

Steps (reduced) |
1905370 (0) |
3019940 (1114570) |
4424132 (613392) |
5349050 (1538310) |
6591497 (875387) |
7050707 (1334597) |
7788129 (166649) |
8093874 (472394) |
8619059 (997579) |
9256251 (1634771) |
9439577 (1818097) |