# 1517edo

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Prime factorization
37 × 41
Step size
0.791035¢
Fifth
887\1517 (701.648¢)
Semitones (A1:m2)
141:116 (111.5¢ : 91.76¢)
Dual sharp fifth
888\1517 (702.439¢) (→24\41)
Dual flat fifth
887\1517 (701.648¢)
Dual major 2nd
258\1517 (204.087¢)
Consistency limit
5
Distinct consistency limit
5

← 1516edo | 1517edo | 1518edo → |

The **1517 equal divisions of the octave**, or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.

## Theory

1517edo is a dual fifths system with a consistency limit of only 5.

The first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 subgroup, 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, [18 -12 2 1 1 0⟩, [44 -4 -9 1 0 -1⟩}.

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | -0.307 | -0.289 | +0.192 | +0.177 | +0.033 | +0.342 | +0.195 | +0.252 | -0.084 | -0.115 | -0.193 |

relative (%) | -39 | -36 | +24 | +22 | +4 | +43 | +25 | +32 | -11 | -15 | -24 | |

Steps (reduced) |
2404 (887) |
3522 (488) |
4259 (1225) |
4809 (258) |
5248 (697) |
5614 (1063) |
5927 (1376) |
6201 (133) |
6444 (376) |
6663 (595) |
6862 (794) |