# Ed5/4

The **equal division of 5/4** (**ed5/4**) is a tuning obtained by dividing the just major third (5/4) in a certain number of equal steps.

## Properties

Division of 5/4 into equal parts does not necessarily imply directly using this interval as an equivalence. The question of equivalence is still in its infancy. The utility of 5/4 as a base though, is apparent by providing a novel consonance after 3, and being the octave-reduced basis for 5-limit harmony. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

5/4 is particularly narrow as far as equivalences go and it is difficult to fit consonant chords in it, so we might consider using 5/4^{2} = 25/16 as the equivalence instead.

ED5/4 tuning systems that accurately represent the intervals 10/9 and 9/8 include: 17ed5/4 (0.61 cent error), 19ed5/4 (0.59 cent error), and 36ed5/4 (0.02 cent error).

17ed5/4, 19ed5/4 and 36ed5/4 are to the division of the major third what 13ed4/3, 15ed4/3, and 28ed4/3 are to the division of the fourth, what 9ed3/2, 11ed3/2, and 20ed3/2 are to the division of the fifth, and what 5edo, 7edo, and 12edo are to the division of the octave.

## Individual pages for ed5/4's

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |

20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |

30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |

40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |