Equal Division of the Octave (EDO)

EDO stands for Equal Division of the Octave: the number of equal pieces, or intervals, into which an octave is divided. In Dorico Pro, you can create any number of divisions of an octave and design custom key signatures and custom accidentals for each tonality system.

Traditional Western harmony is based on equal temperament, another method used to describe tonality systems, or 12-EDO, as the traditional scale from C-C is made up of twelve steps spread across the seven notes in the scale.

When you edit the 12-EDO tonality system in the Edit Tonality System dialog, you can see how these steps are divided across each interval in the scale. For example, between the notes A and B there are two steps, but between B and C there is one step. This is because in 12-EDO, each step represents a half-step (semitone), and there are two half-steps between A and B according to standard equal temperament, but only one half-step between B and C.

To have the smallest step in the tonality system be a quarter tone rather than a half-step (semitone), the octave must be divided into twice as many equal divisions as 12-EDO. Therefore, to be able to use quarter tone accidentals in a project, you must choose the Equal temperament (24-EDO) tonality system for the project.

Although you can divide the octave into any number of divisions, to be able to show a standard Western key signature, the number of equal divisions in the octave must be divisible by 12.

EDO also allows you to map non-conventional Western pitches on to the seven note names A-G, and create a coherent notation to express that, because there is no limit to how you can divide the octave. For example, Turkish music is traditionally divided in 53-EDO, the division of which is usually spread across the notes A-A with the following number of divisions for each interval: 9-4-9-9-9-4-9.