Sharpness

The sharpness of an EDO is the number of steps it maps the apotome to; in other words, it is the difference between seven of its best approximation of 3/2 and four octaves.

For example, 12edo maps the apotome to one step; it has a sharpness of 1. We could say it is a sharp-1 EDO. On the other hand, 17edo maps the apotome to two steps, so it is a sharp-2 EDO.

Some EDOs, such as 16edo, have fifths flat enough that the apotome is mapped to a negative number of steps. Since 16edo has the apotome mapped to −1 step, it is a flat-1 EDO.

A sharp-0 EDO is also known as a "perfect EDO".

See also

Kite's theory using the nomenclature of sharpness: (perhaps introducing?)

n-EDO Retuner plugin for Musescore 3.4+: uses sharpness to categorize EDOs for retuning

Sagittal notation's Periodic Table of EDOs: arranges EDOs by their sharpness