31 Tone Equal Temperament

Enharmonic Equivalents in 31-ET

An enharmonic equivalent refers to two or more spellings that refer to the same note. The enharmonic equivalents in 31-ET are different from those in 12-ET. There are enharmonic equivalents in 12-ET that refer to two different notes in 31-ET.

Enharmonic Equivalents in 12-ET are not Equivalent in 31-ET

In 12-ET, notes of the diatonic scale are separated by two half-steps, except for E/F and B/C, which are separated by one half step. The enharmonic equivalences that exist in this system are thus of the form C#=Db, or E#=F and E=Fb. None of these notes are equivalent in 31-ET. In 31-ET, these pairings all involve two distinct notes, separated by a diesis, the smallest step in this tuning.

The Enharmonic Equivalences of 31-ET

In 31-ET, there are not just sharps and flats but semisharps and semiflats; see music notation in 31-ET for a full explanation. The enharmonic equivalences in 31-ET all involve semisharps or semiflats. It is useful to know that in 31-ET, two notes are never enharmonically equivalent unless exactly one of them is a semi-accidental.

Between two of the wider-spaced notes, such as C and D, there are four enharmonic equivalents: C semisharp=D double flat, C sharp = D flat-and-a-half, C sharp-and-a-half=D flat, and C double sharp = D semiflat.

Between two of the closer-spaced notes, such as E and F, there are two enharmonic equivalents: E semisharp = F flat, and E sharp = F semiflat.

Back to notation in 31-ET.