19EDO

19-Equal-Divided Octave

One very popular and compatible alternative to twelve tone equally divided octave tuning (standard tuning in the western world) is the nineteen tone equally divided octave.

This tuning offers some intervals closer to just intonation, while not giving up too much with other intervals.  The tuning matches very well with the Germanic music notation of A-G with sharps and flats (I will use # and b as sharp and flat symbols, as I find it to be clear enough for my purposes).  No half sharps nor half flats are necessary.

The notes are

A - 0 cents

A# - 63.16 cents

Bb - 126.32 cents

B - 189.47 cents

B# or Cb - 252.63 cents

C - 315.79 cents

C# - 378.95 cents

Db - 442.11 cents

D - 505.26 cents

D# - 568.42 cents

Eb - 631.58 cents

E - 694.74 cents

E# or Fb - 757.89 cents

F - 821.05 cents

F# - 884.21 cents

Gb - 947.37 cents

G - 1010.53 cents

G# - 1073.68 cents

Ab - 1136.84 cents

This offers advantages in cleaner thirds and sixths at the cost of losing a little from the fifths and fourths; however, the added intervals allow differentiation between many intervals that were enharmonically equivalent in 12-EDO (standard tuning).

Music can be notated with the standard musical staff with the standard set of accidentals.

Fretted instruments are easily constructed with nineteen frets per octave, as the fret spacing is still manageable, and the fret do not need to be curved.

The circle of fifths familiar to most musicians still works, albeit in a different way, yet it is still a closed loop that covers all keys, which is somewhat rare with microtonal music.