Guitar in 19-EDO

Introduction

The layout of the guitar lends itself to equal temperament. It's easier to cut fret slots in straight lines and it is easier the leave frets unbent.

Any tuning with a small interval between notes might be difficult to construct a playable fretboard, but, it seems anything up to 24 EDO is generally playable over two octaves at 647 mm scale, with some examples out there of 31-EDO and 34-EDO as well, sometimes going fretless in the upper octave.

19-EDO is easy to construct and fairly easy to play.

Tuning the strings:

There are dozens of ways to tune a guitar in 12-EDO, so, I guess you could say there are nineteens of ways to tune in 19-EDO.

My approach is to use a chromatic tuner that displays cents.

I assume A=440 Hz to be my general reference point, so tuning the A string is easy - just tune it to A.

Every fourth up tunes 5.26 cents sharp, and every fourth down tunes 5.26 cents flat. So, tune E 5.3 cents flat and D 5.3 cents sharp, then tune G 10.5 cents sharp and B 10.5 cents flat.

Chords and scales:

Playing the 19-EDO guitar is a lot like playing the 12-EDO guitar, especially if you aren't looking at what you are doing. There are more frets, but the hand positions are more or less the same. The tricky part is stopping to think if something is a sharp or a flat, but noodling around, you can quickly find what works and what does not work.

If you want to play an open A chord, you might have a little trouble at first, cramming three fingers into one fret, now that that one fret is essentially 2/3 the size. If you are staring at your hand, it might be tempting to fret the second fret as you would in 12-EDO, but that will just yield an A half diminished chord with an augmented seventh. Pretty icky-sounding, if you expect an A chord. Instead, fret the third fret. Bingo.

If you are familiar with the movable form of that chord, you can now do that as well, simply by keeping two frets space between bars instead of one.

Now, try an open E chord. Again, you might think to fret the first fret on the third string and the second fret on the fourth and fifth strings. The first fret will be correct, because the chord has G# there, but you will want E and B natural for it to sound right, so the other fret should be moved up to three.

You can also formulate a movable shape from that.