How to tune a 19edo guitar by ear

If you have a tuner that shows cents, or a synthesizer you can tune to, it's an easy matter to tune the open strings of your 19edo guitar to precise 19edo reference frequencies. This article is about how to get it very close to 19edo (and more importantly sounding good) with no other devices.

1. Tune the strings very roughly to EADGBE (either by ear or using the frets). If you start with some of the strings very far off, the change in tension during tuning can cause the neck to change shape slightly, so it's best to start with it in rough tune.
2. Tune the high E string precisely to whatever you want E to be. Keep in mind that at most one pitch can be exactly shared between 19edo and 12edo-A440, so unless you want that pitch to be E, E should be something different from the standard 12edo-A440 value of 659.255 Hz. Which option to choose depends only on any other instruments you happen to be playing along with. (See also The Great Xenharmonic Fixed-Pitch Instrument Database.)
3. Tune the G string to a beatless 5/3 below E. This uses the mathematical coincidence that the difference between a pure 5/3 and a 19edo major sixth is a mere 0.148 cents and therefore negligible.
4. Tune the B string so that the G-B major third and the C-E major third (using the C at fret 2 on the B string) are equally flat. This may be the trickiest part of the procedure, because if you tune G-B to a pure 5/4 then major thirds between the top two strings will be much too flat, and vice versa. During this step, use your ear to achieve a fair compromise between the two kinds of major thirds. Note: If your guitar is set up poorly (for example if the nut height is wrong), the intonation on the first several frets is likely to be off. If so, ignore the C-E major third and use another major third between the B and E strings, higher up the fretboard. Then when you get around to it, set up your guitar correctly. =)
5. Tune the D string to a beatless 5/3 below B.
6. Now tune low E and A strings however you wish. I usually tune the low E to be in tune with the high E, tune A so that the E-A and A-D fourths are equally sharp, and then perhaps make adjustments after listening to a few chords. Tuning the bottom two strings should not be difficult once the top four are perfectly in tune.
7. Enjoy the perfectly sweet 5-limit chords of your 19edo guitar. If some major chords have thirds which are too flat and sour, you most likely need to return to step 4.
8. An alternate and acceptable method is to tune the E on each string to be the same pitch or a beatless octave. This method relies on the quality of the work of the luthier and would not be recommended for temporary fret solutions such as cable tie frets.