Skip fretting system 27 2 9

A good way to play 27-edo on a 13.5-edo guitar is to tune each pair of adjacent strings 9/27 apart, or the familiar 400 cent major third shared with 12edo.

Among the possible skip fretting systems for 27-edo, the (27, 2, 9) system is especially effective because it makes 5-limit chords easy to play, every interval can be reached with a stretch of 4 frets or less (equivalent to 3.55 on a 12edo guitar) and it can be quickly & easily tuned using an ordinary 12edo guitar tuner, making it well suited to live performance. Since it makes it particularly easy to play music composed using augmented temperament, it could also be called an augmented or major thirds guitar.

It does limit your ability to play more complex septimal and higher-limit chords compared to a full 27edo guitar though, so you might want to use a partial system with the full set of frets in the lower octave and skip-fretting higher up, or have multiple instruments adding the more complex upper range harmonies.

Here is where all the prime intervals lie.

note	fretboard position
0 steps = 1 % 1	string 0 fret 0
27 steps = 2 % 1	string 3 fret 0
16 steps = 3 % 2	string 2 fret -1
9 steps = 5 % 4	string 1 fret 0
22 steps = 7 % 4	string 2 fret 2
12 steps = 11 % 8	string 2 fret -3
19 steps = 13 % 8	string 3 fret -4
2 steps = 17 % 16	string 0 fret 1
7 steps = 19 % 16	string 1 fret -1
14 steps = 23 % 16	string 2 fret -1
23 steps = 29 % 16	string 3 fret -2
26 steps = 31 % 16	string 2 fret 4

From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).