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).

Approximating using a standard guitar

As 27ed4 is not that far from 12edo in step size, this tuning is quite amenable to the Moving the bridge hack. To do this, you will need an archtop guitar with a floating bridge with at least 2+1/2 inches of play behind the standard bridge position. (You could also entirely unscrew the bridge on another type of guitar and move it back, but this will require drilling new holes, making it a permanent modification that affects the appearance of your guitar.)

As 27ed4 does not have a fret where the octave is, you cannot use that to check for intonation. Instead, the optimal way to tune it is to move the bridge far back enough that the 9th fret is 800 cents above the open tuning. (The precise length needed to do this on a 25.5" scale guitar is 27.9365", but you're unlikely to be able to get that level of precision with a floating bridge, so anywhere between 27.9 and 28 inches should give acceptable results.) This will let you check your intonation both by octaves on the string above and unisons on the string two steps up, allowing you to tweak the position until it sounds right.

If done correctly, it will sound near identical to 27ed4 nearly all the way up to the cutaway, with inconsistent sweet spots at frets 17 and 21 where the notes are one or two steps below what a true 27ed4 guitar would give at that position that can still be highly useful.

Fret number	Cents	Deviation from 27ed4
0 (nut)	0.000	0.000
1	91.841	2.952
2	181.608	3.830
3	271.661	4.994
4	361.189	5.634
5	450.167	5.723
6	538.562	5.229
7	626.350	4.127
8	713.504	2.393
9	800	0.0
10	885.805	-3.083
11	970.889	-6.888
12	1055.234	-11.432
13	1138.795	-16.759
14	1221.544	-22.900
15	1303.466	-29.868
16	1384.501	-37.720 (+6.724)
17	1464.643	-46.467 (-2.023)
18	1543.846	-56.143 (-11.699)
19	1622.081	-66.807
20	1699.315	-78.461
21	1775.519	-91.146 (-2.258)
22	1850.661	-104.894