Skip fretting system 48 2 13

One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible skip fretting systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group. Since it makes it particularly easy to play music composed in doublewide temperament, it could also be called a doublewide guitar.

Here is where all the primes intervals lie.

note	fretboard position
0 steps = 1 % 1	string 0 fret 0
48 steps = 2 % 1	string 4 fret -2
28 steps = 3 % 2	string 2 fret 1
15 steps = 5 % 4	string 1 fret 1
39 steps = 7 % 4	string 3 fret 0
22 steps = 11 % 8	string 2 fret -2
34 steps = 13 % 8	string 2 fret 4
4 steps = 17 % 16	string 0 fret 2
12 steps = 19 % 16	string 0 fret 6
25 steps = 23 % 16	string 1 fret 6
41 steps = 29 % 16	string 3 fret 1
46 steps = 31 % 16	string 4 fret -3

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).