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, this one 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.

Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, 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).

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