# Skip fretting system 63 3 17

One way to play 63-edo on a 21-edo guitar is to tune each pair of adjacent strings 17\63 apart. That's about 323.8 cents, or 8.2 cents sharp of 6:5.

Among the possible skip fretting systems for 63-edo, the (63,3,21) system is especially convenient in that every 11-limit interval, and in fact every interval in the 2.3.5.7.11.17.29.31 subgroup, spans at most four frets.

Here is where all the primes intervals lie:

note fretboard position
0 steps = 1 % 1 string 0 fret 0
63 steps = 2 % 1 string 3 fret 4
37 steps = 3 % 2 string 2 fret 1
20 steps = 5 % 4 string 1 fret 1
51 steps = 7 % 4 string 3 fret 0
29 steps = 11 % 8 string 1 fret 4
44 steps = 13 % 8 string 1 fret 9
6 steps = 17 % 16 string 0 fret 2
16 steps = 19 % 16 string - 1 fret 11
33 steps = 23 % 16 string 0 fret 11
54 steps = 29 % 16 string 3 fret 1
60 steps = 31 % 16 string 3 fret 3

From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See Skip fretting system 48 2 13 for details on how that's done.