Skip fretting system 58 2 15

One way to play 58-edo on a 29-edo guitar is to tune each pair of adjacent strings 15\58 apart. That's about 310.3 cents, or 5.3 cents flat of 6:5.

Among the possible skip fretting systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets.

Here is where all the primes intervals in the (58,2,15) system lie:

note	fretboard position
0 steps = 1 % 1	string 0 fret 0
58 steps = 2 % 1	string 4 fret - 1
34 steps = 3 % 2	string 2 fret 2
19 steps = 5 % 4	string 1 fret 2
47 steps = 7 % 4	string 3 fret 1
27 steps = 11 % 8	string 1 fret 6
41 steps = 13 % 8	string 3 fret - 2
5 steps = 17 % 16	string - 1 fret 10
14 steps = 19 % 16	string 0 fret 7
30 steps = 23 % 16	string 2 fret 0
50 steps = 29 % 16	string 2 fret 10
55 steps = 31 % 16	string 3 fret 5

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.

Comparison to 31-edo

A 29-edo guitar is not much easier to play than a 31-edo guitar. In particular you'll need to use your fingernail to fret the highest notes. A skip-fretting system is substantially more confusing than one that includes every note. While 58-edo is more faithful to the harmonic series, 31-edo is nonetheless exceptionally good.