Skip fretting system 38 2 11
One way to play 38-edo on a 19-edo guitar is to tune each pair of adjacent strings 11\38 apart, or 347 cents.
Among the possible skip fretting systems for 38-edo, this is particularly convenient because 11/38 is an essentially perfect 11/9, just 0.04 cents from just, making it easy to tune adjacent strings by ear if you can sound the appropriate harmonics, while every other string is a perfect 5th apart, making 5-limit chords intuitive to play if you have previous experience playing members of the mandolin family, while also improving on 19-edo's approximations of nearly all the higher limit harmonics.
Here is where all the primes intervals lie:
note | fretboard position |
---|---|
0 steps = 1 % 1 | string 0 fret 0 |
38 steps = 2 % 1 | string 4 fret - 3 |
22 steps = 3 % 2 | string 2 fret 0 |
12 steps = 5 % 4 | string 2 fret -5 |
31 steps = 7 % 4 | string 3 fret -1 |
17 steps = 11 % 8 | string 1 fret 3 |
27 steps = 13 % 8 | string 3 fret -3 |
3 steps = 17 % 16 | string 1 fret -4 |
9 steps = 19 % 16 | string 1 fret -1 |
20 steps = 23 % 16 | string 2 fret -1 |
33 steps = 29 % 16 | string 3 fret 0 |
36 steps = 31 % 16 | string 4 fret - 4 |
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.