# Skip fretting system 90 5 17

One can play in 90-edo on an 18-edo guitar, by tuning the strings 17\90 (226 and 2/3 cents) apart. The resulting system allows a player to reach any 13-limit interval by crossing a maximum of only 4 frets. Octaves lie across six open strings and one fret, or on the same string 18 frets up (because 90 is divisible by 18).

For string players, a drawback of this system is that harmonics 3, 7 and 13 all lie on the same string, so only one of them can be played at a time. (For keyboardists this is irrelevant, as all three notes can be played simultaneously.)

The primes intervals lie in the following places:

note fretboard position
0 steps = 1 % 1 string 0 fret 0
90 steps = 2 % 1 string 5 fret 1
53 steps = 3 % 2 string 4 fret - 3
29 steps = 5 % 4 string 2 fret - 1
73 steps = 7 % 4 string 4 fret 1
41 steps = 11 % 8 string 3 fret - 2
63 steps = 13 % 8 string 4 fret - 1
8 steps = 17 % 16 string - 1 fret 5
22 steps = 19 % 16 string 1 fret 1
47 steps = 23 % 16 string 1 fret 6
77 steps = 29 % 16 string 1 fret 12
86 steps = 31 % 16 string 3 fret 7

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.