# Skip fretting system 87 2 17

One way to play 87-edo is on a 43.5-edo guitar, tuning each pair of adjacent strings 17\87 apart. That's 234.5 cents, 3.4 cents sharp of a just 8:7.

This tuning is probably more applicable to keyboards than real stringed instruments -- but then again Ron Sword has built a 46-edo guitar, and claims it is playable.

Among the possible skip fretting systems for 87-edo, one reason (87,2,17) is special is that every 17-limit interval spans at most 8 frets.

The following table describes where all the primes intervals lie in the (87,2,17) system:

note fretboard position
0 steps = 1 % 1 string 0 fret 0
87 steps = 2 % 1 string 5 fret 1
51 steps = 3 % 2 string 3 fret 0
28 steps = 5 % 4 string 2 fret - 3
70 steps = 7 % 4 string 4 fret 1
40 steps = 11 % 8 string 2 fret 3
61 steps = 13 % 8 string 3 fret 5
8 steps = 17 % 16 string 0 fret 4
22 steps = 19 % 16 string 0 fret 11
46 steps = 23 % 16 string 2 fret 6
75 steps = 29 % 16 string 3 fret 12
83 steps = 31 % 16 string 5 fret - 1

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.