Skip fretting system 34 2 9

One way to play 34-edo on a 17-edo guitar is to tune each pair of adjacent strings 9\34 apart. That's 317.6 cents, just 2 cents sharp of a just 6:5.

Among the possible skip fretting systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.) Since it makes playing music composed using keemun temperament particularly easy, it could also be called a Keemun or Kleismic guitar.

Where the first primes intervals lie

As a diagram

In the following the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.

         headstock on this side
            - 15  9  - 13  -
           13  - 19  -  -  -
            -  -  -  -  - 17
            - 17  -  -  -  -
            -  -  -  -  -  -
   bass     -  - 11  -  1  -  treble
   side     1  - 23  7  -  5  side
            -  5  3  -  - 21
            - 21  - 15  9  -
            9  - 13  - 19  -
           19  -  -  -  -  -
          bridge on this side

As a table

note	fretboard position
0 steps = 1 % 1	string 0 fret 0
34 steps = 2 % 1	string 4 fret - 1
20 steps = 3 % 2	string 2 fret 1
11 steps = 5 % 4	string 1 fret 1
27 steps = 7 % 4	string 3 fret 0
16 steps = 11 % 8	string 2 fret - 1
24 steps = 13 % 8	string 2 fret 3
3 steps = 17 % 16	string - 1 fret 6
8 steps = 19 % 16	string 0 fret 4
18 steps = 23 % 16	string 2 fret 0
29 steps = 29 % 16	string 3 fret 1
32 steps = 31 % 16	string 4 fret - 2

From these, the location of most compound intervals 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.