Skip fretting system 34 2 9

Revision as of 03:43, 2 May 2021 by Jeff Brown (talk | contribs) (start)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.)

Here is where all the primes intervals lie:

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 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.