Skip fretting system 94 7 16

One way to play 94-edo on a two-dimension grid is to put 7\94 between each column and 16\94 between each row of notes.

Among the possible layouts for 94-edo, the 7\94 x 16\94 system is remarkably convenient, in that every 13-limit interval spans at most 6 columns ("strings") and 8 rows ("frets"), and minor and major triads in close position fit in a 4x3 grid. In the 9-limit the octave is even more compact, spanning only 6 strings by 5 frets.

Feasibility for stringed instruments

The 7\94 x 16\94 layout is feasible as a skip fretting system for stringed instruments. It requires only 94/7 = 13.429 frets per octave. However, on an instrument with only 6 strings and 24 frets, there will be no unisons, and no octaves available for notes on the middle four strings.

Layout

frequency	fretboard position
0 steps ~ 1 % 1	string 0 fret 0
0 steps ~ 1 % 1	string 0 fret 0
94 steps ~ 2 % 1	string 5 fret 2
55 steps ~ 3 % 2	string 3 fret 1
30 steps ~ 5 % 4	string 1 fret 2
76 steps ~ 7 % 4	string 3 fret 4
16 steps ~ 9 % 8	string 1 fret 0
43 steps ~ 11 % 8	string 4 fret -3
66 steps ~ 13 % 8	string 5 fret -2
85 steps ~ 15 % 8	string 4 fret 3
8 steps ~ 17 % 16	string 4 fret -8
23 steps ~ 19 % 16	string 1 fret 1
37 steps ~ 21 % 16	string 1 fret 3
49 steps ~ 23 % 16	string 0 fret 7
61 steps ~ 25 % 16	string 6 fret -5
71 steps ~ 27 % 16	string 4 fret 1
81 steps ~ 29 % 16	string 2 fret 7
90 steps ~ 31 % 16	string 3 fret 6

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 an exmaple of how that's done.