Skip fretting system 58 4 15

Revision as of 16:36, 10 May 2023 by Jeff Brown (talk | contribs) (Replace some text, which doesn't display correctly on a phone, with an image that has to)

One way to play 58-edo on a 14.5-edo guitar is to tune each pair of adjacent strings 15\58 apart. That's about 310.3 cents, or 5.3 cents flat of 6:5.

Where the first primes intervals lie

In the diagram 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.

Since 58-edo is consistent in the 17-limit plus 29 group, the positions of the harmonics in that group imply how to play every interval in it. For instance, the interval 10:7 lies two strings up on the same fret, because that will take you from harmonic 7 to harmonic 5.

 
Where the harmonics lie in the 15\58 x 4\58 isomorphic layout