Skip fretting

(Note: Despite it's name, skip-fretting is relevant not only to fretted stringed instruments, but to the layout of isomorphic two-dimensional grid instruments like the Lumatone and the monome.)

Introduction

Skip fretting (a.k.a. Thanos tuning) allows a player of a fretted stringed instrument to play in a higher EDO than would otherwise be possible or convenient. In most skip-fretting systems, the guitar skips every other fret, so each string has only half of the notes.

The most familiar skip-fretting systems allow someone with an ordinary 12-edo guitar to tune to 24-edo by retuning their guitar, for instance by tuning 450 cents between every pair of adjacent strings. 350 cents, 550 cents etc. would all work too. The even strings have half the notes, and the odd strings have the other half.

Partial skip-fretting

Because the frets on a fretted instrument get closer together toward the bridge - at the first octave they are twice as dense, and at the second octave, four times -- it could be reasonable to include all the frets near the nut, and then switch to a skip-fretting system somewhere for the high notes. To this author's knowledge a partially skip-fretted instrument has not yet been made.

Some notation

Skip-fretting systems can be "isomorphic", with the same distance between every pair of adjacent strings, but they don't have to be. An isomorphic skip-fretting system can be described with three numbers: The EDO it allows one to play, the fraction of that EDO's notes on any particular string, and the number of steps in the EDO between adjacent strings. So, for instance, the system described above for playing 24-edo on a 12-edo guitar could be called a "24 2 9" system (9\24 being equal to 450 cents).

[In retrospect, I wish I had used notation like "2,13\41" instead of "(41,2,13)". Both of those represent the Kite guitar tuning equally unambiguously, but I think the first is clearer.]

Some skip-fretting systems

• The Kite Guitar, system 41 2 13: 41-edo on a 20.5-edo guitar.
• Skip fretting system 48 2 13: 48-edo on a 24-edo guitar.
• Skip fretting system 44 2 11: 44-edo on a 22-edo guitar.
• Skip fretting system 63 3 17: 63-edo on a 21-edo guitar.
• Skip fretting system 58 2 15: 58-edo on a 29-edo guitar.
• Skip fretting system 34 2 9: 34-edo on a 17-edo guitar.
• Skip fretting system 31 2 9: Make the higher register of a 31-edo guitar easier to play by omitting every other fret, while keeping all the frets in the lower register.
• Skip fretting system 41 2 11: A bit narrower than the Kite guitar, with easier-to-reach higher-limit intervals.