A near-universal microtonal fretting system

Many of you will be aware of my "Choob" guitar design whose frets are made by lacing a continuous length of 1 mm dia nylon monofilament through holes drilled in a carbon-fibre tube.

I had the idea to instead screw on two strips of aluminium, one on each side of the fingerboard with 1 mm grooves machined in it at the fret positions so that it could be refretted very quickly and easily by wrapping the fret-line right around the tube instead of painstakingly feeding it through holes while peering down inside the tube.

This opens up the possibility of having _many_ grooves machined so that the fretting could be changed easily between different temperaments and even JI.

It turns out that if you have adjustable saddles with +-6 mm of travel about their compensated position you can obtain an extraordinary number of popular microtonal frettings exactly. The trick is to cut grooves for 154-EDO, i.e. 154 fret positions to the octave, with the saddles at the middle of their travel. Then by moving the saddles toward the nut we can cause first the 153rd and then the 152nd fret poition to become the octave position (approx halfway between saddle and nut) and by moving the saddles away from the nut we can cause the 155th and 156th fret positions to become the octave.

If you look at this list of 5 consecutive large EDOs you will find the following popular subsets.

152 Every 8th position gives 19-EDO
153 Every 9th position gives 17-EDO
154 Every 7th position gives 22-ED0
155 Every 5th position gives 31-EDO
156 Every 13th position gives 12-EDO

152 also supports 5-limit JI to high precision and gives near-11-limit-JI.

Complete list of EDOs supported exactly:
5 6 7 8 9 11 12 13 14 17 19 22 26 31 38 39 51 52 76 77 78 152 153 154 155 156

Perhaps someone can generate a list of all the notable linear temperaments that are thereby supported.

All these available on the one instrument just by re-wrapping the fretline and adjusting the saddles! I hasten to add that such an instrument doesn't yet exist. There are a number of problems still to be solved.

-- Dave Keenan