Magic Guitar

Guitars Designed for Magic Temperament

Magic Temperament is a good, mainstream choice for an unequal guitar fretting. It's almost as simple as Meantone but with much improved 9-limit harmony. It can be close enough to just intonation to sound clean within the inherent imprecision of a physical guitar. It has well tuned perfect fifths that will be familiar from 12 note equal temperament. It can be tuned to 41-edo while minimizing the number of frets spaced by a single step. As it isn't a Meantone, it will have comma problems when playing conventional music. Magic supports full 11-limit harmony with acceptable tuning within the appropriate gamut for a guitar.

Fretting Options

A simple Magic fretting can follow either a 19 note (Pengcheng) or 22 note (Haizhou) MOS. A Pengcheng fretting is good ergonomically because the frets will be spaced at intervals of (approximately) two or three steps from 41-edo. It is poor for playing diatonic music because it allows for no comma shifts. A Haizhou fretting has a few frets spaced a comma apart and still allows the 19 notes of the Pengcheng scale to be played on frets spaced a semitoe, 2 steps from 41-edo, apart.

Most frets on either a Haizhou or Pengcheng are spaced a semitoe apart. In both cases, there are three discontinuities to an octave. An isomorphic fretting with equal semitoes right down the neck is possible. In the general case, each string sits on a different foot of Tripod Notation. With equal temperament, a string can morph from one foot to another to become a skip fretting. Given 41-edo, this leads to a fret spacing of 2 steps from 41-edo or 20½-edo or the Kite Guitar.