RE: [tuning] construction of a guitar tuning to play barbershop i n.

Justin -- it's been shown pretty convincingly that barbershop tuning is
adaptive -- i.e., it relies on its effect on the ability of a given pitch
class to be intoned in several slightly different ways -- so it could be
tricky to find a fretting that works. For example, it seems that the melody
(usually sung by the second-highest and loudest voice) tends to be in
Pythagorean while the harmonies are often just (up to 9-limit) relative to
that. So you'd need a way to be able to play each note of the Pythagorean
scale as the root, third, fifth, seventh, or ninth of a 4:5:6:7:9 dominant
ninth chord in order to cover a good chunk of what Barbershop does -- right
off the bat, I'm not seeing a simple solution with a relatively small number
of frets.