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Similar to the radius on a double bass, in other words? Has any company made one? I do understand all of the reasons not to want a large radius. But I'd still like to play one.
You probably mean large curvature (= small radius). On a string bass the fingerboard radius might be 3.5" (it's probably a compound radius) -- so you can bow one string at a time. Never heard of a guitar with so much curvature. On guitars the fretboard radius (if the fretboard isn't flat) might be anywhere from 12" to maybe 16" (sometimes less -- old Fenders maybe were 7.5").
I've played some old Hofners and Framus guitars which had a a really small radius. They were very uncomfortable to play, why would you want to play one especially a gyspy guitar.
The only electric instrument that I am aware of that has this is a custom made Fodera electric bass that was made for Victor Wooten.
I'm sure Fodera would make a guitar version, but it won't be cheap.
Yes, I did mean to ask about a small radius. It may seem like a peculiar thing to want. It comes from playing a cello, holding it like a guitar. This may seem absurd, given the obvious limitations--the way the right hand would have to move to strike strings, the difficulty of striking chords with a pick, etc. My question arises, however, from experimenting with playing a cello like a guitar, and fingerpicking, which avoids the problems with the pick. This may seem to be a stretch, but it's something that cello players, faced with a small radius neck, experiment with, with varying degrees of success. Not me, here, and not a swing song:
The trouble is that the strings are of course heavier, so cellists end up playing it much like a bass. What's appealing about it, as a guitarist, is that it allows one to grab and pull strings more cleanly--since the strings are not on the same plane, and are more widely spaced apart, the right-hand fingers can pull them with more force without having to worry about striking adjacent strings. (Navigating the left hand around a curved shape is tactilely interesting, too, but that seems too obscure a pleasure to celebrate.)
Oddly enough, this showed up on someone's IG story today. https://www.instagram.com/p/CQWnDEqqnGV/?utm_medium=copy_link
You should try playing a bass or tenor "viola da gamba." They are bowed insruments but have 6 strings, a wide and curved neck, and even frets! They're even tuned (relatively) like a lute.
I have two Guitarra Portuguesa, both have a radius around 4 or 4.5 inches, although obviously a shorter scale length...perhaps a relative like a cittern, octave mandola or bouzouki might have a similar tight radius.