I am doing the math to see if I could fit just a full octave on the fingerboard and keep it inside the 22in maximum length. I also thought about making it a headless neck and putting some kind of tuner on the tail end, but I have no experience with that type of setup, so I am not sure that is an option.
Anybody got any suggestions or comments?
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If i look at this picture and estimate how big it is compared to the guy holding it i'd say it's in about the same targetarea as your build.
Allthough i do think you are going to need some real heavy string's if you want to stay in the guitar-range, this link could help you decide a stringauge for your build and the actual pitch you want it to be tuned to http://www.mcdonaldstrings.com/stringxxiii.html
You could use a normal set of string's but then you have to raise the pitch of the intire tunning.
Normally I wouldn't go less than 22 inches for the scale with a guitar, tho' I have got at nylon strung kid's guitar at 17 inch scale length and an Aria kid's steel string at 19 inch scale, but they are a real compromise in terms of string gauge and getting them to play in tune.
Uncle Bob Project
lapstick
Have a look at Fergus Morris's page for inspiration. Clever young chap put the tuners in the cigar box rather than on the headstock....