someone gave me a beautiful small, 6x6x3h, box and i want to us it for m next build.  Could someone help me figure out what size to build.  Is there a formula or rule for scale length based on size of] box? for scale length based on size of] box?

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I think scale appearance may be more important than what kind of sound will you get.  I think a short VSL maybe in the scale of a Uke might be better visually.  I think the deep box should give you good sound but you might want to put a pickup on it for volume unless that's not a factor to you.

I would think because it is so square it would make a great amp.  An ukulele would probably work.

Not ready to build and amp but I found a site, http://ukeleleunderground.com/, which has given me a new outlook on ukeleles. Any advise is greatly appreciated. Thanks

Bass works better with big boxes. Your box is quite on the smallish side, it means there will be not so much bass sound anyway -- ergo -- you can go for a 24" or shorter. Depending on the top strength, fret/fretless and your playing technique your sound will be something between uke/banjo and cello.

I have a similar sized box, (about an inch deeper) a friend found for me that I plan on being my second build. Figuring on three string fretless with a 25.5 scale length and hoping that the added depth will carry the tone I'm looking for and I like the look of the longer neck. Just have fun and be creative.

Go with a 23 or 24 inch scale and you will be fine, the slightly shorter neck will look better(in my opinion, and you did ask for it) I bet that little box will have a nice sound. Build it and see!

Just a thought on the size of your "Small Box", if you figure out the size of the average cigar box in cubic inches ( length times width times depth), which is what gives the resonance to the instrument it seems that the "standard shaped cigar boxes run between 102 and 130 or so cubic inches. Your 6X6X3 box works out at 108 so the sound may be bigger than you expect. However it works out that box looks like it will build a beautiful guitar for you. Post pictures of your progress.

I would build a soprano Uke, likely make it electric. I started on an A Fuente box, like the one linked below,it'll be a 2 watt amp.

http://www.cuencacigars.com/productimage.php?product_id=15284

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