I had a 20 by 1.5 inch slab of oak, so I designed an ocarina that could be assembled from cross-sections that would fit on it. I cut the parts on the laser cutter, glued them together, and it still didn't work until I took Bre's suggestion and coated the entire thing with glue to plug up any tiny holes.
If you have access to a laser cutter, you can get the plans and assembly instructions from http://www.thingiverse.com/thing:1816
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