Model originally uploaded to Thingiverse at https://www.thingiverse.com/thing:910645.
OKAY, NOT QUITE TUNED, ONLY SORTA PLAYABLE.
Inspired by the linked ocarina, which is delightfully printable but not tuned to any particular scale. These two ocarinas were designed to (hopefully) play in tune. Each covers an octave and a half, including sharps and flats, per the same fingering chart which you can download.
The "alto" ocarina should run from A4 = 440Hz through F6. The "soprano" should run an octave higher, from A5 = 880Hz through F7.
I designed this using a genetic algorithm and the equation for a Helmholtz resonator, and posted the STL so people could test it out while I was on the road. I've since gotten home and printed one, and it's not bad considering: the first few notes are in tune, but only if you blow fairly hard. The higher notes are progressively flat. I'll have to do some experiments to see what went wrong.