This workshop presents three different design strategies for tuning an ocarina so that it can play a full-octave diatonic scale. The first strategy involves “thinking like a pianist,” yielding a seven-hole instrument. The second strategy involves “thinking like a mathematician,” yielding four holes (the minimum possible). The third strategy involves “thinking like a potter-designer” and introduces aesthetic preferences that may influence the final number of holes. Workshop participants will be invited to build their own clay ocarinas. Thinking like mathematicians, our goal will minimally be to use two holes to produce the first four tones of an ascending diatonic scale.