On an ocarina, where you drill the holes barely matters
A recorder's notes depend on where its holes sit along the tube. An ocarina ignores that rule. Its whole egg-shaped body rings as one resonating chamber, so pitch depends on how much hole area is open compared with the volume inside, and a hole's size matters far more than its position.
Physically, an ocarina is a Helmholtz resonator, the same principle that makes a bottle hum when you blow across it. Air is steered through a narrow duct in the mouthpiece onto a sharp edge, first producing a breathy noise; the chamber then amplifies the one frequency matching its current opening. Because such a chamber is unusually selective, the result is a pure tone almost free of overtones. Covering holes lowers the note and uncovering them raises it.
That purity comes with quirks. Breath pressure shifts the tuning, not just the volume, so blowing harder sharpens a note by up to several semitones. That is why the instrument has almost no dynamic range, no tuning mechanism and a reputation for being hard to play in tune. Overblowing to reach higher notes gives a muddy result, so range is capped by total hole area. Makers work around this by fusing two or three chambers into one body, each with its own mouthpiece, stretching a double version past two octaves.
The family is ancient, thought to reach back over 12,000 years, with important early forms in China and Mesoamerica. Expeditions including Cortés's carried Aztec versions to European courts, where they became toys. In 1853 a 17-year-old from Budrio near Bologna, Giuseppe Donati, turned the toy into a proper instrument with up to ten holes and named it after the local dialect word for little goose. In 1964 the English mathematician John Taylor devised a fingering that squeezes a full chromatic octave out of just four holes, now standard for small pendant models.
Serious composers have written for it: Ligeti used four in his 1993 Violin Concerto, and Penderecki gave 50 to the choir in his Eighth Symphony. Its biggest boost came from a video game, the 1998 Nintendo 64 hit The Legend of Zelda: Ocarina of Time, credited with lifting ocarina sales.
Source: Ocarina