Ocarina pitch depends on total opening area, not hole placement

Evidence

Ocarinas have a fipple (a stream of air directed at an edge; see figure 14.4) blown by the player, which generates an edge tone cooperating with the Helmholtz resonance. The resonant frequency of the ocarina is raised by opening holes, as many as 12 of them. Unlike in a flute or clarinet, in the ocarina it does not matter very much where the holes are, nor what the shape of the instrument is, as long as it is more or less a cavity. According to formula 13.1, the frequency depends only on effective neck area, neck length, and the volume of the cavity. This follows ultimately because the Helmholtz mode pressure rises and falls uniformly everywhere inside the chamber. Each hole increases the total neck area of the resonator, and adds only a little to the effective length L of the neck. This causes the Helmholtz frequency and the pitch of the ocarina to rise as more holes are opened. — Eric J. Heller, Why You Hear What You Hear- An…, 1207

Categorization

• XREF: Connects to the earlier flute/clarinet physics (different instruments where hole location matters) discussed in this or nearby chapters.
• CANDY: A fun fact: unlike flutes where hole placement is everything, ocarina pitch is just total hole area, so the instrument can be any shape.