How does an Ocarina work?Edit
The Ocarina is a Helmholtz Resonator.
The simplest example of such a resonator is a water bottle. The less air space, the more water, the higher the pitch; the more air space, the less water, the lower the note. The Ocarina follows a similar way of producing sound, just that to maintain the same volume of air in the ocarina and still be able to change the notes, we need a mouthpiece, a very well made sound hole or voicing, and finger holes.
The mouthpiece and the voicing are part of the ocarina, but chinese Xuns worked like blowing a bottle. The finger holes positions are not critical at all, in contrast with that of any other flute, in which the position of the holes and the length of the pipe is very important; instead, the diameter and size of the holes is the most critical part. An ocarina's finger holes can be arranged to fit one's hand, but their size is of critical importance.
The way the ocarina works is that depending on the total area covered, a note is produced: Four holes ocarinas are designed for changing from note to note with an accurate area covering designated by the combination of finger holes covered. The same holes may be covered many times, but the complete area covered is what matters. In fact, an ocarina player can play semitones by covering a not designated hole in the between the sequence, or they can cover half of the previous hole that was indeed designated, but because of covering the half of it, the semitone is produced. In other ocarinas, the finger holes are arranged so that every note that rises, the player lifts one finger from right to left; however the player could as well cover any other number of holes and make the same note as long as the same area is being covered. This allows to produce semitones and tones close to the semitones.
The size of the ocarina changes the range of notes that it can play by uncovering holes, but however, there is a limit of area that can be uncovered, so in the higher notes, the sound will start to get airy, because the voicing vacuum and pushing effect will get to a point where the sound doesn't resonate. In soprano Ocarinas, the volume is smaller so the sound does get to resonate in higher notes, but also these have a limit of notes. That's why multi-chamber ocarinas are used when the player needs a larger range.
The voicing works by creating a repeating sequence of making a vacuum inside the ocarina, forcing air inside and then pushing it out, then forcing it inside again. The more times this sequence is repeated by second, the higher the pitch.
For info on the Sound producing physics : http://www.greenverdugo.com/ocarina-making-tutorial/ocarina-making-voicing.html
For more detailed info:
The Principles of the Ocarina - http://www.fl-oca.com/eng/ocarina1.htm
The Clay pot that sings, article on the ocarina (check the last pages for this subject) - http://www.recorderhomepage.net/ocarina.pdf
Helmholtz Resonance on Wikipedia - http://en.wikipedia.org/wiki/Helmholtz_resonance