I'm a maker of concert-tuned transverse ocarinas, which are a kind of Helmholtz resonator, however that does not tell the whole story as they are driven with an air-reed. This set up seems to differ from what is defined by the Helmholtz resonator equation in that it does not have a single resonant frequency. The pitch is highly dependent on air velocity and freely varies up/down by several semitones. Now the main thing which is causing trouble for me is that of 'harmonic' frequency generation. From what I understand a 'pure' Helmholtz resonator has no harmonics, yet ocarinas can and do generate 'overtones'. This is especially if they are overblown, but they also show up while playing steady state notes. If you look at an FFT graph of the different notes, they all have notable peaks of overtones. The following image shows a particularly bad example: http://pureocarinas.com/wp-content/uploads/2015/02/ocarina_harmonic.png The problem I have is that I have no understanding of the physical mechanism by which these originate, it just shows up randomly in my work. Depending on the relation to the fundamental tone, they can give the instrument an unpleasant 'shrieking' tone. So far I've been able to get away with making minor changes to the voicing, but it's unpredictable and time consuming. It shows up unpredictably in ocarinas of different base tunings. Relating to the above image, this is of an alto C ocarina playing it's top D note, and it has an unpleasant screeching tone. It's played by opening all holes besides right thumb/left pinky. As this appears to show a peak at the octave of the fundamental, one idea that I had was if the chamber is forming a standing wave due to it's length in relation to the wavelength. The length of the chamber is approximately 12.7CM and the problem note is a D6 which has a wavelength of 29.37CM. The first octave of this is 14.9CM which is close to the length of the chamber, yet not exactly. So I'm uncertain if this is relevant or not.