Abstract

The “warble” is a peculiar sound in many old Native American flutes. It is perceived as a spontaneous oscillation between two octaves of the flute’s lowest note at a rate of a few Hz, and spectrograms reveal amplitude modulation of all partials during the warble period. The modulation of the fundamental is assumed to be generated through interference with difference signals generated from detuned upper partials. We propose the detuned partials are temporarily locked with natural resonance frequencies that are inharmonic due to the construction characteristics of the flute, namely the bore length and the chimney configuration at the sound hole. Natural resonances of several flutes were measured, and then the fundamental note was played using a mechanical blower that slowly increased pressure to produce the warble. Spectrograms showed the harmonic spectrum increase in frequency until the onset of the warble as the third partial locked to the third natural resonance frequency. The results were analyzed using the Alder equation to describe locking and unlocking of the third partial with the natural resonance frequency to establish conditions for warbling. Proper placement of the third resonance frequency is essential to enable the warble, and the necessary construction details are discussed.

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