Control of natural resonance frequencies in warbling native American flutes

Abstract

The natural resonances in Native American flutes are inharmonic, and in many instances the arrangement of these frequencies can support production of a traditional warble. The bore dimensions and the configuration of a chimney around the sound hole affect those resonance frequencies. In this work the passive frequencies of flutes configured with five bore lengths and 13 chimney depths were investigated to characterize how the parameters control the placement of those frequencies, with emphasis on conditions that enable the warble. Each configuration was excited by a pure tone from an external speaker in a simple anechoic chamber. A microphone capsule was positioned near pressure antinodes and the excitation frequency was adjusted to maximize peaks and measure the first five resonant frequencies. Open tubes were tested as well. End corrections for each resonant frequency were determined and plotted versus frequency and wavelength. Analysis revealed nonlinearly decreasing end corrections versus frequency at the mouth as well as at the open foot, with the relative placement of the inharmonic resonance frequencies relative to the fundamental note being a function of bore length and chimney depth. Finally, parameters that favored warbling were identified, informing the relationship between flute design for warble production.