Roughness of organ pipe sound due to frequency comb

Abstract

In the sound spectrum of flue organ pipes in addition to the usual harmonic partials, sometimes a series of equidistant but not harmonic lines can be found. This phenomenon has been observed in the recorded sound of pipes from different pipe ranks. The second set of spectral lines is similar to "frequency combs" used in optics for accurate measurement of optical frequencies. Analysis of measured sound spectra with and without frequency comb and simulations are presented and discussed in the paper. The appearance of frequency combs in the sound spectrum is explained by a model that assumes the presence of a mouth tone in addition to the pipe sound. Mouth tone bursts are generated when the oscillating air jet passes the upper lip. The burst repetition frequency is locked to the fundamental frequency of the pipe and the bursts are coherent with a pulse-to-pulse phase shift. The phase shift explains the observed frequency offset of the frequency comb to the harmonic frequencies. The simulations also show that weak and fluctuating mouth tones cannot generate frequency comb due to a lack of coherence.