Harmonic generation in organ pipes, recorders, and flutes

A simplified treatment is given of the mechanism of sound production in musical instruments driven by air jets, which is sufficiently explicit that semiquantitative predictions can be made about the effects of certain variables upon the harmonic structure of the sound produced. In particular it is found that the amplitude of the even harmonics, generally, and of the second harmonic, particularly, is quite critically dependent upon the offset of the pipe lip from the symmetry plane of the jet. A completely symmetrical relationship (zero offset) reduces the generated amplitude of the second harmonic by a large factor. Experimental results with an adjustable organ pipe are found to confirm these predictions. The implications of these results for the voicing of organ pipes and recorders and for subtle tonal variation in flute playing are briefly discussed. PACS numbers: 43,75.Np pipe, and then interacts with the pipe lip. The acoustic flow out of the pipe mouth associated with the vibration of the pipe air column induces waves on the jet which grow in amplitude as they propagate so that the trans- verse motion of the jet at the pipe lip is generally com- parable with the jet width when the pipe is sounding normally. The jet blowing alternately into and outside