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Acoustics of Organ Pipes
 Figure 7. Measured spectra of a Diapason (normal; a), a Flute (wide; b), and a Salicional (narrow; c) pipe.
where the partials of the fundamental are usually weak. The high-frequency noise content can be very effectively reduced by nicking, e.g., cutting grooves in the languid (metal plate separating the pipe foot and the pipe body; Figure 2; Ang- ster et al., 1997). This method can increase the ratio of the harmonic partials to the baseline very significantly.
Envelope of the Harmonic Partials
The form of the envelope depends on the total losses in the pipe that include the volume losses in the air, the surface losses at the pipe wall due to viscosity and heat conduction, the radiation losses at the openings, and the energy loss due
to the coupling of the sound to the wall vibrations. For or- gan pipes, the surface and radiation losses are much larger than the other two effects. At the same frequency, the surface losses are relatively larger and the radiation losses are rela- tively smaller for narrow pipes than for wide pipes. Because the surface losses decrease and the radiation losses increase with the frequency, a loss minimum occurs at a certain fre- quency. Indeed, such a loss minimum can be observed in narrow pipes. Looked at in another way, the largest ampli- tude occurs not for the fundamental but for a higher partial. Measured sound spectra of a normal, a wide, and a narrow pipe are shown in Figure 7. In the case of wide/narrow pipe resonators, there are less/more partials, respectively, than by the normal pipe resonator.
Radiation losses occur through sound radiation at the pipe openings (mouth and open end). Because the openings are much smaller than the wavelength of the sound, both of the pipe openings can be regarded as simple sources (monopoles; Angster and Miklós, 1998). Measurements by an acoustic camera system confirm this simple source model (Angster et al., 2011). Figure 8 shows that the sources of the sound are really the openings at the mouth and at the open end of the pipe. Based on the recording of the first partial (fundamen- tal) in Figure 8a (see the sound is radiated in phase but with different intensity. The sound pressure is larger at the mouth. Figure 8b (see http:// shows that the two sources radi- ate in opposite phase. The simple source at the mouth is usu- ally much stronger than the source at the open end.
The envelope of the harmonics of the sound spectrum at the mouth shows a formant-like structure with a conspicu- ous minimum (see Figures 4b and 7) because of the rela- tive position of the harmonic partials and the neighboring eigenmodes. Due to the stretching of the eigenfrequencies, the harmonic partials are gradually shifted from the peaks of the eigenmodes into the valley between them and then fur- ther toward the peak of the neighboring lower eigenmode. If the harmonic frequency is close to the eigenfrequency, the partial will be amplified by the eigenresonance. A harmonic partial lying midway between two eigenmodes will not be amplified while the partial closest to the minimum between two eigenmodes will be the smallest one. Thus, a formant minimum can be observed in the spectra measured at the mouth. Because the stretching is more pronounced for wid- er pipes, the position of the formant minimum depends on the diameter-to-length ratio of the pipe. Sound spectra mea-
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