Parameter Value Parameter Value
Pitch C3 (131 Hz) Tuning temperature (T0) 23◦C
Resonator length∗(LP) 600 mm Material 75%tin,25%lead
Inner diameter∗(DP) 79 mm Wall thickness 0.9 mm
Mouth width∗(WM) 60 mm Length of foot 200 mm
Mouth height∗(HM) 19 mm Languid thickness 6 mm
Chimney length∗(LC) 180 mm Languid angle 70◦
Chimney inner diameter∗(DC) 19 mm Flue width 0.8 mm
∗Parameters used for the optimization process
Table 5.3.Design parameters of the reference pipe.
Name (optimized for . . . ) A2 (3rd) A3 (3rd) B4 (4th) C5 (5th) Main resonator length [mm] 564.0 576.7 742.9 852.5
Chimney length [mm] 193.3 118.0 99.1 51.1
Inner diameter of chimney [mm] 10.7 14.3 29.4 29.3 Table 5.4.Optimized dimensions for the four experimental pipes
5.3 Sound design of experimental chimney pipes
5.3.1 Laboratory measurements of optimized pipes
The applicability of the optimization algorithm was tested by designing chimney pipes to
con-form to the desired sound spectra. As a starting point a design by an organ builder reference pipe (Werkstätte für Orgelbau Mühleisen, Leonberg, Germany) was selected. The dimensions of a 4’ C3 chimney pipe2 were applied as initial data for the optimization process. The dimensions of this reference pipe are given in Table 5.3.
The parameters marked by∗in Table 5.3 can be used for the optimization process. At first, the general properties of chimney pipes were studied by means of the optimization software. It was found that three different sorts of chimneys may be used for optimization: (1) thin and medium long chimneys (LC ∼ λ/15,DC < 2DP/7), (2) short and medium wide chimneys (LC ∼ λ/20, 2DP/7< DC<2DP/5), and (3) long and wide chimneys (LC> λ/12,DC ∼DP/2).
For the comparison measurements three dimensions of the pipes, which cannot be changed easily in practice (i.e. the inner diameter of the pipe, the mouth width and the cutup) were fixed.
Optimizations by the remaining three free parameters led to nine different musically meaningful scenarios: the pipe was optimized for the third, fourth, fifth (twice), sixth and seventh partial and three times for two neighboring partials (fourth–fifth, fifth–sixth, sixth–seventh).
In order totest the optimization, one reference pipe and three experimental pipes (pipes A, test pipes B and C) were built with different body lengths but the same inner diameter, mouth width and
cutup. Adjustable plugs, designed to hold the chimneys and mount them in the corresponding pipe, were fabricated for each chimney diameter given by the optimization. Thus, ten plugs were made, one for the reference pipe and nine for realizing the nine different scenarios. These plugs provide a tight mount of the chimneys in the pipes with the possibility of adjusting the active length of the main resonator. The full lengths of the main resonator of pipes A, B, and C are 723,812, and883 mm, respectively. The four optimized set of dimensions given in Table 5.4 are selected from the nine scenarios for presenting the results of the comparison measurements.
2Here and in the sequel pitches are numbered using thescientific pitch notation.
Pipe A1
Figure 5.6.Comparison of the measured sound pressure spectrum to the calculated input admittance curve of the reference pipe A1. (The first five harmonic partials are marked by arrows.)
The experiments
test setup were performed in the following way. First, the dimensions of the reference pipe were adjusted to the values given in Table 5.3, and the pipe was tuned and voiced at700 Pa wind pressure in the windchest to131 Hzfrequency and to a proper attack of the sound. Then pipes A, B, and C were adjusted to the same dimensions and were voiced also to the same fre-quency and sound at700 Pa. From this point on, the dimensions and the voicing setup of the pipes were kept constant during the experiments.
The results of the optimization process were tested by adjusting the dimensions of the ex-perimental pipe to the values calculated by the optimization process.
tuning and voicing
The pipe was placed on the windchest beside the reference pipe, and the resonator length was modified slightly until the same frequency was obtained. This tuning was achieved by minimizing the beating between the pipes. This step was necessary, because the recorded sounds of the nine experimental pipes and of the reference pipe were intended to be used for subsequent subjective evaluation.
The sound sound
recordings
of the pipes were measured in the anechoic room of the Fraunhofer Institute for Building Physics (IBP) by two microphones, located close (50±5 mm) to the mouth and the open end of the chimney, respectively. A third microphone was placed at a distance of2 mfrom the pipe, in order to record the sound for listening tests. The microphone signals were recorded in a PC using an 8-channel 16-bit sound card (RME Hammerfall DSP).
The recorded signals of the three microphones were analyzed by aMatlab-based in-house sound analysis software tool (see Appendix A). The measured sound spectra and the calculated optimized input admittance funtions of the reference pipe and the four selected experimental pipes are shown and discussed in the next section.
5.3.2 Validation of admittance calculations with spectrum measurements
The spectrum of the sound pressure measured near the mouth of the reference pipe (pipe A1) and the input admittance calculated from the dimensions of the pipe are shown in Figure 5.6. For all following figures the vertical scale is given indBsound pressure level (SPL). The amplitude of the admittance curve is also measured indB, and is shifted to match the spectrum.
As admittance
and spectrum
can be seen in Figure 5.6 the significant curve progression of the measured sound pressure spectrum matches the calculated input admittance curve very well; the frequency positions of the maxima and minima are the same and the profile of the admittance curve follows almost exactly the baseline of the spectrum. The only difference is that the maxima and minima of the admittance curve are sharper than that of the measured spectrum. It means that the real losses in the chimney pipes are larger than the calculated ones. This problem will be discussed in more
5.3. SOUND DESIGN OF EXPERIMENTAL CHIMNEY PIPES 63 detail later. Harmonic partials can be found in the sound spectrum as sharp peaks (marked by arrows in Figures 5.6–5.10). These lines are not present in the calculated admittance, because sustained oscillations cannot be treated by the applied acoustic model.
It can be seen in Figure 5.6 that the third and the fifth harmonic partials have higher fre- pipe A1 quency than the closest eigenfrequencies. Therefore, these partials are not amplified effectively;
the sound is dominated by the fundamental component. The second strongest component, which is the third partial, is more than30 dBweaker than the fundamental. The total sound pressure levelLpwas measured as108.7 dBat the pipe mouth.
Pipe A2was optimized for the third partial. The input admittance curve, resulted by the op- pipe A2 timization process and the measured sound spectrum are shown in Figure 5.7. The overlapping
of the third partial with the second eigenfrequency is perfect, and the third eigenfrequency is shifted closer to the fifth partial. As a result, the third partial becomes about15 dBstronger than before. The fifth partial is also stronger now by about5 dB. The total sound pressure level is also higher, it has increased toLp= 111.2 dB.
The next pipe (B4), was optimized to the fourth partial. The corresponding spectrum and pipe B4 input admittance curve are shown in Figure 5.8. The optimization process was also entirely
successful in this case. The perfect overlapping of the third eigenfrequency with the fourth partial has resulted in a significant enhancement of the fourth partial. Due to the quite large downward shift of the eigenfrequencies, the third and fifth partials are located now in the “valleys” and are very weak therefore. The sound spectrum is very different from the spectra of pipe A1 (Figure 5.6) and pipe A2 (Figure 5.7); while those can be characterized by strong odd partials, the third and fifth partials in the spectrum of pipe B4 (Figure 5.8) are weak.
The next exampleis the optimization of the experimental chimney pipe to the fifth harmonic pipe A3 partial. This goal can be achieved by bringing the third eigenfrequency to overlap with the fifth
harmonic partial. This solution was described in [86] and the corresponding spectrum and input admittance curve of our laboratory experiments are shown in Figure 5.9. In this case, even though the pipe is optimized for the fifth partial, the third partial will also be strong, sometimes even stronger than the fifth partial. Therefore, in order to arrive at a strong fifth harmonic partial and a considerably weaker third, another possibility for the optimization was also explored, as discussed in the next paragraph.
Thecalculated input admittance curve and the measured sound spectrum of pipe C5 can be pipe C5 seen in Figure 5.10. In this case the eigenfrequencies are shifted further downwards; the fourth
eigenfrequency is brought to overlap with the fifth partial. As a consequence, the fifth partial is enhanced. However, the second partial is also stronger, both partials have increased by about
Pipe A2 Optimization
Figure 5.7.Comparison of the measured sound pressure spectrum to the calculated input admittance curve of pipe A2. (Harmonic partials are marked by arrows.)
Pipe B4 Optimization
Figure 5.8.Comparison of the measured sound pressure spectrum to the calculated input admittance curve of pipe B4. (Harmonic partials are marked by arrows.)
Pipe A3 Optimization
Figure 5.9.Comparison of the measured sound pressure spectrum to the calculated input admittance curve of pipe A3. (Harmonic partials are marked by arrows.)
Pipe C5 Optimization
Figure 5.10.Comparison of the measured sound pressure spectrum to the calculated input admittance curve of pipe C5. (Harmonic partials are marked by arrows.)