Experiments on the influence of pipe scaling parameters on the sound of flue organ pipes

Transcription

1 Experiments on the influence of pipe scaling parameters on the sound of flue organ pipes Judit Angster, Tilo Wik, Christian Taesch, András Miklós Fraunhofer-Inst. Bauphysik, Nobelstraße 12. D Stuttgart, Yumiko Sakamoto Dept. of Acoustic Design, Graduate School of Design, Kyushu Univ. Fukuoka, Japan,, When basic phenomena of the physics of flue organ pipes are studied, experiments on models are acceptable. But frequently, these models differ considerably from real organ pipes. For this reason, the fine details of pipe sounds should be investigated on real pipes. The sound quality of an organ pipe is mainly influenced by the attack transients. This onset is first dominated by the edge tone, while later the pipe resonator will play a more important role. To understand the physics of a flue organ pipe, it is necessary to measure the acoustic properties of the pipe resonator, to analyse the edge tone, the attack transient and the stationary sound of the pipe. Several special pipes with the same pitch have been investigated: pipes with different diameters; a pipe, of which the cut-up, and a pipe, of which the length is adjustable. By the evaluation all physical effects contributing to the production of sound were taken into account. The results together with the results of subjective listening tests will be used for developing a scaling method for dimensioning labial organ pipes and a software for designing organ pipe dimensions of the most important ranks. 1 Introduction Regarding the physics, the flue organ pipe is an extremely complicated system. Until now, the mechanisms of sound production are not completely clarified. Yet, it is important to understand these mechanisms, if the sound of an organ is to be voiced. As until now, the craftsmanship of organ building is more often characterized by tradition and experience than by physical knowledge, it is all the more important to do research in this field. The aim of this work is to investigate the physical aspects of the pipe sound and its production. Special consideration is to be given to the attack transient, i.e. the transition from mouth tone to stationary sound. A better knowledge of the physics of the flue organ pipes may allow organ building companies to dimension pipes in advance and in a way that the desired sound character is achieved by an appropriate voicing. For this purpose, sound analyses of the attack transient and of the stationary sound are carried out among other things. These analyses were carried out by means of software, developed in-house and specifically designed for organ pipe research, which is based on Fast Fourier Transformation with running window and synchronized sampling rate [1, 2]. With the help of this software, users may find easy access to certain parameters, so that the analyses can be carried out in a most flexible way. 2 Experimental setup, method of analysis 2.1 Experimental setup The research was carried out in the acoustic laboratory of the Fraunhofer IBP. A small slider chest was placed in the anechoic room, the wind was supplied by a centrifugal fan through a bellows. The fan and the bellows were located outside the anechoic room. A flexible tube with 80 mm diameter was used for connecting the bellows to the slider chest. The pallet in the slider chest was operated by an electromagnet, or it was manually fixed in an open position for measuring stationary sound. 2.2 Pitch-synchronous spectrogram Analysis based on Fourier Transformation has been used. Time-shifted, overlapping windows were applied to the signal and a FFT was performed on each window. This provides a time-frequency representation of the signal, a spectrogram or sonogram (Figures 1 and 2). The aim of this method is to find a compromise between frequency and time resolution. Several combinations of the parameters (FFT-Size, overlap and window-type) were applied to find the best graphical representation of the sound. 603

2 frequency resolution. Amplitude or frequency modulations cannot be simultaneously analyzed. Therefore an additional iteration step was applied based on the comparison of the amplitudes of the 3 frequency values in the main-lobe of the applied window function (here: Hanning) and readjusting the resampling rate in every time window. In this way, each chosen partial can be accurately followed in frequency, in the attack and in the stationary sound (Figure 3). Figure 1: Surface plotted spectrogram of the attack (FFT-Size 512, overlap 97 %, rectangular window). To improve the localization of the harmonic components, those frequencies, which are always full number multiples of the fundamental frequency, the sampling rate of the signals was synchronized to the fundamental frequency by a resampling step. This way the resulting position of the frequency values of the FFT will exactly overlap with the harmonic partials and offer a good understanding to follow the harmonic and non-harmonic components in the attack transient. Figure 3: Tracking of the frequency of the 2 nd harmonic in attack and stationary sound. 2.4 The measured flue pipes Two special open metallic pipes were built for the measurements. Pipe1 (P1) had a continuously adjustable cut-up whereas concerning pipe2 (P2), the length of the resonator was continuously adjustable. Both pipes were diapason pipes, with the same nominal pitch. The accurate pipe dimensions are summarized in Table 1. The wind pressure was 60 mm water column (~600 Pa). Figure 2: Sonogram view of the attack, FFT-Size 512, overlap 97 %, rectangular window). 2.3 Frequency tracking Pipe Diameter Length of resonator Cut-up height Mouth width P adjustable 45 P adjust Table 1: Dimensions of the measured diapason pipes. In the given method, analysis of frequency modulations of the partials is not possible, because of the low 604

3 3 Pipe with adjustable cut-up The measurement of the mouth tones (tones that are generated by the oscillating jet system [3]), was carried out by filling the pipe with absorbing material, so that no standing waves could be formed and therefore the resonator effect is switched off. The steady spectrum of the mouth tone of the experimental pipe with a cut-up height of 16.1 mm is given in Figure 4. Several peaks indicate the mouth tone modes. Regarding the 6 analyzed cut-up heights, their number varied from 3 to 4, their amplitudes and Q-factors varied in a wide range. The first mode has nearly always the maximal amplitude and Q-factor. mode and a spectral proximity to a harmonic partial contribute to modulations of the affected partials. In case of an accurate adjustment of a mouth tone mode on a frequency of a partial, this partial can be perceptually emphasized or accelerated [5]. Also the typical chiff transients could be achieved by making the mouth tone more broadband-noisy with less spectral preference [6]. Figure 4: Steady spectrum of the mouth tone of pipe P1 with a cut-up height of 16.1 mm. It can be demonstrated that the mouth tone modes are involved in the very early attack stage of the sound signal. Figure 2 shows that close to the mouth tone frequencies 336 Hz and 909 Hz high amplitude components appear in the attack and disappear, when the pipe sound reaches its steady state. Several other components that are not harmonic to the fundamental frequency can also be observed. Their origin is partly explained by the mouth tone modes, but also the excitation of resonator modes must be taken into account, as shown by Miklós [4]. Moreover, a linear dependence between the cut-up height and the mouth tone mode frequencies were found for the 6 cut-up heights, as illustrated in Figure 5. In terms of voicing, this means that the mouth tone modes can be linearly frequency-shifted by increasing the cut-up. Another phenomenon is inherent in Figure 3. Analysis of the second partial shows strongly modulated frequency behaviour around a nominal value of 388 Hz. This is probably due to the spectral proximity to the 1 st mouth tone mode, which influences the partial even during the stationary sound. This tendency can be followed for all mouth tone frequencies throughout the measurements. Amplitude, Q-factor of a mouth tone Figure 5: Connection between cut-up height and frequencies of mouth tone modes. The described features are obviously important for perception. Therefore it is essential for the voicing process that the mouth tones are properly adjusted in relation to the harmonic partials to reach a desired sound and furthermore to form the sound in an artistic way through voicing. 4 Pipe with adjustable length Pipe2 (P2) was measured and analyzed by 41 different lengths. The resonator was lengthened in steps of one cm respectively, from 77cm to 117cm. It was to be expected in theory that the fundamental frequency became continuously lower, the longer the resonator was, as the wave length of the standing wave changes in the resonator. Whether the sound also changed, remains to be investigated in the following. Figure 6 indicates the dependence of the fundamental frequency on the length of the resonator. The expected proportionality is obvious. Yet, an irregularity occurred in the range of a resonator length between 100 and 110 cm. Regarding the amplitudes of the first 5 partials of the stationary sound spectra in Figure 7, it is obvious that it is exactly in this range, where an immense break in the partial amplitudes is observed. 605

4 Within this range, the sound changes dramatically. The pipe sound becomes unsteady, the attack transient until a steady stationary sound is achieved, takes an the amplitude. The third partial does not at all achieve a steady state in amplitude. In the process, amplitude oscillations are accompanied by frequency oscillations of the individual partials, as shown in Figures 11 and 12, where the time function of the frequency of the first two partials is described. Figure 6: The fundamental frequency as a function of the length of the pipe resonator (Pipe1). Figure 8: Time function of the pipe sound at a resonator length of 103 cm (sound duration: 6s, Pipe2) Figure 7: The amplitude of the first five partials as a function of the length of the pipe resonator (Pipe1). extremely long time (up to 2 or 3 seconds!). Figures 8 and 9 describe the signal of the sound with a resonator length of 103 and 104 cm as example. This description clearly shows the different states of the pipe sound. The amplitudes of the single partials give a more precise description. Figure10 indicates the amplitudes of the first three partials of the attack transient with a resonator length of 103cm. It takes approx. 0.8 seconds until the fundamental achieves a steady state. The amplitude oscillates strongly before. The reciprocal behaviour is found with the second partial. It rapidly increases up to a short-time relatively steady and strong amplitude, in order to decline and oscillate strongly in Figure 9: Time function of the pipe sound at a resonator length of 104 cm (sound duration: 6s, Pipe2) The second partial is only steady in frequency at the onset of the sound, whereas the fundamental shows frequency oscillations first and then becomes steady approx. 0.9s after the first sound signal. It is interesting to see that the second partial does not start at the correct harmonic frequency of 305Hz (fundamental is around 152,5Hz) at the beginning of the attack transient, but slightly below at approx. 293Hz, although no peak of a mouth tone exists in this 606

5 frequency range, to determine the frequency. It is obvious that the synchronisation between air band oscillation and air column oscillation of the resonator is disturbed. Figure 10: Time function of the amplitudes of the first three partials at a resonator length of 103 cm. Figure 13: Stationary spectrum of the first state (1-3s) of the attack transient at a resonator length of 104 cm. Figure 11: Time function of the frequency of the fundamental at a resonator length of 103 cm. Figure 14: Stationary spectrum of the second state (4-7s) of the attack transient at a resonator length of 104 cm. Figure 12: Time function of the frequency of the 2 nd partial at a resonator length of 103 cm. In this case the properties of the excitation system were not changed (as with pipe P1), but only the resonator properties were changed. It is obviously not always possible to harmonize the systems in a way that a steady sound production is achieved. The particularly long first state in the attack transient of the sound at a resonator length of 104cm (in Figure 9 of approx. 1 to 3s) allows a further interesting analysis: the stationary sound spectrum of this state may be compared with the stationary sound spectrum of the second state, see Figures 13 and 14. Both spectra show obvious differences. In the first state, the second partial is very strong, but the pipe 607

6 does not overblow. Higher partials around 1200 and 2200Hz appear more often compared to the second state. Moreover, the frequencies of the partials in the first state are clearly lower. The frequencies of the first five partials are indicated in Table 2. partial frequency state 1 [Hz] frequency state 2[Hz] Table 2: Frequencies of the first five partials for both states at a resonator length of 104cm. Regarding the stationary sound spectra at different resonator lengths, it is obvious that strong sound differences occur with the change of the resonator length. As expected, the number of partials in the spectra increased with the lengthened resonator. Figures 15 and 17 indicate the stationary sound spectra at a resonator length of 77 and 117cm. The transfer functions of the resonator at the respective length are also indicated for comparison. Figure 16: Eigenmode spectrum of the pipe resonator at a length of 77 cm. In the spectrum with a resonator length of 117cm it is obvious that the second partial is stronger than the fundamental. Considering Figure 7, it is evident that this behaviour can already be observed from a resonator length of 107cm (exactly after the break in the amplitude). Yet, there is no overblowing of the pipe. As the excitation system (mouth tone) does not change, this must be an effect of the lengthening of the Figure 17: The stationary spectrum at a resonator length of 117 cm (Pipe 2). Figure 15: The stationary spectrum at a resonator length of 77 cm (Pipe 2). Figure 18: Eigenmode spectrum of the pipe resonator at a length of 117 cm. 608

7 resonator. The diagrams (Figures 16 and 18) of the two transfer functions show that the amplitude of the second eigenmode at a resonator length of 117cm is greater in comparison to a length of 77cm, whereas the amplitude of the first eigenmode behaves vice versa. This explains why the amplitude of the second partial at a resonator length of 117cm is larger than at a length of 77cm. 5 Summary Compared to previous publications on the flue pipe physics [3,4], new phenomena were observed. For the first time, slight frequency fluctuations of the partials of the pipe sound were found by means of the frequency tracking method. Moreover, it was possible, by means of a flexible adjustable software, to observe the fine details of the attack transient and the transition phase from the mouth tone to the stationary sound. By means of the pipes, which were especially produced for the measurements, it was possible to analyse the influence of important pipe dimensioning parameters on the produced sound. The pipe with adjustable length showed an unusual behaviour. At a certain resonator length, strong breaks in the partial amplitudes occurred and the sound was very unsteady. In addition, a clear displacement of the pitch in the attack transient could be perceived in this unsteady range after a few seconds in some cases. This was an indication that the oscillation of the air band at the lip cannot be synchronized at any scaling with the oscillation of the air column in the resonator. By means of the pipe with an adjustable cut-up height it was possible to investigate, how the sound was changed by the various cut-up heights. Different harmonic structures of the pipe sound were obtained by various cut-up heights. In addition, a clear correlation of the frequencies of the mouth tone peaks and the cutup height could be observed. The observed phenomena can explain certain traditional scaling rules of organ building. However, more research is needed for an understanding of the role of pipe scaling in the production of sound in labial organ pipes. This is the aim of the European research project presently running at the musical acoustic group of the IBP. 6 References [1] Wik, Tilo: Analysis of the Attack Transients of the Sounds of Pipe Organs and Guitars with Modern Measurement Methods (in German), Diploma thesis, 1. Institute of Physics, University of Stuttgart (2004) [2] Täsch, Christian: Measurements and Characterisation of the Sounds of Labial Organ Pipes, Diploma thesis, Institute of Electronic Music und Acoustics, University of Music and Fine Arts, Graz (2003) [3] Castellengo, Michèle: Acoustical analysis of initial transients in flute like instruments. Acustica/acta acustica, Vol. 82 (1999), S [4] Miklós, András; Angster, Judit: Properties of the sound of flue organ pipes. Acustica/acta acustica, Vol. 86 (2000), S [5] Angster, Judit, Pitsch Stephan, Miklos, Andras; Objektive und subjektive Untersuchung der Klänge verschiedener Orgelregister. Instrumentenbau- Zeitschrift 51 (1997), H.1-2, S [6] Nolle, W.: Some voicing adjustments of flue organ pipes. J. Acoust. Soc. Am 66 (1979) Acknowledgement This work was supported by the European Commission in the frame of a CRAFT research project (Contract No: G1ST-CT DEMORGPIPE). The support of the following organ builder firms is also acknowledged: Werkstätte für Orgelbau Mühleisen GmbH, Leonberg, Germany (Project co-ordinator), Manufacture d orgues Muhleisen, Strasbourg, France, Christian Scheffler Orgelwerkstatt, Sieversdorf (Frankfurt/Oder), Germany, Orgelbau Schumacher, Baelen, Belgium, Blancafort, Orgueners de Montserrat S. L., Collbato, Spain, Oficina e Escola de Organasia, Ltd., Esmoriz (Porto), Portugal, Fratelli Ruffatti Pipe organ Builders, Padova, Italy, Marc Garnier Orgues, Les Fins, France, Pécsi Orgonaépitö Manufaktura KFT, Pécs, Hungary, Mander Organs, London, U.K., Orgelmakerij Boogaard, Rijssen, Netherlands. 609