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Page 94 ï~~METHOD FOR AUTOMATIC EVALUATION OF TIMBRE AND FLUCTUATIONS OF PIPE ORGAN SOUNDS Massimo Dal Sasso, Giovanni B. Debiasi, Giovanni Spagiari D.E.I. - C.S.C. - Universitat di Padova Via Gradenigo 6a, 35131 PADOVA Tel +39 -49 -8287500 Fax +39 -49 -8287699 ABSTRACT Organ pipes, like all musical instruments, produce nearly periodic waveform, whose spectral components fluctuate both in the amplitude and in frequency. For the acoustic characterization of their sounds it's very important the knowledge of these fluctuations, during the transients and during the steady-state. In this paper we explain the improvements we brought in some methods of analysis of sound fluctuations. Our improved methods, after several laboratory tests, have been used for an extensive investigation on a valuable baroque pipe organ in the Province of Venice. A very large amount of data have been evaluated in a rather short time, giving a complete acoustic description of the organ and suggesting very interesting hypotheses about the charm of its sounds. 1 - Introduction Sounds from musical instruments, and from voice, have spectral components that fluctuate both in the amplitude and in the frequency: so period and shape of the waveform vary continuously. We call these fluctuations "microvariations", in order to separate them from the variations imposed on the sounds for the sake of tremolo, portamento and so on. Recently the study of the microvariations suggested many interesting works, e.g. from C.Chafe , from R.T.Schumacher and C.Chafe  and from T.Kabayashi and H.Sekine . A different approach has been proposed in 1985 by C.Padgham . He devised the direct assessment of steady-state pipe organ timbre, in a two dimension polar chart: namely tone (angle @) and complexity (radius C): so each timbre has a corresponding point on the polar chart. The evaluation of the tone and of the complexity is based, in the Padgham work, on the judgements of trained observers. They listened to each of the sounds four times in four widely spaced sessions, and for each tone the mean angular position @ was tabulated on the basis of perceptual assessment depending on the first partials. The mean complexity (radius C) was evaluated from the contribution of the higher order partials of each sound. This method enables a quantitative treatment of pipe organ sounds, but it's time wasting and expensive. 2 - Polar chart methods improvements Pipe organ sounds are rather different from sounds of other instruments. First of all they have no standard timbre: a Diapason is often stated as a basic organ tone, but there are different stops with this name and with quite different timbres. Secondly, in a same rank of pipes, there are often differences of tone from pipe to pipe. Thirdly, the harmonic structure of the pipe organ sounds can be varied by the player, by the addition of pipes of different pitch from that of the fundamental. So, the study of pipe organ acoustics needs fast and accurate methods for processing quickly a very large amount of data. ICMC 94
Page 95 ï~~With this goal in mind we improved the Padgham method using a digital signal processing system that directly computes the tone (angle C) and the complexity (radius C) of the timbre, plotting the resulting timbre with a point on the polar chart. Details of this method are given in a previous paper . The method is very sensitive and fast and so it doesn't only give the evaluation of a steady-state timbre, but also tracks its evolution during the transients and detects small fluctuations of timbre during the steady state related to the microvariations. A further improvement of the method has been made, on this work, adding a digital heterodyne filtering system: it measures, in a very fine way, the amplitude and frequency fluctuations of the first six partials of the sound related to the timbre fluctuations. (We remember that, as stated in , the tone @ shall be computed from a linear set of the measures of the first six partials, and the complexity C is depending on a weighted sum of the measures of all the partials). The digital heterodyne filtering system is well known from the literature , , , . For microvariation detection aim, we implemented an algorithm that avoids problems of phase discontinuity and that shifts each spectral component at the zero frequency, so that the frequency fluctuations appear around the zero frequency line (marked with the nominal frequency of the component) and they can be amplified by a frequency scale expansion. Other details about our heterodyne filtering algorithms are explained in ; they run, like the algorithms for computing the tone @ and the complexity C, on any PC. 3 - Study of the acoustic characteristics of a pipe organ After several laboratory tests, aiming to check the dependability of our method, the latter has been used for an extensive investigation on the acoustic characteristics of a valuable baroque pipe organ in the Province of Venice. It is a masterpiece of the well known organ builder Gaetano Callido, built in Gambarare in the Province of Venice between 1786 and 1798 and in very good working condition. We recorded and digitized the sounds of all the notes of the stops of the following list. Principal 8' Ottava 4' Flute 4' Bassoon 8' Trombone 8' Tromboncini 8' Vox Humana 8' + Principal 8' Double-bass 16' + Ottava of Double-bass 8' Double-bass 16' + Ottava of Double-bass 8' + Principal 8' Mixture (Principal 8' + Ottava 4' + XV 2' + XIX 1'1/3 + XXII 1' + XXVI 2/3' + XXIX 1/2' + XXXIII 1/3' + XXXVI 1/4') We analysed, for a first step, just two notes for each octave, i.e. the C and the F-sharp. We evaluated the microvariations of tone @ and complexity C on the starting transient and on the steady-state and plotted the microvariations of frequency and amplitude of the first six partials of each analysed sound. ICMC 95
Page 96 ï~~As an example, few figures show some interesting results we obtained. Fig. 1 is referring to the note C4 of the Principal 8'. Fig. la and lb give the evolution of the tone @ and of the complexity C on the starting transient: a line every 20 ms. Fig. lc is a polar chart of the timbre. There are five sectors on this chart; the area of each sector collects the timbres of one of the five most important families of stops, i.e. Flutes, Bourdons, Principals (Open Diapasons), Strings, Reeds. In Fig. ic we may note very well that, during the initial transient, the timbre starts from the sector of the Strings (point # 1), with an high complexity, and evolves to the sector of Principales, with lower complexity. On the steady-state there are microvariations of timbre, shown from the stretched cluster around point # 6. Fig. 2a and Fig. 2b show the microvariations of amplitude and frequency of the fundamental on the steady-state of the same note. Fig. 3 shows the timbres on the steady-state of the ten analysed notes of Principal 8', from C2 to F-sharp6: there are remarkable differences, but all timbres are in the sector of the Principals. From a general point of view, we found that all flues stops of this Callido organ show the law of a considerable counterclockwise rotation of the tone and of a decrease of the complexity during the starting transient. The timbres of the reed stops, on the contrary, are very stable during the initial transient and on the steady-state and show a very high complexity. In the rank of pipes of the same stops, there are always rather high differences of timbre from pipe to pipe, but the timbres lie generally on the proper sector. There are also remarkable microvariations of frequency and amplitude on the starting transient and on the steady-state. It could be an open question if this high variability is a peculiar characteristic of the baroque organs, contributing to create the liveliness and charm of its sounds. We hope to answer this question studying many other baroque organs with our method, starting, of course, from the Callido organs. References  C.Chafe, "Pulsed Noise in Self-sustained Oscillations of Musical Instruments", CH2847 - 2/90 - p.1157,1160 - 1990 IEEE.  R.T.Schumacher and C.Chafe, "Characterisation of Aperiodicity in Nearly Periodic Signals", CH2847 - 2/90 - p.1161,1164 - 1900 IEEE.  T.Kobayashi and H.Sekine, "Statistical Properties of Fluctuation of Pitch Intervals and its Modeling for Natural Synthetic Speech", CH2847 - 2/90 - p.321,324 - 1990 IEEE.  C.Padgham, "The Scaling of the Timbre of the Pipe Organ", Acoustica vol.60 n.3, p.189,204, May 1986.  G.B.Debiasi and M.Dal Sasso, "Metodo per la Valutazione Automatica dei Timbri di Organi a Canne", Atti VIII Colloquio di Informatica Musicale, p.17,25, Cagliari, Ottobre 1989. [61 J.A.Moorer, "The Heterodyne Filter as a Tool for Analysis of Transient Waveforms", Stanford A.I. Lab., MEMO-AIM-208.  M.D. Freedman, "A Method for Analysing Musical Tones", J. Audio Eng. Soc. vol.16 n.4, 1968. [81 J.S.Keeler, "The Attack Transient of Some Organ Pipes", IEEE AU 20 n.5, 1972. ICMC 96
Page 97 ï~~(91 M. Pullin, "Sistema di Analisi Numnerica di Suoni Musicali", Tesi di laurea in Ingegneria Elettronica, Universitat di Padova, A.A. 1983/84. [101 G. B. Debiasi and G. Spagiari, "Metodi di Analisi delle Microvariazioni di Ampiezza e Frequenza dei Suoni Musicali", to be published in Atti IX Colloquio di Informatica Musicale, Genova, 1991. F a),yC I ( 11." I 1- I +1 (r I i Ii! 1illHIiHW I PLCTE S\ 1 3 5 7 9 11 13 15 17 19 b) 1 3 5 7 9 11 13 15 17 19 r I, III -- I "- 8ouQ~oMl REED.S Z / '1 I Fig. 1I- Starting transient of Principal 8' C4. a) Evolution of the tone @. b) Evolution of the complexity C. c) Polar chart. up i eza a. ai1-_ max. 10129. Fi nes tra teripor ale = 2 _3 751023751 E +02 Ms 1 d i i s ione=2.3 751 823 751E+01 rus a) Fv'eqsievna (14z) F ines tva teuwpo'a l e 2.3 751 02375 1E +02 F's 1 d i'i siorue = 2.3751023751E+01 rus +4" ' r' r/ S FLUTES.. A 8OUQboNS l ' I t. REEbS \ sr~&s 3 PRIuJCIPALs/ +2 262 -2' -4i v "1 I--- *f'~ ~ 1 --r.- *- I fig. 2 - Microvariations on steady-state of the fundamental of Principal 8' C4. a) Amplitude microvariations. b) Frequecy microvariations. Fig. 3 - Steady-state fluctuations of timbre of Principal 8': 1 =C2,...,1O 0F-sharp6. ICMC 97