Harmonics + Noise. Extraction: A Tool For The Description. Of Flue Organ Pipe Sounds. Vincent Rioux (PhD student), Mendel Kleiner (Supervisor),

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1 Harmonics + Noise Extraction: A Tool For The Description Of Flue Organ Pipe Sounds Vincent Rioux (PhD student), Mendel Kleiner (Supervisor), Munetaka Yokota (Organ builder) Chalmers Room Acoustics Group (CRAG) Gothenburg Chalmers University Of Technology & GOArt (Gbg Organ Center)

2 Abstract A signal processing oriented model of an organ pipe is discussed.the sound of such a musical instrument is strongly harmonic but acoustical sources of noise (e.g. turbulences provided by the jet) are ltered by the pipe body and give the typical noisy sound character of a particular pipe especially during the transient part. Straightforward techniques to extract harmonic and noise contents are presented. They are thought to be used as tools to enhance verbal description of sounds, and to chek computer physical models of ue organ pipe. Chalmers University Of Technology & GOArt (Gbg Organ Center) 1

3 Motivation This work is motivated by a collaboration of nearly two years held with an expert organ-builder. His current task is to rebuild a 17th century-like organ. His main concerns are the metal composition of pipes and old-voicing techniques. Pipes from this period are more likely to produce \noisy" transient bursts sometimes called `chi' or `hiss' and `cough' (onomatopeia). But this is still not much discussed by many organ experts... Chalmers University Of Technology & GOArt (Gbg Organ Center) 2

4 Plan Schematic physical model of a ue organ pipe From a `Signal processing' point of view Harmonics/noise extraction { Algorithms { Choice of lters Example of analysis Conclusion & Discussion Chalmers University Of Technology & GOArt (Gbg Organ Center) 3

5 Physical model Block scheme of the feedback loop in a ue instrument Chalmers University Of Technology & GOArt (Gbg Organ Center) 4

6 A `signal processing' model mouth jet-labium interaction body / resonator deterministic a(t) f(a)=b b(t) b h=c c(t) jet stochastic w(t) Non Linear function f edgetone x(t) Linear filtering impulse h(t) Linear filtering impulse h(t) x h=y + + y(t) z(t Decomposition of output sound z(t) into its harmonic and `noisy' components Chalmers University Of Technology & GOArt (Gbg Organ Center) 5

7 Assumptions & Remarks Linear function is time invariant The fundamental is mode-locked on an air-column mode The uencies of the air-modes are not harmonic Valid at one point of measurement Chalmers University Of Technology & GOArt (Gbg Organ Center) 6

8 Filtering process of the noise nk(t) n(t)=z(t) n(t)=np(t) e-j2πk.f1.t, shift the spectrum towards hig uencies by k.f1 Chalmers University Of Technology & GOArt (Gbg Organ Center) 7

9 Filtering process of harmonics 2.abs() zek(t) z(t) + + zk(t) conjugate Chalmers University Of Technology & GOArt (Gbg Organ Center) 8

10 Vincent Rioux, `Harmonics+noise extraction, a tool for the description of organ pipe sounds'nam 98 IIR elliptic lters 4th order Original Harmonics Step (1 ms) High pass Low pass Time [s] Chalmers University Of Technology & GOArt (Gbg Organ Center) 9

11 The pipe sample Chalmers University Of Technology & GOArt (Gbg Organ Center) 1

12 Vincent Rioux, `Harmonics+noise extraction, a tool for the description of organ pipe sounds'nam 98 Spectrograms Frequency [Hz] Frequency [Hz] Before Time [s] After Time [s] litude [db] litude [db] Chalmers University Of Technology & GOArt (Gbg Organ Center) 11

13 Vincent Rioux, `Harmonics+noise extraction, a tool for the description of organ pipe sounds'nam 98 Harmonics 2 4 litude [db] Harmonics Time [s] 3 & the `brightness' curve, Number of Harmonic Time [s] obtained by P p k=1 kzenv k rms(n(t))+ P p (t) k=1 zenv k (t) Chalmers University Of Technology & GOArt (Gbg Organ Center) 12

14 Vincent Rioux, `Harmonics+noise extraction, a tool for the description of organ pipe sounds'nam 98 Conclusion & Discussion straightforward ltering fast and high sound quality technique necessary for physical prms extraction useful for noise quality evaluation introduced in listening tests practical use for builders? Chalmers University Of Technology & GOArt (Gbg Organ Center) 13

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