VITA 2010

  Vienna Talk 2010 on Music Acoustics
"Bridging the Gaps"
      September 19–21


Special topic: Nonlinear effects in wind instruments (M. Campbell): Description

Nonlinear effects in wind instruments and the reason for brassiness of brass wind instruments have recently got specific attention. All new findings on these topics should be presented in this special topic session.

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Campbell; Murray: 
(Keynote) / O
Over the last five centuries or more, the musical brass family has evolved into an extended tribe of instruments of widely varying shapes, sizes and materials. There is no doubt that this diversity of form and construction reflects a variety of musical function which is demanded and prized by composers, performers and audiences. On the other hand, brass instruments share many common features: they all start with the same type of sound generator (the human lips), and apart from the side-hole instruments they all radiate the sound through a single terminating bell. Indeed, at low dynamic levels it can be difficult to distinguish the timbre of one brass instrument from another. This talk reviews the features of design and construction which contribute to the striking differences in timbre evident in musical performance on different types of brass instruments, and attempts to relate these to the underlying linear and nonlinear acoustical principles.
Beauchamp; James: 
(Invited) / O
Source/filter models are frequently used to model sound production of the vocal apparatus and musical instruments. They certainly seem to work very well for the voice and for instruments where there is loose coupling between excitation and resonator as in the case of classical string instruments, but it may be a different situation for wind instruments. Beginning in 1968, in an effort to measure a filter characteristic (aka transmission response) of a trombone while it is being played by an expert musician, sound pressure waveforms from the mouthpiece and the bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s filter characteristic. The first such recordings were done on professional 1/4 inch stereo tape. Results showed that the filter was a high-pass with a cutoff frequency around 900 Hz. Whereas the characteristic below cutoff was quite stable, above cutoff it was extremely variable. In addition, measurements made using a swept sine wave system verified the high-pass characteristic, but it also showed a series of resonances whose minima correspond to the harmonic frequencies under playing conditions. For frequencies below cutoff the two types of measurements corresponded well, but above cutoff there was a considerable difference. The general effect is that output harmonics above 900 Hz are greater than would be expected from linear filter theory, and this effect becomes stronger as performance dynamic increases. Indeed, this effect was verified by theory and measurements in the 1990’s and early 2000’s which showed that nonlinear propagation takes place in the trombone causing a wave sharpening effect at high amplitudes, thus increasing the strength of the upper harmonics [Hirschberg, Gilbert, Msallam, and Wijnands, J. Acoust. Soc. Am., 1996; Thompson and Strong, J. Acoust. Soc. Am., 2001]. Recently this author made new digital recordings of trombone mouthpiece and anechoic output signals which he believes will allow more accurate measurement of the trombone filter characteristic. Also, a real-time musical sound analysis program was developed that can be used to display the input/output filter response in real time [Madden and Beauchamp, Proc. 1999 Int. Computer Music Conf.].

Related experiments in the 1980s and 1990s were aimed at brass synthesis. The first used a source/filter model for brass synthesis where the source was created by nonlinear distortion of a variable-amplitude sine wave, and the filter was a second-order high-pass type with a cutoff frequency tailored to the particular instrument. In the 1990s a version using multiple waveforms which were interpolated to select spectral-envelope-indexed spectral envelopes and a spectral centroid-vs-time function was used for trumpet synthesis.
Kemp; Jonathan: 
(Invited) / O
The subject of super high notes in playing the trumpet or horn is a current area of controversy. Playing these notes might be expected to involve vibrating the lips at a frequency higher than the cut-off frequency of the horn predicted by linear acoustic theory. No reflections of acoustic energy would thus influence the player’s lip vibration. This would in turn imply that the notes would not be controlled by the instrument resonances. Statements by players contradict this theory in that they report that the super-high notes are “slotted” in that the instrument resonances influence the notes that can be played in the super-high range.

It is well known that non-linear effects occur in brass instruments in playing loud notes. This has been demonstrated by various researchers, for instance by measurement of the pressure signals which show a far greater number of harmonics at the bell in comparison to the mouthpiece. Recent research has demonstrated separation of forward and backward going waves while a horn is being played. This study will work towards wave separation within an instrument bore to demonstrate whether reflections from the instrument influence lip vibration and whether non-linear effects are always present during super high note playing.
Pyle; Robert: 
(Invited) / O
The degree of spectral enrichment of brass-instrument tone due to non-linear propagation in the instrument depends not only on the amplitude of the sound, but also on the maximum rate of change of the sound pressure in the mouthpiece. A skilled player has some control over the generated wave shape, but the internal contour of the mouthpiece is also very important. Judging from the sounds produced, a funnel-shaped (horn-like) mouthpiece encourages a less steep waveform than does a bowl-shaped (trumpet-like) mouthpiece. This talk will open with a review of the physics of finite-amplitude sound propagation in a flaring tube, and how this has led to the definition of a ``brassiness coefficient'' that predicts the relative degree of spectral enrichment for various brass instruments. The remainder of the talk will focus on the influence of the mouthpiece. Internal (within the mouthpiece) and external (beyond the bell) measurements of sound pressure and spectrum will be shown for a trumpet equipped with both a conventional trumpet mouthpiece and a flugelhorn mouthpiece.
Vergez; Christophe: 
(Invited) / O
Most of the time, wave propagation in musical wind instruments is justifiably considered to be linear. The acoustic propagation inside the bore of the instruments may then be described though a linear formalism both in the time and in the frequency domains : impedance, admittance, transmission line theory, convolution …
A well-known counter-example is the case of brass instruments (especially trumpets, trombones like instruments) at high sound level. In this case, the nonlinear effects become dominant. They account for the graduated waveshape distortion due to their cumulative nature which eventually leads to the arrival of shock-waves.
We present an exact method to solve a one-dimensional nonlinear wave equation in a dissipative non homogeneous media when the damping is frequency-independent. This work was motivated by the case of brass musical instruments. Though in that latter case, the medium is homogeneous, our approach is more general. Sound examples will be presented to emphasize the influence of nonlinear propagation effects in sound synthesis.
Measurement and emulation of audio systems (devices, environments and soundboxes) have been walked in these years. The most used methods to obtain information about an audio system are those based on measuring its impulse response (IR). Once the IR has been caught it is possible to recreate, by the use of linear convolution, the output signal that the audio system will generate when it is physically driven by any input signal. This method gives great results if the system is linear and time-invariant (environments behaviour is much linear and therefore its reverberant effect can be faithfully recreated using IRs) but not satisfactory in other cases, such as the emulation of tube preamps (mainly nonlinear) and musical instruments. Since the musical instruments cannot be considered completely linear, their musical performance might be analysed properly considering also their nonlinear behaviour.
By the use of Volterra series it is possible to represent the input-output relationship of nonlinear systems. This mathematical theory uses a set of impulse responses to describe the system and not only one as before. By an enhanced impulse response measurement method it is possible to obtain this set of impulses and then by Volterra series it will be possible to have the output of the audio system driven by any input. A special numerical tool has been developed to recreate the system behaviour by using this method. Satisfactory results have been obtained in comparison with the traditional linear convolution based approach.
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