Chaos: An Interdisciplinary Journal of Nonlinear Science
The Impulse Pattern Formulation (IPF) is an analytical modeling approach for synergetic systems i... more The Impulse Pattern Formulation (IPF) is an analytical modeling approach for synergetic systems in general, motivated by research on musical instruments. Based on the assumption that the coupling of system components can be described by the interaction between individually propagating and exponentially damped impulse trains, the IPF describes tone generation in musical instruments as self-organized systems. In contrast to other nonlinear recursive functions such as the Logistic Map, system predictions cannot be derived easily from knowledge on other theories, neither can the system be completely examined analytically. Therefore, several numerical simulations are performed to explore stable regions and limits of the IPF.
A sound field synthesis method taking psychoacoustic perception constraints into account is propo... more A sound field synthesis method taking psychoacoustic perception constraints into account is proposed and experimentally verified. It aims at reconstructing a desired sound field within an extended listening area. The essential innovations in this sound field synthesis approach are the radiation method and the precedence fade which are introduced in this paper. The principle is kept flexible to be compatible with audio systems such as 5.1 surround, ambisonics setups, wave field synthesis installations from a small to a very large number of loudspeakers as well as with unsymmetrical loudspeaker distributions like automotive audio systems. By capturing and reconstructing the sound radiation characteristics of musical instruments a spatial sound impression can be created. Psychoacoustic considerations are implemented to allow for wave fronts arriving from different angles and at different points in time while maintaining a pre- cise source localization and a natural and spatial sound impression. Furthermore, the psychoa- coustic considerations reduce the computational costs. Strengths and weaknesses, benefits and limitations of the psychoacoustic sound field synthesis approach are investigated in a listen- ing test. Future developments, combinations with other wave field synthesis approaches and applications for musical performance practice and for research are discussed in the prospects.
The pat wain, a unique drum circle found in Myanmar is investigated in terms of its tuning. The 2... more The pat wain, a unique drum circle found in Myanmar is investigated in terms of its tuning. The 21 drums are pitched, where tuning is achieved by adding a paste to the drum heads. Additionally, as percussion instruments do not have a perfect harmonic overtone structure, the drums need to be tuned within their spectrum. Using a Finite-Difference model of the drum it is shown that the pitches of the drum decreases with additional mass on the drum head. Still also the overtone structure of the sound changes relative to the fundamental frequency, where applying paste at about half of the drum radius leads to a best fit of the second and third harmonic towards frequency relations of 2:1 and 3:1 respectively. The drum head has a strong internal damping, leading to a very fast decay of the overtones. Still the fundamental decays slowly due to tuning the drum back head to the same frequency as the front membrane. The second and third partials are prolonged as they fit within eigenmodes of the drum air volume. The strong damping, enhanced by the paste, does not change the pitches considerably, which is shown using a viscoelastic Finite-Difference Time Domain model.
The tuning of the Myanmar pat wain, a unique drum circle consisting of 20 double-headed drums of ... more The tuning of the Myanmar pat wain, a unique drum circle consisting of 20 double-headed drums of a hsain wain orchestra is investigated. The drums have clear pitches over three and a half octaves, unusual for a percussion instrument, and are tuned by adding a paste pa sa on the drum head consisting of rice and ashes. It was investigated by the author during a field trip in northern Myanmar during its tuning process. The drum head is modeled using a time-dependent Finite-Difference Method (FDM), solving the differential equation of the two membranes on a 63x63 grid each, with a sample rate of 96kHz, using a Gauss-shaped impulse as driver. The internal air is modeled as a delay line between the two drums. The aim was to estimate pitch and mode changes on the beating membrane due to adding of the paste. To estimate the influence of viscoelasticity on the pitches, the membrane differential equation was enlarged to a viscoelastic model using a complex, frequency dependent Young's modulus transferred into the time domain using a Laplace transform. The calculation was performed on a NVIDIA GTX960 GPU, which is highly parallel, where calculating one second of a drum sound needed about 10 seconds. The sound was calculated as integral of the radiating of the beating membrane points with respect to a place above this membrane. The material properties on the FDM grid were implemented according to the mass distribution of the leather membrane and the paste. It appears that the strong pitch impression of the drum is caused by several factors. The fundamental shows a long decay due to the interaction of the front with the back membrane. The second and third harmonics are enhanced by the inclosed air. Both are tuned near harmonic relations to the fundamental by the distribution of the paste, which changes the harmonic relations, a result previously also found for Indian tabla drums. The higher harmonics are damped due to strong internal damping of the membrane. The viscoelastic FDM for the upper drum head showed strong that the viscoelastic internal damping due to the paste does not change the pitches considerably. The results are compared to the field recordings, which show considerable damping and pitch glides with low-pitched drums. Also the tuning of the drum circle is compared to different tuning systems showing similarities to a tuning pattern of Cambodian roneat deik metalophone.
The Journal of the Acoustical Society of America, 2016
A synchronization experiment on two mutual interacting organ pipes is compared with a theoretical... more A synchronization experiment on two mutual interacting organ pipes is compared with a theoretical model which takes into account the coupling mechanisms by the underlying first principles of fluid mechanics and aeroacoustics. The focus is on the Arnold-tongue, a mathematical object in the parameter space of detuning and coupling strength which quantitatively captures the interaction of the synchronized sound sources. From the experiment, a nonlinearly shaped Arnold-tongue is obtained, describing the coupling of the synchronized pipe-pipe system. This is in contrast to the linear shaped Arnold-tongue found in a preliminary experiment of the coupled system pipe-loudspeaker. To understand the experimental result, a coarse-grained model of two nonlinear coupled self-sustained oscillators is developed. The model, integrated numerically, is in very good agreement with the synchronization experiment for separation distances of the pipes in the far field and in the intermediate field. The m...
Abstract Three guitars are characterized using 96 initial transients each, recorded over four str... more Abstract Three guitars are characterized using 96 initial transients each, recorded over four strings, playing with four notes on each string, apoyando and tirando and in three different loudnesses. These initial sounds have been analysed using the fractal correlation ...
Acoustical Society of America Journal, Apr 1, 2005
... the tonal frequency range compared to psychoacoustic discrimination tasks by listeners. Micro... more ... the tonal frequency range compared to psychoacoustic discrimination tasks by listeners. Microrhythm here is defined as the temporal distance between two amplitude peaks. As initial transients are a crucial part of the sound ...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015
Measured auditory nervous spikes often show synchronization, phase-locking, or entrainment (P. Ca... more Measured auditory nervous spikes often show synchronization, phase-locking, or entrainment (P. Cariani, Neural Plast. 6(4), 142-172 (1999) and Kumaresana et al., J. Acoust. Soc. Am. 133(6), 4290-4310 (2013). Physiologically synchronization is found in the anteroventral cochlear nucleus (Joris et al., J. Neurophysiol. 71(3), 1022-1036 (1994)) or in the trapezoid body also between critical bandwidths (Louage et al., Auditory Signal Processing: Physiology, Psychoacoustics, and Models (Springer, New York, 2004), pp. 100-106). The effect is an enhancement of pitch detection, spatial localization, or speech intelligibility. To investigate the presence of synchronization already in the cochlea, in the present paper, a finite-difference time-domain model of the cochlea is implemented with conditions for spike excitation caused by mechanical basilar membrane displacement. This model shows synchronization already in the cochlea at the transition from mechanical waves to nerve spike excitation. Using a sound as model input consisting of ten harmonic overtones with random phase relations, the output spikes are strongly phase aligned after this transition. When using a two-sinusoidal complex as input, and altering the phase relations between the two sinusoidals, the output spikes show the higher sinusoidal shifting the phase of the lower one in its direction in a systematic way. Therefore, already during the transition from mechanical to electrical excitation within the cochlea, synchronization appears to be improving perception of pitch, speech, or localization.
Chaos: An Interdisciplinary Journal of Nonlinear Science
The Impulse Pattern Formulation (IPF) is an analytical modeling approach for synergetic systems i... more The Impulse Pattern Formulation (IPF) is an analytical modeling approach for synergetic systems in general, motivated by research on musical instruments. Based on the assumption that the coupling of system components can be described by the interaction between individually propagating and exponentially damped impulse trains, the IPF describes tone generation in musical instruments as self-organized systems. In contrast to other nonlinear recursive functions such as the Logistic Map, system predictions cannot be derived easily from knowledge on other theories, neither can the system be completely examined analytically. Therefore, several numerical simulations are performed to explore stable regions and limits of the IPF.
A sound field synthesis method taking psychoacoustic perception constraints into account is propo... more A sound field synthesis method taking psychoacoustic perception constraints into account is proposed and experimentally verified. It aims at reconstructing a desired sound field within an extended listening area. The essential innovations in this sound field synthesis approach are the radiation method and the precedence fade which are introduced in this paper. The principle is kept flexible to be compatible with audio systems such as 5.1 surround, ambisonics setups, wave field synthesis installations from a small to a very large number of loudspeakers as well as with unsymmetrical loudspeaker distributions like automotive audio systems. By capturing and reconstructing the sound radiation characteristics of musical instruments a spatial sound impression can be created. Psychoacoustic considerations are implemented to allow for wave fronts arriving from different angles and at different points in time while maintaining a pre- cise source localization and a natural and spatial sound impression. Furthermore, the psychoa- coustic considerations reduce the computational costs. Strengths and weaknesses, benefits and limitations of the psychoacoustic sound field synthesis approach are investigated in a listen- ing test. Future developments, combinations with other wave field synthesis approaches and applications for musical performance practice and for research are discussed in the prospects.
The pat wain, a unique drum circle found in Myanmar is investigated in terms of its tuning. The 2... more The pat wain, a unique drum circle found in Myanmar is investigated in terms of its tuning. The 21 drums are pitched, where tuning is achieved by adding a paste to the drum heads. Additionally, as percussion instruments do not have a perfect harmonic overtone structure, the drums need to be tuned within their spectrum. Using a Finite-Difference model of the drum it is shown that the pitches of the drum decreases with additional mass on the drum head. Still also the overtone structure of the sound changes relative to the fundamental frequency, where applying paste at about half of the drum radius leads to a best fit of the second and third harmonic towards frequency relations of 2:1 and 3:1 respectively. The drum head has a strong internal damping, leading to a very fast decay of the overtones. Still the fundamental decays slowly due to tuning the drum back head to the same frequency as the front membrane. The second and third partials are prolonged as they fit within eigenmodes of the drum air volume. The strong damping, enhanced by the paste, does not change the pitches considerably, which is shown using a viscoelastic Finite-Difference Time Domain model.
The tuning of the Myanmar pat wain, a unique drum circle consisting of 20 double-headed drums of ... more The tuning of the Myanmar pat wain, a unique drum circle consisting of 20 double-headed drums of a hsain wain orchestra is investigated. The drums have clear pitches over three and a half octaves, unusual for a percussion instrument, and are tuned by adding a paste pa sa on the drum head consisting of rice and ashes. It was investigated by the author during a field trip in northern Myanmar during its tuning process. The drum head is modeled using a time-dependent Finite-Difference Method (FDM), solving the differential equation of the two membranes on a 63x63 grid each, with a sample rate of 96kHz, using a Gauss-shaped impulse as driver. The internal air is modeled as a delay line between the two drums. The aim was to estimate pitch and mode changes on the beating membrane due to adding of the paste. To estimate the influence of viscoelasticity on the pitches, the membrane differential equation was enlarged to a viscoelastic model using a complex, frequency dependent Young's modulus transferred into the time domain using a Laplace transform. The calculation was performed on a NVIDIA GTX960 GPU, which is highly parallel, where calculating one second of a drum sound needed about 10 seconds. The sound was calculated as integral of the radiating of the beating membrane points with respect to a place above this membrane. The material properties on the FDM grid were implemented according to the mass distribution of the leather membrane and the paste. It appears that the strong pitch impression of the drum is caused by several factors. The fundamental shows a long decay due to the interaction of the front with the back membrane. The second and third harmonics are enhanced by the inclosed air. Both are tuned near harmonic relations to the fundamental by the distribution of the paste, which changes the harmonic relations, a result previously also found for Indian tabla drums. The higher harmonics are damped due to strong internal damping of the membrane. The viscoelastic FDM for the upper drum head showed strong that the viscoelastic internal damping due to the paste does not change the pitches considerably. The results are compared to the field recordings, which show considerable damping and pitch glides with low-pitched drums. Also the tuning of the drum circle is compared to different tuning systems showing similarities to a tuning pattern of Cambodian roneat deik metalophone.
The Journal of the Acoustical Society of America, 2016
A synchronization experiment on two mutual interacting organ pipes is compared with a theoretical... more A synchronization experiment on two mutual interacting organ pipes is compared with a theoretical model which takes into account the coupling mechanisms by the underlying first principles of fluid mechanics and aeroacoustics. The focus is on the Arnold-tongue, a mathematical object in the parameter space of detuning and coupling strength which quantitatively captures the interaction of the synchronized sound sources. From the experiment, a nonlinearly shaped Arnold-tongue is obtained, describing the coupling of the synchronized pipe-pipe system. This is in contrast to the linear shaped Arnold-tongue found in a preliminary experiment of the coupled system pipe-loudspeaker. To understand the experimental result, a coarse-grained model of two nonlinear coupled self-sustained oscillators is developed. The model, integrated numerically, is in very good agreement with the synchronization experiment for separation distances of the pipes in the far field and in the intermediate field. The m...
Abstract Three guitars are characterized using 96 initial transients each, recorded over four str... more Abstract Three guitars are characterized using 96 initial transients each, recorded over four strings, playing with four notes on each string, apoyando and tirando and in three different loudnesses. These initial sounds have been analysed using the fractal correlation ...
Acoustical Society of America Journal, Apr 1, 2005
... the tonal frequency range compared to psychoacoustic discrimination tasks by listeners. Micro... more ... the tonal frequency range compared to psychoacoustic discrimination tasks by listeners. Microrhythm here is defined as the temporal distance between two amplitude peaks. As initial transients are a crucial part of the sound ...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015
Measured auditory nervous spikes often show synchronization, phase-locking, or entrainment (P. Ca... more Measured auditory nervous spikes often show synchronization, phase-locking, or entrainment (P. Cariani, Neural Plast. 6(4), 142-172 (1999) and Kumaresana et al., J. Acoust. Soc. Am. 133(6), 4290-4310 (2013). Physiologically synchronization is found in the anteroventral cochlear nucleus (Joris et al., J. Neurophysiol. 71(3), 1022-1036 (1994)) or in the trapezoid body also between critical bandwidths (Louage et al., Auditory Signal Processing: Physiology, Psychoacoustics, and Models (Springer, New York, 2004), pp. 100-106). The effect is an enhancement of pitch detection, spatial localization, or speech intelligibility. To investigate the presence of synchronization already in the cochlea, in the present paper, a finite-difference time-domain model of the cochlea is implemented with conditions for spike excitation caused by mechanical basilar membrane displacement. This model shows synchronization already in the cochlea at the transition from mechanical waves to nerve spike excitation. Using a sound as model input consisting of ten harmonic overtones with random phase relations, the output spikes are strongly phase aligned after this transition. When using a two-sinusoidal complex as input, and altering the phase relations between the two sinusoidals, the output spikes show the higher sinusoidal shifting the phase of the lower one in its direction in a systematic way. Therefore, already during the transition from mechanical to electrical excitation within the cochlea, synchronization appears to be improving perception of pitch, speech, or localization.
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Papers by Rolf Bader