Physical modelling synthesis
The Physical Modeling (English Physical Modeling ), also called PM- synthesis, a method for sound production or mutation, the physical properties of a musical instrument or sound device is in the music reflects in a mathematical model. The respective physical properties are as free parameters changeable and can be combined in the model.
Distinction between
The PM- synthesis is a special case of the mathematical modeling of physical processes specifically for the needs of acoustics with particular attention to musical boundary conditions and is comprised of mainly second-order equations of vibration.
The term has nothing to do with the general concept of physics model.
Principle of operation
The Physical modeling is used on the one hand to mimic analog instruments such as flute, violin, sitar and piano. The first digital piano with this technology was the V-Piano of Roland. On the other hand so that acoustic and electro-acoustic devices such as Gitarrenverzerrer or amplifier can be simulated. In addition, new sounds, virtual instruments and devices can be created.
When replicating an instrument it is analyzed in its structure and in its function and, accordingly, divided into modules. The more aspects and influencing parameters are modeled, the more realistic is the behavior of the virtual instrument.
Examples
A vibrating string
A vibrating string is often described simplistically with a sine curve. It is, however, embezzled, strictly speaking, that it takes a two-dimensional movement and the instrument made by repercussions of the suspension on the string tension and thus already the fundamental principle is not exactly sinusoidal. In addition, a plucked, painted or plucked string, each with different starting conditions begins to oscillate. While the attack is a very complicated harmonic behavior is a by which these cases differ from each other. Specifically, formed by plucking with a plectrum or finger nail a triangular course of the string, which rapidly decays after the release and does not produce the fundamental note of the string matching overtones. When a string is plucked like the piano, however, the initial elongation is indeed larger, but limited, " round " and locally, thereby totally different harmonics are generated. When painting a violin string Zerrtöne further added that arise from the permanent snagging and slipping of the string when moving the arc. The vibrations of the instrument body and the finger used act sounded forming and absorbing.
These effects can either take account of the fact that they are analyzed separately and modeled in order empirically to be superimposed later, or to model the string and the sound body by they are divided into small sections, this describes the basic physics formulas and the interaction with neighboring sections into account, resulting in the oscillation behavior by itself.
Saxophone
A saxophone is simplified form of a mouthpiece, a resonance tube and a funnel. In the mouthpiece, the acoustic waves are generated by blowing on a wood flakes; the length of the oscillatory air column in the tube determines the pitch and is changeable by the flaps; through the funnel of the outlet of the large part of the sound radiation characteristics and frequency response can be influenced. All three affect the signal varying elements, and depending on the other elements. Also, the elements influence each other, as occur, for example Structure-borne sound waves, which cause the resonance of the instrument and generate harmonics. If this behavior transferred into a mathematical formula system as the basis for a virtually generated saxophone is created.
Virtual analog synthesizer
Within the sound synthesis by physical modeling company called Virtual Analog Synthesizer up a large room. Here, the structure of the traditional analog synthesizer is modeled by the electrical behavior of the component is simulated by means of the formulas for currents and voltages, their shortcomings are considered.
Electronic Devices
Also in the acoustic music electronic effects play a role in microphones, amplifiers and electronic distortion involved. With the help of the PM, the acoustic behavior of certain types of microphones can be replicated and applied to electronic data streams. Often the behavior of tape devices is simulated with magnetic recording or tube amplifiers and mixed with the sound. Such functions are, inter alia, integrated into digital signal processors, and also available as finished devices as stand-alone instruments, such as can be considered as Gitarrenverzerrer.
Advantages of the virtual model
The advantage of the method is to generate the peculiarities of the instrument corresponding, more live sound. External influences such as the game of the musician can be inserted easily and directly in this way without having any knowledge about the impact since the model takes account of these. The History Forum of the sound and the transition between different playing techniques is continuous. An example of this is the over-blowing an instrument, in which the virtual model behaves quite the model accordingly. This is by sampling or other synthetic forms of non or very difficult and requires knowledge of how to play louder effect on the sound. So, for example, must carried out the aggressive sound of a harder sound when battered wings in the conventional methods through increased Show an additional, harmonic- rich tone, which although may sound similar, but extremely limiting the possibilities.
A major advantage is that the sound of a model always is continuous and there is no end of the sound, while for samples a continuous tone must be produced by forming a loop, which leads to phase shifts in the harmonics - is also becoming increasingly same course of harmonics repeatedly to the fundamental wave steadily. This gives rise to artifacts and unnatural pattern can be where sample-based music easily recognized.
Another advantage is the possibility to combine elements of different instruments, even if this combination would not be possible with real instruments. Distinction must be made only between resonators and pathogens. In the example of the model is the saxophone mouthpiece of the excitation - in which also the transients occur - and the pipe and the bell are resonators. It now has, for example, the ability to connect the mouthpiece of the saxophone with the resonance chamber of a violin. This creates a new virtual instrument with its own sound characteristics. However, it is also only single parameter of an instrument to be changed, such as material composition, size or velocity.
An important advantage is that the parameters of the model by the musician in real time can be changed. Thus it is possible to take during the performance intuitively on the properties of the simulated instrument influence. Thus, for example, continuously affect the attenuation of a virtual piano hammer or even the mood and intonation of Diskants and customize the performance.
Disadvantages of a virtual model
The Physical modeling requires in comparison to other methods by far the highest performance in the synthesizer or computer. Depending on the type of scope of the model must be solved sometimes differential equations and expected high temporal resolutions. In order, for example, simulate the vibration of a guitar string in real time, taking into account also the forming resonances with the body and interact with other strings, more complex equations and their solutions are for each to be calculated sample to find that need to be oversampled at a sufficiently high factor in order to counteract the accumulation of errors. Even at generic equations in which there is no feedback in the calculation paths, thousands of processing steps are often required to calculate a sample. This one comes easily to the limits of the possibilities of technology, and much earlier in the economy. Therefore, models are still simplistic to expect current DSP platforms or even computers, a sufficiently large number of voices can. However, the simplifications made to remove the sound again from the theoretical ideal.
Platforms
In addition to some realizations in C software, which can be used as a plug -in for the relevant music programs or are integrated into classical sampler programs, especially DSP platforms and FPGA platforms are used in the PM- synthetic processes. DSPs are more economical and easier to handle; FPGAs offer the highest computing capacity and bandwidth for high sample rates due to real parallel processing. A more recent approach is the use of graphics cards that have advantages especially in FEM -based computational models.