Physical modeling (sound generation)

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The physical modeling ( English Physical Modeling ), also called PM synthesis , is a method in music for generating or modifying sound , which maps the physical properties of a musical instrument or acoustic device in a mathematical model . The respective physical properties can be freely changed and combined as parameters in the model.

Definition of terms

The PM synthesis is a special case of the mathematical modeling of physical processes especially for the concerns of the acoustics with special consideration of musical boundary conditions and mainly comprises oscillation equations of the second order.

The term has nothing to do with the general concept of a model in physics .

Working principle

Physical modeling is used to create sound to imitate acoustic instruments such as flute, violin, sitar , guitar, harp or piano. The first digital piano with this technology was the Roland V-Piano . On the other hand, it can be used to simulate electroacoustic devices such as guitar distortion units or amplifiers .

When simulating an instrument, its structure and functions are analyzed and broken down into modules accordingly. This affects both the mechanics and their vibration behavior, including any electronics that may be present. The more aspects and influencing parameters that are modeled, the more realistic the behavior of the virtual instrument is.

By varying the parameters beyond the real limits, new sounds can also be created.

Examples

Vibrating string

A vibrating string is often described in a simplified manner with a sine curve. However, the fact that, strictly speaking, it performs a two-dimensional movement and, depending on the instrument, the suspension has repercussions on the string tension, and therefore the fundamental wave is not exactly sinusoidal. In addition, a plucked, bowed or struck string begins to vibrate with different starting conditions. During the settling phase, a very complex harmonic behavior occurs, which distinguishes these cases from one another. Specifically, plucking with a pick or a fingernail creates a triangular shape of the string, which quickly fades out after letting go and creates overtones that do not match the fundamental tone of the string. On the other hand, when a string is struck, as on the piano, the initial elongation is larger, but more "round" and locally limited, which creates completely different harmonics. When a violin string is bowed, there are additional tones caused by the permanent snagging and slipping of the string when the bow is moved. The vibrations of the instrument body and the fingers placed on it also have a sound-forming and dampening effect.

These effects can either be taken into account by analyzing and modeling them separately from one another in order to superimpose them empirically later, or by modeling the string and the sound body by dividing them into small sections, describing them with basic physical formulas and the interaction with their neighboring sections are taken into account, whereby the vibration behavior results automatically.

saxophone

In simplified terms , a saxophone consists of a mouthpiece , a resonance tube and a funnel. In the mouthpiece, the sound waves are generated by blowing onto a piece of wood; the length of the vibrating column of air in the pipe determines the pitch and can be changed using the flaps ; The funnel, from which the majority of the sound emerges, influences the radiation characteristics and frequency response . All three elements influence the signal differently and depending on the other elements. The elements also influence each other. B. Structure-borne sound waves, which cause the resonances of the instrument and generate overtones. If this behavior is transferred to a mathematical formula system, the basis for a virtually generated saxophone is created.

Virtual analog synthesizer

So-called virtual analog synthesizers take up a large part of the sound synthesis in electronic music using physical modeling . In these, the structure of the classic analog synthesizer is modeled by simulating the electrotechnical behavior of the components using formulas for currents and voltages, whereby weaknesses of the components are also taken into account.

Electronic equipment

Electronic effects also play a role in acoustic music when microphones , amplifiers and distortions are involved. With the help of the PM, the acoustic behavior of certain microphone types can be simulated and applied to mathematical data streams. Often the behavior of tape recorders with magnetic recording or tube amplifiers is simulated and mixed with the sound. Such functions include a. integrated in digital signal processors and also available as finished devices that can be used as independent musical instruments, e.g. B. can be viewed as a guitar distortion.

Advantages of the virtual model

The advantage of the process is to produce a more lively sound that corresponds to the characteristics of the respective instrument . In this way, external influences such as the musician's playing can be introduced very easily and directly, without knowing the effects, since the model takes them into account. The course of the sound and the transition between different playing techniques is continuous. An example of this is overblowing an instrument, in which the virtual model behaves entirely according to the original. This is difficult or impossible with sampling or other forms of synthesis and requires knowledge of how louder playing affects the sound. So z. For example, the more aggressive sound of a harder struck note on a grand piano can be achieved with conventional methods by fading in an additional, harmonic-rich tone, which may sound similar, but extremely restricts the possibilities.

A major advantage is that the tone signal of a model is always continuous and there is no end of the tone, while with samples a continuous tone has to be generated by forming a loop, which leads to phase jumps in the harmonics - in addition, the harmonics are always the same to the fundamental repeatedly repeated. This creates artifacts and unnatural patterns by which sample-based music can be easily recognized.

Another advantage is the ability to combine elements from different instruments, even if this combination with real instruments would not be possible. A distinction only needs to be made between resonators and pathogens. In the example of the saxophone model, the mouthpiece is the exciter - at which the transients also arise - and the pipe and the bell are resonators. For example, you now have the option of connecting the mouthpiece of the saxophone to the resonance chamber of a violin . This creates a new virtual instrument with its own sound characteristics. However, only individual parameters of an instrument can be changed, such as material properties, size or velocity.

An important advantage is that the parameters of the model can be changed by the musician in real time . It is thus possible to intuitively influence the properties of the instrument to be simulated during the performance. So z. B. continuously influence the damping of a virtual piano hammer or even the mood or intonation of the treble and adapt it to the performance.

Disadvantages of a virtual model

Compared to other methods, physical modeling requires by far the highest computing power in a computer or synthesizer . Depending on the type and scope of the model, differential equations must sometimes be solved and calculated with high clock frequencies . To z. For example, to simulate the vibration of a guitar string in real time and also to take into account the resonances that develop with the body and the interaction with other strings, several complex equations and their solutions must be found for each sample to be calculated, which are calculated with a sufficiently high oversampling must be used to counteract the accumulation of errors. Even with generic equations, where there is no feedback in the calculation paths, thousands of calculation steps are often necessary to calculate a sample of a sound. In doing so, you quickly reach the limits of the capabilities of the processors and even earlier on the limits of economic efficiency. Therefore, the models are still very much simplified in order to be able to calculate a sufficiently large number of voices with current DSP platforms or even computers. The simplifications made remove the sound from the physical ideal.

Platforms

In addition to some realizations in C software that can be used as a plug-in for the relevant music programs or are integrated into classic sampler programs, DSP platforms and FPGA platforms are mainly used in PM synthesis . DSPs are more economical and easier to use; Due to their real parallel processing, FPGAs offer the highest computing capacities and bandwidths for high sample rates. A more recent approach is the use of graphics cards, which have advantages especially with FEM -based calculation models.

PM synthesis is found today primarily in professional synthesizers and some DSP-based sound cards. The first card available that featured a simple form of the PM was the Creative Soundblaster AWE 64 in 1996 .

Due to the advancing technology, there are now also DIY projects with single-board computers and microcontrollers such as AVR and STM32 as modules for your own structures.  

literature

  • Uwe G. Hoenig: Workshop Synthesizer. Sound generation for musicians. From analog to digital to software synthesizer PPV, Presse-Project-Verlag, Bergkirchen 2002, ISBN 3-932275-27-6 .
  • Thomas Görne: Sound engineering. Fachbuchverlag Leipzig by Carl Hanser Verlag, Munich a. a. 2006, ISBN 3-446-40198-9 .

Web links

Individual evidence

  1. ↑ Henri Hagenow: Digital synthesis of complex waveforms for the simulation of acoustic, electrical and optical eigenstates (PDF; 5.5 MB). Diploma thesis at TU Berlin, 2001.
  2. ↑ Sadjad Siddiq: The arithmetical replica of the sitar (PDF; 10.2 MB). Diploma thesis at the University of Vienna, 2010
  3. ^ Gilette Guitars, Joe Wolfe: Guitar acoustics. UNSW Australia, 2006, accessed 2020 (Australian English).
  4. ↑ Joe Wolfe: Harp Acoustics. University of New South Wales, 2006, accessed 2020 (Australian English).
  5. ↑ Test: Roland V-Piano, Stage & Grand E-Piano. In: AMAZONA.de. February 17, 2010, accessed August 2020 .
  6. ↑ Chris Nova: Creative Labs Awe64 Gold (Nov 1996). old school daw, August 25, 2017, accessed on July 19, 2020 .
  7. ↑ Creative Labs AWE64. In: webarchive. Sound on Sound, June 6, 2015, accessed July 19, 2020 .
  8. ↑ TW: Zynthian: A complete open source synthesizer on Raspberry-Pi. Keyboard World, June 11, 2018, accessed August 2020 .
  9. ↑ SAM: 17 channel Avr Synthesizer in Asm - Mikrocontroller.net. In: UCNET. Andreas Schwarz, September 21, 2011, accessed August 2020 .
  10. ↑ Plonk - Physical Modeling Percussion Synthesizer. Intellijel, 2020, accessed August 2020 (American English).