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A string excitation model for audio synthesis of bowed string instruments Disclosure Number: IPCOM000234615D
Original Publication Date: 2014-Jan-22
Included in the Prior Art Database: 2014-Jan-22
Document File: 4 page(s) / 144K

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Linux Defenders

Related People

Volker Schatz: AUTHOR


This disclosure describes an audio synthesis model for the excitation of the strings of a musical string instrument by a bow. Inspired by research results pertaining to block-sliding motion, it superimposes regular pulse trains in a self-similar manner. The result is perturbed randomly to account for natural variations and thereby yields a statistically self-similar pulse-train.

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A string excitation model for audio synthesis of bowed string instruments

Volker Schatz

Keywords: musical instrument synthesis, bowed strings, string excitation


This invention forms one component of a physical model for synthesizing the sound of a bowed string instrument. Such physical synthesis requires a model of the string excitation, of the string itself and of the instrument body, with the output of each component fed into the next, as displayed in the figure below.

An excitation model describes how the bow drives the oscillation of the string when moved across it. The string model describes the resonance of the string and usually includes a backfeed loop. The simplest string model is that of Karplus and Strong which consists of a feedback delay line with an order-2 lowpass. More complex string models take the two transverse oscillation modes of a string and their interac- tion at the bridge and at the bow into account. Body resonance models range from reverberation filters to physical models of the instrument body.

Description of the model

This invention was inspired by a model for a block-sliding motion [1]. It is statisti- cally self-similar, accounting for the fact that real-world materials show similar struc- tures at different scales [2]. As described in [1], a block sliding on an inclined surface moves in lurches, with larger lurches being less frequent according to a power law. This principle can be transferred to string excitation by generating a small plucking of the string for each lurch of the bow. Accordingly, this excitation model generates a statistically self-similar pulse train in which the intervals between pulses of a given height are smaller for smaller pulse heights.

The self-similar pulse train is generated by adding up several regular pulse trains whose intervals differ by constant factors and whose amplitudes are related to their intervals by a power law:

f(t) =



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January 2014

Excitation model

String model

Body resonance model

`i ~( `i; t) ,


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where is the interval of the largest regular pulse train, ` < 1 the scaling factor by which the intervals of successive component pulse trains differ and0 the exponent of the power law between interval and height. The function ~ describes a regular pulse train and is defined as follows in a continuous and discretised formu- lation of the model, respectively:

continuous: ~(d; t) =




Compared to the strictly self-similar formula (1), the model introduces two kinds of randomness to make the output more natural. The intervals and pulse heights of each regular component pulse train are perturbed independently by a normal- distributed relative variation. Secondly, the component pulse trains are time-shifted randomly relative to each other so that not all first pulses coincide at t = 0.

When pulses coincide, their amplitudes are not added, but only the larger pulse is output. This can occur repeatedly as a consequence of...