Energy-Based Synthesis of Tension Modulation in Strings - Sound Examples
This is the homepage of the paper

Balázs Bank, "Energy-Based Synthesis of Tension Modulation in Strings," Proceedings of the 12th International Conference on Digital Audio Effects (DAFx-09), Paper ID: 76, Como, Italy, Sept. 2009.

Abstract

Above a certain amplitude, the string vibration becomes nonlinear due to the variation of tension. An important special case is when the tension varies with time but spatially uniform along the string. The most important effect of this tension modulation is the exponential decay of the pitch (pitch glide). In the case of nonrigid string termination, the generation of double frequency terms and the excitation of missing modes also occurs, but this is perceptually less relevant for most of the cases. Several modeling strategies have been developed for tension modulated strings. However, their computational complexity is significantly higher compared to linear string models. This paper proposes efficient techniques for modeling the quasistatic part (short-time average) of the tension variation that gives rise to the most relevant pitch glide effect. The modeling is based on the linear relationship between the energy of the string and quasistatic tension variation. When this feature is added to linear string models, the computational complexity is increased by a negligible amount, leading to significant savings compared to earlier tension modulated string models.

Sound examples

Recorded sounds

A few examples to show how tension modulation sounds in real instruments:

Electric guitar
A low E electric guitar string (f0=82.1 Hz), with a pluck amplitude around 3 mm. (Courtesy of Jyri Pakarinen).

Tom-tom drum
Tension modulation is also important in drums. Altough this paper is about string modeling, the idea seems to be applicable for drums as well, which is part of future research.

Similated sound examples

The sound examples presented here are for a low E electric guitar string (f0=82.1 Hz), with a pluck amplitude of 5 mm. The modeling is done with a 100 element finite difference model and the output is the velocity of the string at pickup position, filtered by a second-order lowpass, which corresponds to a simplified model of the electric guitar pickup. The plucking is modeled by setting the initial displacement to a triangle shape. The terminations of the string are infinitelly rigid.

Linear string model
This is a linear string model where the tension is constant during vibration (no tension modulation, thus, no pitch glide).

Tension modulated string model
In this case the tension is calculated from the elongation of the string (tension modulated synthesis used by the literature).

Energy-based tension modulation
Now only the quasistatic temporal variation of the tension is modeled, which is calculated from the energy of the string, leading to significant computational savings (see Secs. 4. and 5.1 in the paper).

Physically informed tension calculation based on an energy model
Similar to the previous example, but here a separate model (basically, a first order lowpass filter) estimates the energy of the string (see Sec. 5.2 in the paper).

Additional examples

The same examples as above, but now the guitar pluck amplitude is double as before (10 mm), which makes the pitch glide more audible. Note that this is for illustrative purposes only, it is not typical to have such a large pitch glide in electric guitars.

Linear string model

Tension modulated string model

Energy-based tension modulation

Physically informed tension calculation based on an energy model


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Last modified: 30.08.2009