... ¹

Work supported by the Wallenberg Global Learning Network

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... CCRMA²

http://ccrma.stanford.edu/planetccrma/software/

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...PASP;³

http://ccrma.stanford.edu/~jos/pasp/Digital_Waveguide_Theory.html

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...Karplus⁴

See also http://en.wikipedia.org/wiki/Karplus-Strong_string_synthesis

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...JOSFP.⁵

http://ccrma.stanford.edu/~jos/filters/Phase_Delay.html

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... average.⁶

Exact resonance tuning is found by determining the poles of the system and their angles in the $z$-plane [12]. More relevant perceptually are the frequencies of local maxima in the magnitude frequency response.

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... composition⁷

``Silicon Valley Breakdown'' by David A. Jaffe

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... integer.⁸

One may also use rounding to the nearest integer, which can be defined as $\lfloor x+0.5\rfloor$.

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... phenomenon:⁹

A ``spectral modeling filter'' of this nature is only needed for spectrally monotonous excitations such as the KS digitar noise burst. A proper physical string-excitation model should have this behavior built in.

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....¹⁰

The $-3$dB-gain frequency $\omega_1$ is often called the break frequency in the context of classical control design. This is because, as frequency $\omega$ increases from $0$, the pole at $s=-\omega_1$ has little effect on the frequency response until $\omega\approx\omega_1$, where the pole ``breaks,'' resulting in a $-6$dB/octave roll-off in the amplitude response for higher frequencies ( $\omega\gg\omega_1$).

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...PASP,¹¹

http://ccrma.stanford.edu/~jos/pasp/Making_Virtual_Electric_Guitars.html

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... guitars.¹²

http://ccrma.stanford.edu/~jos/pasp/Sound_Examples.html

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...fig:cnl.¹³

The faust2pd distribution includes a ``Fuzz effect,'' based on taking an absolute value, in the file karplusplus.dsp.

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...PASP.¹⁴

http://ccrma.stanford.edu/~jos/pasp/Two_Ideal_Strings_Coupled.html

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...JOSFP¹⁵

http://ccrma.stanford.edu/~jos/filters/BiQuad_Section.html

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... pedal¹⁶

``Original CryBaby,'' Model GCB-95

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... Octave¹⁷

http://www.octave.org

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...BerdahlAndSmithTFM.¹⁸

http://ccrma.stanford.edu/realsimple/imp_meas/

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... matlab¹⁹

Here, ``matlab'' refers to the matlab language, as opposed to the Matlab product by The Mathworks, Inc. The program octave (http://www.octave.org), including the octave-forge collection, was used to execute all matlab scripts in this module. In a few cases, octplot was used for figures in place of the standard gnuplot used by octave. All software used for this project is free and open-source, to the author's knowledge.

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...²⁰

http://ccrma.stanford.edu/~jos/pasp/Impulse_Invariant_Method.html

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...JOSFP.²¹

http://ccrma.stanford.edu/~jos/filters/Minimum_Phase_Polynomials.html

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... code.²²

http://ccrma.stanford.edu/realsimple/imp_meas/tf_meas.zip

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