The Basic Plucked String


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In these pages, we値l build a model of a bowed cello, complete with a resonating wooden body. We値l then modify that model to imitate a violin, a viola, and a contrabass.


This will be, by far, the most complicated model in these pages. In fact, we値l need all four DSPs in a G2 to play a single note.




Getting started


Before we bow a string, we値l pluck it. Plucking is easier to patch, and easier to understand, so we値l begin there.


Of course, the G2 already has a String Oscillator module, which simulates a plucked string. Unfortunately, we値l have to bypass it, and make our own from scratch. We値l eventually see why.


Below is a plucked string patch. It痴 the standard waveguide-type physical model of a plucked string.





How does it work?


The string itself is made up of the two yellow sections labeled 撤luck To Nut and 撤luck To Bridge. If it looks familiar, it痴 because it痴 the same resonator used by our reed woodwind model. That model was called a 澱lown string. Well, here again is the string part of the model, in its basic form.


Let痴 trace the signal flow again. We値l begin with the 撤luck To Nut section. This section contains a delay line and a gain control. The output then goes to the 撤luck To Bridge section, and is inverted as it enters. The 撤luck To Bridge section is identical. It contains another delay line, another gain control, and a lowpass filter. The output then returns to the 撤luck To Nut section, and is again inverted as it enters.


The delay in the 撤luck To Nut section represents the length of string from the pick to the nut, and the other delay represents the length of string from the pick to the bridge. The lowpass filter and the inverting gain controls represent the reflections and energy losses at the bridge and nut. Some waveguide models of strings have an additional lowpass filter at the nut, but we致e left that out to save a module.


To pluck the string, we値l inject a short noise pulse into both delays simultaneously. That痴 the job of the 撤luck Excitation circuit in red. The pulse will travel through the loop made by the delay lines again and again. With each trip it will get a little softer, because the gain controls are less than unity. It will also get a little duller, because the lowpass filter will trim off some high-frequency energy.


This is actually quite near to how a real string works. When you pluck a string, the pulse travels in both directions toward the bridge and nut. When it reaches the end of the string, it is reflected back. Its polarity changes and it loses some energy. High frequencies experience more loss than low frequencies. This is all modeled by the delays, the inverters, the VCAs, and the lowpass filters.




Some odds and ends.


The position of the pluck point depends on the ratio of the two delay lengths, and the pitch of the string is related to the sum of the two delay lengths. Here痴 some boilerplate copied from the reed woodwind model: