Back from the grave

Guitar/fretboard Interactions

The collision interaction plays a central role in many types of musical instruments, including all percussion instruments, where the hammer or mallet collides with a resonating object such as a bar or plate, as well as various stringed instruments, such as the guitar and violin, which involve various collisions between the strings and the fingers, and also between the strings and the fretboard. Though strongly nonlinear models were indeed a focus of the NESS project from the outset, part way through the project we got very interested in this topic, and in the problem of trying to design robust and stable numerical methods for synthesis. This interaction is covered in various papers, but especially this article which covers many systems in musical acoustics.

The guitar is an interesting case study. It is composed of a set of strings coupled to a body; the body itself is in contact with the acoustic field, and the strings are in contact with a fretboard, as well as with fingers which serve to both excite the instrument, through plucking, as well as stop the strings. In the NESS project, we focused only on the string/finger/fretboard interactions. A fully articulated guitar model is covered in this paper.

It’s worth backing up a little to the case of a string in isolation, vibrating under linear (low amplitude) conditions, under a plucked excitation. This is the usual model which appears in synthesis applications, whether based on digital waveguides or modal techniques. Have a look below at a video illustrating such string vibration calculated through an FDTD scheme (not the most efficient choice under such simple conditions!). The resulting sound is recognisably guitar-like, at least for an isolated note. But when we try to simulate multiple strings and strumming, we begin to hear the deficiencies in the model, which does not exhibit a change in timbre with increasing pluck amplitude.

A single plucked guitar note.

Time evolution of string profile for a single plucked guitar note.

A series of strums on linear guitar strings.

A series of plucks on a set of six guitar strings.

Suppose now that a backing fretboard is introduced. It has a flat profile, but with raised bumps at the fret locations. Now the interaction of the string with the fretboard is highly amplitude-dependent. This is easily heard in plucked gestures at high amplitudes. Here, we’re only modelling vibration of the string transverse to the fretboard—the true situation is of course more complicated, but has been dealt with in the case of the violin by Charlote Desvages—see her article here.

Multiple plucks in the presence of a fretboard.

Strumming gestures of variable amplitude.

Beyond plucking, one can also introduce a model of stopping fingers, which themselves collide with the string! One can easily model tapping gestures, which introduce inharmonic timbres, as well as rattling effects.

A finger contacting a string and trapping it against the fretboard

A randomly generated set of tapping sounds.

Here’s a sound example, produced through hard tapping (or slapping) of a four-string bass guitar. This is a particularly raucous sound, and you can hear the jangling of the string against the frets!

Of course, one can go much further, and introduce motion of the stopping fingers, to emulate pitch changes. These are accompanied, again, by characteristic rattling sounds as the fingers pass between frets.

Moving finger in contact with the string and fretboard

Plucking gestures, accompanied by a moving stopping finger

Finally, we can introduce multiple fingers, which may move together, to emulate barre-chord slides, or move independently, or also play on the harmonics depending on how hard we push on the strings!

A set of six moving fingers (!) in contact with the fretboard.

Various six-string gestures

We now have a relatively fast port of an N-string guitar, with full design control over the strings and fretboard, as well as over the precise type of gesture you want to play. It’s available by subscription to the NESS GPU service; contact us if you want to have a play with it!