Sympathetic Resonance: Acoustic and Digital String Resonances

Sympathetic resonance is an essential part of any piano sound. These resonances occur between harmonically related notes, hence the term “sympathetic”. While the interaction of strings and damper is the source of sympathetic resonance on an acoustic piano, it must be artificially recreated on a digital piano.

String Resonances Are Complex

Damper resonance on digital pianos refers to resonances that occur in direct connection with the damper (sustain) pedal. Here, all strings are free to vibrate. In contrast, in acoustic and upright pianos the string of a single note (played without sustain pedal) can also resonate in sympathy when you play other notes. How and to what extent a string resonates depends on whether the notes struck match the overtone spectrum of the undamped string. When talking about digital pianos, this overtone-dependent interaction is for example called Sympathetic Resonance (Roland Piano Designer), String Resonance (KAWAI Virtual Technician), or Virtual Resonance Modeling (VRM, Yamaha Piano Room/Smart Pianist).

There must be a relation between the overtones of the resonating notes. If that’s the case, sympathetic resonance can shape the sound significantly, even when you play in only two voices. However, these resonance effects are much more subtle than the damper resonance when playing the sustain pedal. Nevertheless, they are an essential part of the harmony of the notes and chords you play. The matching overtone spectrum results in complex relations that dynamically influence the sound of an acoustic grand piano.

The sound generators of modern digital pianos have fairly authentic-sounding simulations of sympathetic resonance. In addition, you can even customize the sound characteristics. Some digital pianos generate string resonances using special samples, while others use physical modeling technology.

Making Sympathetic Resonance Audible

Figuring out the relations between string resonances yourself is quite simple. First, play a key very softly or silently and hold it. Now briefly play notes that match this fundamental note (staccato). You will notice that the open strings reflect the corresponding overtones as resonance. So if you hold the C as shown in the picture and briefly play the G, the G will continue to vibrate softly as an overtone in the held C.

String Resonances & Piano Playing

The example above is for illustrative purposes only, though you can play very melodically using overtones if you wish. In modern piano literature, you can even find instructions for playing notes and chords silently, so that these notes – now undamped – act as harmonic resonators for the notes you play with the other hand.

Even if you just hold a single note, it will affect the sound, as the harmonic relations change over time. This naturally depends on the other notes you are playing in the context, e.g. in two-part melodies with sustained notes. If you play the C note as in the example above, notes in the melodic progression of the second voice will produce resonances in the decaying note. Digital pianos that cannot accurately reproduce string resonance are missing an essential component.