Piano Synthesis

The main elements of the piano we need to model are the

• hammer (§9.3.2),
• string (Chapter 6, §6.6),
• bridge (§9.2.1), and
• soundboard, enclosure, acoustic space, mic placement, etc.

Since piano strings are audibly stiff, we need to include a dispersion allpass filter in the string model, as introduced in (§6.11.3). The next section provides additional details specific to piano strings.

From the bridge (which runs along the soundboard) to each ``virtual microphone'' (or ``virtual ear''), the soundboard, enclosure, and listening space can be well modeled as a high-order LTI filter characterized by its impulse response (Chapter 8). Such long impulse responses can be converted to more efficient recursive digital filters by various means (Chapter 3,§8.6.2).

A straightforward piano model along the lines indicated above turns out to be relatively expensive computationally. Therefore, we also discuss, in §9.4.4 below, the more specialized commuted piano synthesis technique [469], which is capable of high quality piano synthesis at low cost relative to other model-based approaches. It can be seen as a hybrid method in which the string is physically modeled, the hammer is represented by a signal model, and the acoustic resonators (soundboard, enclosure, etc.) are handled by ordinary sampling (of their impulse response).