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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).
Subsections
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