Modal synthesis

In fact, one could encapsulate physical modelling networks into modules and provide them in a library. But in physical modelling we have access to the units that make up these modules, whereas in modal synthesis we cannot change their inner structure. 

Rgure 4.34 The level of abstraction of modal synthesis is higher that the level of abstraction of physical modelling in the sense that the building blocks of modal synthesis are prefabricated vibratory structures 

The Mosaic system, developed by Jean-Marie Adrien at the University of Paris VI, is a typical example of a tool for implementing modal synthesis (Adrien, 1991). It provides a number of ready-made substructures such as strings, air columns, metal plates and membranes, as well as substructures for the simulation of actions such as bowing and hammering. Instruments are thus programmed by networking these substructures. In Mosaic terms, substructures are called objects and the interactions between objects are referred to as connections. A connection between two objects also acts as an interface between the user and the instrument for example, the connection between a bow and string provides the means for user-customisation of the parameters that drive the interaction, such as pressure, speed, etc. 

It is always hard to compare synthesis methods without first establishing what needs to be achieved what may work satisfactorily for one case might not for another. In comparison to physical modelling, the modal approach has the advantage of the reduction of mathematical complexity and the modularity of the substructures. The instrument designer can add or subtract substructures on a network to create time-varying s)mthesis effects (such as 

---

Figure 4.6 shows a more flexible and general model of modal synthesis. This model allows for the filter input to be arbitrary, rather than just an impulse. It also allows for that input to be processed through a simple brightness... 

Figure 4.6. Flexible parametric modal synthesis algorithm.

A wide variety of sounds can be synthesized using modal synthesis. Any object which exhibits a few modes and is excited by striking or plucking is a likely candidate for modal modeling. Such objects might include metal pots and pans, glasses, etc. Modal synthesis can also work well for simple wooden objects such as blocks, boards, etc. 

In Chapter 4, we developed the notion that individual resonant filters can be used to model each vibrational mode of a system excited by an impulse. Thus, modal synthesis is a form of subtractive synthesis. For modeling the gross peaks in a spectrum, which could correspond to resonances (although these resonances are weaker than the sinusoidal modes we talked about in Chapter 4), we can exploit the resonance-factored form of a filter to perform our subtractive synthesis. The benefits of this are that we can control the resonances (and thus, spectral shape) independently. The filter can be implemented in series or cascade (chain of convolutions) as shown in Figure 8.4. The filter can also be implemented in parallel (separate subband sections of the spectrum added together), as shown in Figure 8.5. 

Physical modeling synthesis endeavors to model and solve the physics of sound-producing systems in order to synthesize sound. Unlike sinusoidal additive and modal synthesis (Chapter 4), or PCM sampling synthesis (Chapter 2), both of which can nse one powerM generic model for any sound, physical modeling reqnires a different model for each family of sound producing object. LPC (Chapter 8) is a spectral modeling techniqne, but also has physical interpretations in the one-dimensional ladder implementation. 

In prior chapters we looked at subtractive synthesis techniques, such as modal synthesis (Chapter 4) and linear predictive coding (Chapter 8). In these methods a complex source is used to excite resonant fQters. The source usually has a flat spectnun, or exhibits a simple roll-off pattern like f or ip (6 dB or 12 dB per octave). The filters, possibly time-varying, shape the spectrum to model the desired sound. 

Curves providing equivalent damping versus period for the first few modes as well as design acceleration for given equivalent damping are constructed. Thus, one can establish a seismic design method on the basis of modal synthesis and spectrum analysis. 

One can suggest that the modal constitution of an artefact (or rather a set of artefacts) is set up in a given context in the shape of a network that also functions as a framework for the users. One can then make a modal analysis as well as a modal synthesis of the modal web of actions in order to reveal the set of implications of the artefact s material and social network/framework. 

We can now express this specific modal constitution as related to a specific network/ framework and to a specific worldmaking process in using a modal analysis and a modal synthesis. In the presentation of the modal analysis and the modal synthesis. 

In the modal synthesis, one makes a synthesis of all the actions implied for each modality ... 

This equation can now be analyzed to deduce the built-up system natural frequencies and mode shapes. It is emphasized that the mass and stiffness matrices for the built-up system here are constmcted in terms of the natural frequencies, and mode shapes of the subsystem in the uncoupled states and knowledge of substructure structural matrices are not needed in this formulation. This enables the introduction of experimentally studied substructures to be embedded into the modal synthesis of the built-up system. 

Here, Gf uf,4) and G iuf, 4) are the ncHilinear forces associated with the interior and coupling dofs, respectively, and//(O is the vector of interaction forces between A and B. The procedure followed here has much in common with the fixed-interface method described earlier for linear substructures (section Fixed-Interface Modal Synthesis ). In order to relate to uf, two separate analyses are done. First, fixed-interface linear modes are computed for A by assuming =0 and ignoring the nonlinear terms in Eq. 11. The governing equation is obtained as Mf uf + = 0, which has... 

---