While intuitively appealing, and perceptually relevant, modal synthesis has a number of serious shortcomings:
First, modal techniques are strictly applicable only to linear and time invariant (LTI) systems, i.e., those for which an eigenvalue problem may be derived. Though this does cover a number of useful cases in musical acoustics, there are many others, often among the most musically interesting, which are not LTI. Under weakly nonlinear conditions, it is possible to draw some mainly qualitative conclusions using perturbation analysis about modal solutions (though this has not, apparently, been done in the context of musical sound synthesis). Perceptual effects such as pitch glides in strings and struck plates may be analyzed in this way. But for stronger nonlinearities, such as those that occur in struck gongs or cymbals, such analysis becomes unwieldy, and of questionable validity.
Second, although for certain simple spatially-uniform structures (such as, e.g., an ideal string or rectangular membrane under fixed or free termination, or an ideal plate under simply-supported conditions), the eigenfunctions and eigenfrequencies (modal shapes and frequencies) may be expressed in closed form, for almost all other geometries and boundary conditions, they can not be, and must be computed numerically, generally before run time. For large problems, this calculation can be enormous. For a static expansions onto (and projections of) the modal functions, it is sufficient to compute the weighting coefficients alone. This is often sufficient in mainstream applications, but definitely not in musical sound synthesis, in which case dynamic input and output parameters are a crucial feature (e.g., if a membrane is to be struck or its output taken at varying locations); the weighting coefficients must be recomputed with any such variation. (The alternative is to simply store all the eigenfunctions, but this can become prohibitively costly in terms of memory use.)
Third, it is important to point out that there is no efficiency advantage, either in terms of the operation count or memory use, in using modal expansions relative to time-domain methods; this follows from
In the cases in which they may be applied, modal methods do, however, possess two significant advantages relative to time-domain techniques. First, because the modal decomposition may be thought of as essentially breaking a system down into a parallel combination of a set of second order linear oscillators, stability is extremely easy to verify; such is not the case
All these difficulties stem from the complexity of the back-and-forth between the time and frequency domains.