There are, of course, many other techniques which have been proposed for sound synthesis; some are variations on the techniques described in the above sections, but there are several which do not fall into the above categories. This is not to say that such techniques have not seen success; it is rather that they do not fit naturally into the evolution of abstract methods into physically-inspired sound synthesis methods, the subject of this book.
One of the more interesting is a technique called waveshaping [136,7,173], in which case an input waveform (of natural or synthetic origin) is used as a time-varying index to a table of data. This, like FM synthesis, is a nonlinear technique--generally, a sinusoid at a given frequency used as the input will generate an output which contains a number of harmonic components, whose relative amplitudes depend on the values stored in the table, and can thus be viewed as a harmonic distortion. Similarly to FM, it is capable of generating rich spectra for the computational cost of a single oscillator, accompanied by a table read; a distinction is that the level of control over the amplitudes of the various partials can be controlled in a direct way, through the use of Chebyshev polynomials expansions as a representation of the table data.
Granular synthesis [43], which is also very popular among composers, refers to a large body of techniques, sometimes very rigorously defined (particularly when related to wavelet decompositions [78]), sometimes very loosely. In this case, the idea is to build complex textures using short duration sound ``grains," which are either synthetic, or derived from analysis of an input waveform. The grains, regardless of how they are obtained, may then be rearranged and manipulated in a variety of ways. Granular synthesis encompasses so many different techniques and methodologies that it is perhaps better thought of as a philosophy, rather than a synthesis technique. See [172] for a historical overview.
Distantly related to granular synthesis are methods based on overlap-adding of pulses of short duration, sometimes, but not always, to emulate vocal sounds. The pulses are of a specified form, and depend on a number of parameters which serve to alter the timbre; in a vocal setting, the rate at which the pulses recur determines the pitch, and a formant structure, dependent on the choice of the free parameters, is imparted to the sound output. Perhaps the best known are the so-called FOF [181], and the VOSIM [114] techniques.