All sounds are comprised of some combination of pure sine waves. Generally, a single "sound" will include a fundamental frequency, and any number of overtones. The frequencies of these overtones are either integer multiples of the fundamental frequency, or integer fractions thereof (subharmonics). This study of how complex waveforms can be alternately represented is covered in Laplace and Fourier transforms.
When natural tonal instruments' sounds are analyzed in the frequency domain (as on a spectrum analyzer), the spectra of their sounds will exhibit amplitude spikes at each of the fundamental tone's harmonics. Some harmonics may have higher amplitudes than others. The specific set of harmonic-vs-amplitude pairs is known as a sound's harmonic content.
When analyzed in the time domain, a sound does not necessarily have the same harmonic content throughout the duration of the sound. Typically, high-frequency harmonics will die out more quickly than the lower harmonics. For a synthesized sound to "sound" right, it requires accurate reproduction of the original sound in both the frequency domain and the time domain.
Percussives and rasps have very low harmonic content, and exhibit spectra that are comprised mainly of noise shaped by the resonant frequencies of the structures that produce the sounds. However, the resonant properties of the instruments (the spectral peaks of which are also referred to as formants) also shape an instrument's spectrum (esp. in string, wind, voice and other natural instruments).
In most conventional synthesizers, for purposes of resynthesis, recordings of real instruments are composed of several components.
These component sounds represent the acoustic responses of different parts of the instrument, the sounds produced by the instrument during different parts of a performance, or the behaviour of the instrument under different playing conditions (pitch, intensity of playing, fingering, etc.) The distinctive timbre, intonation and attack of a real instrument can therefore be created by mixing together these components in such a way as resembles the natural behaviour of the real instrument. Nomenclature varies by synthesizer methodology and manufacturer, but the components are often referred to as oscillators or partials. A higher fidelity reproduction of a natural instrument can typically be achieved using more oscillators, but increased computational power and human programming is required, and most synthesizers use between one and four oscillators by default.