Frequency-modulation (FM) synthesis is widely known as a computationally efficient method for synthesizing musically interesting timbres. However, it has suffered from neglect owing to the difficulty in creating natural-sounding spectra and mapping gestural input to synthesis parameters. Recently, a revival has occurred with the advent of adaptive audio-processing methods, and this work proposes a technique called adaptive FM synthesis. This article derives two novel ways by which an arbitrary input signal can be used to modulate a carrier. We show how phase modulation (PM) can be achieved first by using delay lines and then by heterodyning. By applying these techniques to real-world signals, it is possible to generate transitions between natural-sounding and synthesizerlike sounds. Examples are provided of the spectral consequences of adaptive FM synthesis using inputs of various acoustic instruments and a voice. An assessment of the timbral quality of synthesized sounds demonstrates its effectiveness.