The theory and applications of a variant of the well-known synthesis method of frequency modulation, modified frequency modulation (ModFM), is discussed. The technique addresses some of the shortcomings of classic FM and provides a more smoothly evolving spectrum with respect to variations in the modulation index. A complete description of the method is provided, discussing its characteristics and practical considerations of instrument design. A phase synchronous version of ModFM is presented and its applications on resonant and formant synthesis are explored. Extensions to the technique are introduced, providing means of changing spectral envelope symmetry. Finally its applications as an adaptive effect are discussed. Sound examples for the various applications of the technique are offered online.