We present an application—XronoMorph—for the algorithmic generation of rhythms in the context of creative composition and performance, and of musical analysis and education. XronoMorph makes use of visual and geometrical conceptualizations of rhythms, and allows the user to smoothly morph between rhythms. Sonification of the user generated geometrical constructs is possible using a built-in sampler, VST and AU plugins, or standalone synthesizers via MIDI. The algorithms are based on two underlying mathematical principles: perfect balance and well-formedness, both of which can be derived from coefficients of the discrete Fourier transform of the rhythm. The mathematical background, musical implications, and their implementation in the software are discussed.