This article concerns the generation of waveforms by a digital oscillator in which sampled data in a memory buffer are recycled. The buffer contains a fixed waveform and the output sample rate is also fixed. Despite these constraints, the oscillator is capable of arbitrarily high frequency resolution if the technique of fractional addressing is used. However, fractional addressing introduces distortion. This article gives a theory of fractional addressing, resembling the theory of diffraction in crystal lattices with a basis. The theory shows how the spectrum of the distortion components can be calculated and how the distortion can be minimized. Attention is called to numerous symmetries in the distortion spectrum. These symmetries are especially interesting if the purpose of the system is to make use of the distortion components to create inharmonic signals. Of particular importance is the γpsymmetry theorem, which makes it possible to derive simple formulas for the level of the largest distortion component and for the total distortion power.