This paper focuses on phaseshaping techniques and their relation to classical abstract synthesis methods. Elementary polynomial and geometric phaseshapers, such as those based on the modulo operation and linear transformations, are investigated. They are then applied to the generation of classic and novel oscillator effects by using nested phaseshaping compositions. New oscillator algorithms introduced in this paper include single-oscillator hard sync, triangle modulation, efficient supersaw simulation, and sinusoidal waveshape modulation effects. The digital waveforms produced with phaseshaping techniques are generally discontinuous, which leads to aliasing artifacts. Aliasing can be effectively reduced by modifying samples around each discontinuity using the previously proposed polynomial bandlimited step function (polyBLEP) method.