Digital oscillators with discontinuities in their time domain signal derivative suffer from an increased noise floor due to the unbound spectrum generated by these discontinuities. Common antialiasing schemes that aim to suppress the unwanted fold-back of higher frequencies can become computationally expensive, as they often involve repeated sample rate manipulation and filtering. In this paper, the authors present an effective approach to applying the four-point polyBLAMP method to the continuous order polygonal oscillator by deriving a closed form expression for the derivative jumps which is only valid at the discontinuities. Compared to the traditional oversampling approach, the resulting SNR improvements of 20 dB correspond to 2–4× oversampling at 25× lower computational complexity, all while offering a higher suppression of aliasing artifacts in the audible range.