Circle² implements a cutting-edge technique called Vector Phaseshaping Synthesis (VPS), developed by researchers at the Aalto University School of Electrical Engineering and The National University of Ireland.
We collaborated with two of the original researchers, Victor Lazzarini and Joseph Timoney, to bring this technology into a software synthesizer for the first time!
But, what is VPS?
Fundamentally, the oscillator takes a pair of sine waves with specific frequencies and glues them together at a specific time. With control over two parameters, which determine the frequencies of the sine waves and the location at which they are glued together, a VPS oscillator provides a new level of control over the waveform’s intricate harmonics.
By varying these parameters, a VPS oscillator can create a wide variety of rich sonic textures and distinct timbres; clean, crisp tones for sub-bass; distorted leads; thick rumbles for heavy bass-lines; shiny cyber sounds; growls and glitches.
Digital wave shaping was introduced in the late 1960s which lead to non-linear distortion synthesis methods that are well known and widely used today, such as FM synthesis. The principle of VPS is related to established non-linear Phase Distortion synthesis methods. The established methods allow control over the phase distortion function bending point along the x-axis. VPS opens up a new dimension, allowing for control of both the x-axis and y-axis – amplitude and time – and joins sine waves end-to-end.
The result? Dynamic timbres and unusual harmonics that morph and evolve through time.
A key difficulty we faced while implementing a VPS oscillator in a digital synthesizer is an unwanted auditory effect know as aliasing, which is a form of audio distortion that can lead to incorrect pitch replication. We collaborated with the original inventors of the VPS oscillator to find a solution to this problem and ensure that our new oscillator produces pitch-perfect output for a wide range of parameter choices.
If you want to get even deeper or if you love equations, have a look at the original research paper.
VPS Banner illustration by Juanma Mota.