Research Brief

Formula is an open-source VST & AU plugin to create custom audio effects inside your DAW, developed by Soundspear. The plugin is available for Windows, macOS and Linux and can be downloaded from the GitHub repository at https://github.com/soundspear/formula. Effects within Formula are made using the C programming language, and the concept is simple: you are writing C code that is compiled on the fly and routed to your DAW in multi-mono or stereo. The entry-point takes a float input sample and returns a float output sample. That code will be JIT-compiled & executed in real-time for each sample then streamed to the DAW. To build from source: run the platform-specific configuration script (configure-windows.ps1, configure-mac.sh, or configure-linux.sh) which downloads dependencies (JUCE, boost, vcpkg, cpprestskd), then use CMake to generate the project. Reviews indicate the plugin ships with approximately 50 bundled algorithms, not the hundreds initially promised. A Formula Cloud subscription was previously offered to browse community effects, though Soundspear has since made more than 50 audio effects available for free.

Plugin Doctor (by DDMF) is the analysis tool demonstrated in the video. Plugindoctor fills a longstanding gap in the market: a cross-platform and cross-bitformat plugin analyzer for VST and AU plugins. It offers harmonic analysis: highly accurate frequency response analysis to a sinusoidal input signal. Input strength and frequency can be varied for THD/THD+N calculation. Switchable intermodular distortion modus. Plugindoctor v2 is available now from the DDMF website, priced at $39 (https://ddmf.eu/plugindoctor/). The tool supports VST, VST3, AU, and AAX formats and is available both as standalone and as a plugin.

The psychoacoustic claims in the video are well-established. The pitch being perceived with the first harmonic being absent in the waveform is called the missing fundamental phenomenon. It is established in psychoacoustics that the auditory system, with its natural tendency to distinguish a tone from another, will persistently assign a pitch to a complex tone given that a sufficient set of harmonics are present in the spectrum. For example, when a note (that is not a pure tone) has a pitch of 100 Hz, it will consist of frequency components that are integer multiples of that value (e.g. 100, 200, 300, 400, 500.... Hz). However, smaller loudspeakers may not produce low frequencies, so in our example, the 100 Hz component may be missing. Nevertheless, a pitch corresponding to the fundamental may still be heard. In mid-1999, Meir Shashoua of Tel Aviv, co-founder of Waves Audio, patented an algorithm to create the sense of the missing fundamental by synthesizing higher harmonics. Waves Audio released the MaxxBass plug-in to allow computer users to apply the synthesized harmonics to their audio files. A typical solution is based on the psychoacoustic phenomenon known as the "missing fundamental", whereby human auditory system can perceive the fundamental frequency from its higher harmonics. This psychoacoustic bass enhancement system generally uses nonlinear devices (NLD) or phase vocoders (PV) to generate harmonics that enhance bass virtually.

Regarding harmonic distortion types: Symmetrical clipping results in odd harmonics. Asymmetrical clipping creates both even and odd harmonics. Any time invariant symmetrical waveshaping yields odd harmonics only to pure signals. Tanh gives odd harmonics only, and the same is true of any function with odd symmetry. The video's demonstration of squaring (input * input) producing even harmonics and cubing producing odd harmonics is mathematically accurate—a parabola, or x2, curve creates specific harmonic patterns, and for the parabola, and any other xn curves, we have to bias the signal up from zero center, else there would be all harmonics and no fundamental.