Understanding Waveshaping

Physical versus Accoustic Modeling

Synthesizers allow you to model sounds to an extent, but then go beyond any imitation. There are several kinds of modeling:

• Spectral synthesis methods: these approaches just start with some sound and make some abstraction of the components that make it up, with no attempt to look at how the sound was made. At the finest level of granularity, it uses sine blips and noise, but coarser granularity goes all the way from more complex partials to wavelets to granules to wavetables to samples. You make new sounds by combining existing pieces together, or changing their relationship.
  • Spectral synthesis models a sound, not an instrument.
  • Difficult to do in analogue: not friendly for analog DIY
• Functional modeling: also known as abstract synthesis or algorithmic modeling, this uses mathematical functions with known properties, such as frequency, amplitude, ring and phase modulation (FM, AM, RM, PM), in various combinations. You can iteratively approximate a sound by hand using spectrum analysers: see this book for how to do it on FM synthesizers. To some extent it is also possible to model concrete sounds by running the functions ‘in reverse’, and there is good research on sound matching using statistical/genetic/neural operations to select the nearest algorithm and best match parameters for the sound (or distilled sound.)
  • Functional modeling approximates a sound
  • Difficult to do well in analogue: analog modules often do not provide the stability or fine control needed: not friendly for analog DIY
• Accoustic modeling: this approach takes the various parts of an sound and attempts to simulate it, and is the classic analogue synthesis: we create a waveshape with certain harmonics by waveshaping, addition and subtraction representing the excitation signal of the instrument; then we put it through through filters and equalizers representing the body of the instrument; then add dynamics with an envelope; finally add room effect with reverb.
  • Accoustic modeling takes hints from both the instrument and the sound.
  • Well-suited to analogue (and difficult to do digitially!): very friendly for analog DIY
  • Fricko modules generally fit in here!
• Physical Modeling: this approach models the instrument’s physics rather than its waveforms or formants
  • 1D Physical Modeling: , but as a one-dimension multi-way signal that gets put through various slight delays and feedbacks. You make new sounds by setting up semi-impossible instruments, a bowed flute or a double-reed giant trumpet.
  • 2D Physical Modeling (rare): this approach models the air particle’s movement in a 2D model of the instrument.
  • 3D Physical Modeling (still very rare, but based on highly-studied fluid dynamics): models the instrument and air-flow/vibrations in 3D. At this stage, the model is so concrete you could use it to build a physical instrument.
    • Physical modeling models a class of instruments, with parameters for key features such a bore curve, and may use the original sound to trim parameters at the development stage.
    • Difficult to do in analog (requires high performance tunable fine delay lines): not friendly for analog DIY. The computing world gave up trying 50 years ago in favour of digital.

Because physical modeling allows more realistic imitative sounds than acoustic modeling, there has been very little innovation over the last few decades in the repertoire of analog synthesizer modules for waveshaping, with some notable exceptions. And this holds back the range of sounds that pure analog synths can make easily. The fricko waveshapers slot into that gap, by providing waveshapers for several important classes of sounds unavailable elsewhere:

• Constant-wave sounds (such as free-reed and double-reed instruments, as well as instruments whose tone production has some note-independent period, such a violin-bow slippage) with the Blip! waveshaper;
• Waves with irregular harmonic series, and where the early harmonics do not start from loudest to less loud (as is the case with many blown and bowed instruments) with the Shell waveshaper;
• Rich waves based on multiplied saw waves (as found in bowed instruments) with the Rasp waveshaper;
• Waves constructed by the interference of different waves at different phases, getting different enhancement or attenuation of the common harmonics of the input waveforms (as found in resonating instrument bodies), with the ProPulse waveshaper.