We're very happy to announce our new polysynth Generate. Generate takes the ideas we first released in our free chaotic monosynth Pendulate and expands them. Specifically it adds polyphony, effects, tons of modulation, two new wavefolders, and, the topic of this post, FOUR new chaotic oscillator types.

Generate is a really great synth and we're incredibly proud of it. If you'd like to learn more, please check out the product page. However, I'm planning to write a couple different blog posts doing a deep dive into the technology behind it, and this first one is about the Chaotic Generators.

### 1. Chatotic Generator?

Instead of oscillators Generate has chaotic generators. We call them generators because they don't simply oscillate back and forth as an oscillator does, but they provide a chaotic output that shifts over time. Many people think that chaos implies randomness, or noise, and while the output can sometimes seem noisy, it's not random, and the chaotic system leaves a lot of room to explore between the oscillations and the "noise."

The first Chaotic Generator is called Double Pendulum, this is also the one used in Pendulate. This Double Pendulum generator is based on a mathematical model of a double pendulum. Here's a great simulation.

### 2. Modelling Chaos

When you do the math of a moving system you come up with a set of differential equations called a dynamical system, or a dynamical model. These are the model equations for the double pendulum, and building a digital synthesizer model of a physical system is called Physical Modelling Synthesis. (Granted, people often model physical things like trumpets or pianos rather than obscure physics demonstrations, but the terminology holds.)

I did have to do some work to these to tame this double pendulum model into something that work work as a musical oscillator, but the model, in the form of these equations, are still baked into the code. Dynamical systems are feedback systems, and those sin() and cos() terms you see are nonlinear, making this a model of a nonlinear feedback system. I may be wrong, but I believe all chaotic systems are nonlinear feedback systems. This is the how the Double Pendulum Generator in Generate and Pendulate works.

### 3. Model Bending?

Once the double pendulum generator was working well I kept the form of the model, but started swapping out functions or changing the math in different ways. I tried out many different changes to the model, and settled on four which sounded pretty good, those are the additional generators in Generate. The names: Vortex, Pulsar, Discharge, and Turbine are based on what they looked or sounded like to me. They are all based on the same fundamental double pendulum form, but they have very distinct sounds, just because I changed the math.

This is sort of like circuit bending the model. Circuit bending is taking an existing circuit and randomly changing stuff to see what it will sound like. These equations no longer represent any sort of physical system you could build in our universe, so it’s no longer Physical Modeling Synthesis. I’ve been thinking of calling it Model Bending Synthesis, because we start with a real physical model, but then we just mess with it.

### 4. Feedback and Further Work

I'm sure I'm not the first person to try building a physical or analog model, then just futzing with the math to see what it sounds like, but I don’t actually know of an examples. I think this is a very powerful technique that could be applied to a lot of things moving forward. I'd love to compile a list of products or publications that use this technique to explore new and interesting sounds. If anyone knows of any examples of people making a proper physical or analog model, and then just messing with it to see what comes out, I’d love it if you share with me. Either post it here or get in contact via social below.

Thanks, Dan

If you know of anything tag Newfangled Audio on Instagram, Twitter, and Facebook, I'll be sure to get it.

Ooops, two years late on this, but yeah, I’ve been working on analog realizations of physical chaotic systems for ~20 years. Even selling some of them commercially. 😁

Ian Fritz

ijfritz@comcast.net

ijfritz.byethost4.com