Simple rules to sonic chaos: the “three-oscillator problem” & Rob Hordijk’s “Benjolin”
In this video, I talk about the “Three-Body Problem” and created an analogous Pure Data patch, where three oscillators frequency-modulate each other. Just as in the physics problem, this cross-modulation network creates unpredictable, chaotic patterns.
This emergent complexity from simple rules perhaps connects to ideas of motivic development in music, how great artistic works can grown from simple and small ideas.
Performance on traditional, acoustic instruments, of course, produces a huge amount of micro-variation across each note, and so it can be expressively engaging for us to be able to introduce that same imperfection (analog warmth?) in our digital instruments as well.
In this video, I build a bad sine wave by frequency-modulating my oscillator with noise, and then feeding back the output back into the modulation. While I build this out in Pure Data, the same can be done in Reaktor, Kyma, Max/MSP or any other synthesis environment.
0:00 Introduction, The Beauty of Imperfection 1:26 Slider-Controlled Sine Wave 3:28 Adding Noise 4:35 Frequency Modulating with Noise 7:24 Filtering the Noise 8:20 Feeding Back into FM 9:55 I’ve gone too far 13:26 Reaktor Examples 14:18 Closing Thoughts, Next Steps
Building a basic but expandable FM synthesizer in Reaktor 6, making an FM operators that we can duplicate as much as we want.
In FM synthesis, we modulate the frequency of one oscillator (the carrier) with another oscillator in the audible range. We can make an FM synth in Reaktor that’s modular and quickly expandable if we make a macro with the oscillator, an envelope, and a few special controls at the FM input.
0:00 Intro / What is FM Synthesis? 1:30 Sine Oscillator with Amplitude Envelope 3:14 The “F” Input of Sine FM Oscillators 4:20 Modulating the Frequency 5:24 Modulating the Frequency in the Audible Range 6:13 Adding Musical Controls 11:50 Combining Our FM Operators 13:01 Sideband Modulation with Envelope Control 16:12 Chaining FM Operators Together 19:48 Recap / Next Steps
A quick and easy Pure Data patch-from-scratch tutorial building a sequencer that plays dynamically changing timbres for each note though frequency modulation synthesis.
In this patch, we set up a simple sequence of sine wave pitches (frequencies), then a sequence of modulation frequencies of a different length, then a random patterns of deviations, creating a constantly changing series of sounds.
There’s no talking on this one, just building the patch, and listening to it go.
0:00 Sequencing the pitch of a sine wave 1:23 Creating modulation oscillator sequence 2:45 Randomizing the deviation 3:15 Audio math: modulator frequency 3:51 Audio math: deviation 4:09 Audio math: FM synthesis 4:31 Tweaking the numbers 4:52 Commenting the code 5:47 Adding delay (as usual) 6:55 Feedback for the delay 7:17 Listening and more tweaking numbers
More no-talking Pure Data jams and patch-from-scratch videos here: