Advanced Techniques

FM Synthesis

  • Old idea for making interesting sounds with cheap hardware

  • Now used digitally because easier to implement accurately

  • Idea: Think about an LFO being used to provide vibrato

    $$ y[t] = \sin(\omega_0 (t + a ~ \sin(\omega_l t)) $$

  • Well, what happens when $w_l$ gets above 100Hz or so?

  • Turns out, can be modeled as a bunch of harmonics and subharmonics of $w_0$

  • This is the same as FM radio: use an audio signal to make vibrato on a radio signal!

FM Refs

  • Wikipedia has a decent explanation: note "operators"

  • Some nice samples and a tutorial are here

  • The classic synth is the Yamaha DX7. Dexed is a faithful open-source emulation

FM Demo

  • Let's look at some Python code that implements a very simple 2-operator FM synth

  • Note how harmonics and near-harmonics (and subharmonics and near-subharmonics work)

  • Note how amplitude works

Granular Synthesis

  • Recall our discussion of sound time scales earlier

  • 1-50ms is an interesting duration: long enough that tones will be heard as tones, but too short to hear individual notes

  • Idea: Break a sample into overlapping chunks in this time range and treat them as separate "music particles" or "granules"

  • Various games can now be played with the granules: pitch shifting (resample the individual granuals), time stretching (replicate or omit granules), fun synthesis effects (e.g. emit randomly-sampled granules)

Granular Refs

Physical Modeling

  • Idea: Quit trying to be so clever. Build a model of the instrument and run the model to make simulated sound

  • Way harder than sampling synth, but likely to produce way better results

  • Pipe organ is pretty close to perfect: Hauptwerk has some amazing commercial software combining sampling (for individual pipes) with physical modeling (for the instrument as a whole)

  • Piano isn't bad:

    has a nice demo

  • Plucked string modeling is kind of terrible in general: Karplus-Strong is basic plan.

  • Proper modeling requires solving acoustic systems; really hard math and physics. Drums are an active area of research

Last modified: Thursday, 9 May 2019, 3:18 PM