Oscillators • Pitch = sinusoid? only a single color • Real instruments have more harmonics static spectrum determines instrument sound? • Additive: Combine individual harmonics calculating sinusoids in real time is expensive... • Subtractive: Shape harmonics with filters start with a spectrally rich signal “shape” harmonics efficiently with LTI filters

Basic waveforms • Sinusoid • Square wave • Pulse waveform • Sawtooth • Triangle

Aside: Bandlimiting • It’s easy to sample “ideal” simple waveforms but the ideal ones are not bandlimited ➝ lots of aliased energy • Solution: Bandlimited waveforms e.g. fill a table with precalculated sum of sinusoids up to a fixed frequency • Variable waveforms can be derived PWM by integrating bandlimited impulses

Modulation • Stationary spectra sound unnatural real sources have random “jitter” • Variations in pitch “Low Frequency Oscillator” frequency modulation random noise • Variations in timbre can be imposed by filters... Pulse-width modulation

Aside: PWM Spectrum • What are harmonics of Pulse-Width Modulated (PWM) waveforms? consider as impulses convolved with a pulse W ➝ Fourier transforms multiply or integral of sum of two opposite impulse trains with relative delay W (good for bandlimiting)

Envelopes • Notes need to be limited in time simple gating not enough amplitude envelope • Different (real) instruments have clear variations in envelope struck/plucked vs. bowed/blown

ADSR • 4-parameter classic envelope model Attack - initial rise time Decay - fall time immediately following initial attack Sustain - amplitude of asymptote of decay while key is held down Release - decay from sustain to zero after key released

Pd ADSR Abstraction • Any patch can become a “unit”

Filtering • Amplitude modulation alone is not enough real instruments have time-varying spectra e.g. plucked string • Generally just LPF (+ resonance) high frequencies die away after initial transient resonance can give some BPF effect

The Biquad filter • Flexible circuit design to achieve variable cutoff frequency but just single pole-pair LPF (or repeats) constant Q (bandwidth/center freq) resonance • Analog synths provided 12-24 dB/oct rolloff

Examples • Juno-106 preset patches from http://www.synthmania.com/juno-106.htm

Summary • Analog synthesizers provided musical flexibility with simple units 20 years of evolution • Need instrument-like dynamics to make an interesting sound but only up to a point... • Analog synths provide intuitive controls each “knob” has a distinct effect