ELEN E4896 MUSIC SIGNAL PROCESSING Lecture 4: Analog Synthesizers

1. The Problem Of Electronic Synthesis 2. Oscillators 3. Envelopes 4. Filters

Dan Ellis Dept. Electrical Engineering, Columbia University [email protected] http://www.ee.columbia.edu/~dpwe/e4896/ E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 1 /17 1. The Problem of Electronic Synthesis • How can we synthesize notes and music ... and have it sound as good as real instruments? • Real instrument tones are complex

Piano Trumpet

Plucked Violin Bowed Violin E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 2 /17 The Analog Synthesizer • Minimum “useful” configuration Envelope Trigger Pitch + harmonics Pitch t Amplitude variation + + Vibrato Cutoff (dynamics) freq Sound Spectral variation Oscillator Filter + Gain f (1970s technology) t Minimoog, 1972

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 3 /17 Digital Simulation of Analog • E.g. Loomer Aspect http://www.loomer.co.uk/aspect.htm

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 4 /17 PureData (Pd) • Visual metaphor based on analog synths “wires” connect modules

• Tutorial: http://en.flossmanuals.net/PureData/

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 5 /17 2. 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

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 6 /17 Basic waveforms • Sinusoid

• Square wave

• Pulse waveform

• Sawtooth

• Triangle

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 7 /17 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 https://ccrma.stanford.edu/~stilti/papers/blit.pdf

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 8 /17 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

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 9 /17 Aside: PWM Spectrum • What are harmonics of Pulse-Width Modulated (PWM) waveforms? consider as impulses convolved with a pulse W ➝ Fourier transforms multiply = 1.5 1.5 1.5

1 1 1 time 0.5 0.5 0.5 0 0 0

-0.5 -0.5 -0.5 0 500 1000 0 500 1000 0 500 1000 40 40 40

20 20 20

0 0 0 frequency -20 -20 -20

-40 -40 -40 0 200 400 0 200 400 0 200 400 or integral of sum of two opposite impulse trains with relative delay W p (t)= p(t) p(t W )dt w (good for bandlimiting) E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 10 /17 3. 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

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 11 /17 ADSR • 4-parameter classic envelope model Attack - initial rise time Decay - fall time immediately following initial attack Sustain - amplitude of Key depressed asymptote of decay while key is held down Release - decay from sustain to zero after key released Tobias R. - Metoc

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 12 /17 Pd ADSR Abstraction • Any patch can become a “unit”

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 13 /17 4. 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

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 14 /17 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 s plane 50 1 0.5 0 0 Imag

-0.5 dB / gain -1 -50 -1 0 1 -1 0 1 Real 10 10 10 freq / rad/s z plane 50 1 0.5 0 0 Imag

-0.5 dB / gain -1 -50 -1 0 1 0 0.2 0.4 0.6 0.8 1 Real norm freq / π • Analog synths provided 12-24 dB/oct rolloff E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 15 /17 5. Examples • Juno-106 preset patches from http://www.synthmania.com/juno-106.htm

Brass Trumpet

Piano Strings E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 16 /17 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

E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - 17 /17