Synthesis Theory - Additive Synthesis

Fourier's Theorem (Moorer 210)

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Additive Synthesis (Roads 134-44)

• Additive Synthesis: Background
• Fixed-waveform Additive Synthesis
• The Phase Factor
• Addition of Partials
• Time-varying Additive Synthesis
• Demands of Additive Synthesis
• Source of Control Data for Additive Synthesis

Example

• Square wave = sin(wt) + 1/3 sin(3wt) + 1/5 sin(5wt) + ...

;Method 1: Multiple oscillator

; orc file 

        sr = 44100
        kr = 441
        ksmps = 100
        nchnls = 1

        instr   1
a1      oscil   p4, p5, 1
a2      oscil   p4 / 3, p5 * 3, 1
a3      oscil   p4 / 5, p5 * 5, 1
a4      oscil   p4 / 7, p5 * 7, 1
        out     a1+a2+a3+a4
        endin

: score file
f1 0 8192 10 1

i1 0 1 30000 110
e



;Method 2: Wave table

; orc file
        instr   1
a1      oscil   p4, p5, 1
        out     a1
        endin

; score file (GEN 10)
f1 0 8192 10 1 0 0.3 0 0.2 0 0.1428571
i1 0 1 30000 440
e

; score file (GEN 9)
f1 0 8192 9 1 1 0 3 0.3333 0 5 0.2 0 7 0.1428571 0 9 0.1111111 0 11 0.09091 0
i1 0 1 30000 110
e

• Musical Applications of Additive Analysis/Resynthesis
• Method of Sound Analysis for Additive Synthesis
• Data Reduction in Analysis/Resynthesis
• Line-segment Approximation
• Principle Component Analysis
• Spectral Interpolation Synthesis
• Spectral Modeling Synthesis
• Walsh Function Synthesis