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Synthesizing a Clarinet

Synthesizing a Clarinet. Nicole Bennett. Overview. Frequency modulation Using FM to model instrument signals Generating envelopes Producing a clarinet note A-440 note. Frequency Modulation. Used to reproduce signals with frequencies that vary with time

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Synthesizing a Clarinet

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  1. Synthesizing a Clarinet Nicole Bennett

  2. Overview • Frequency modulation • Using FM to model instrument signals • Generating envelopes • Producing a clarinet note • A-440 note

  3. Frequency Modulation • Used to reproduce signals with frequencies that vary with time • General formula: x(t) = A*cos(ψ(t)) • Oscillations of ψ(t) provide changes in instantaneous frequency - (ψ′(t))

  4. Producing Instrument Sounds • ψ(t) must be sinusoidal in order to reproduce both the fundamental frequency and the overtones of an instrument • General equation: x(t) = A(t)*cos(2Π*fc*t + I(t)*cos(2Π*fm*t + Φm) + Φc) ٭٭ ٭٭John M. Chowning, “The Synthesis of Complex Audio Spectra by Means of Frequency Modulation,” Journal of the Audio Engineering Society, vol.21, no. 7, Sept. 1973, pp 526-534.

  5. x(t) = A(t)*cos(2Π*fc*t + I(t)*cos(2Π*fm*t + Φm) + Φc) • A(t): amplitude envelope • Function of time • Allows sound to fade slowly or be cut off quickly • fc: carrier frequency • Frequency without any modulation • fm: modulating frequency • Rate of modulation of the instantaneous frequency

  6. x(t) = A(t)*cos(2Π*fc*t + I(t)*cos(2Π*fm*t + Φm) + Φc) • Φc and Φm: phase constants • Set to Π/2 for this project • I(t): modulation index envelope • Used to vary the harmonic content of the sound • Produces the overtones

  7. Generating A(t) and I(t) • WOODWENV2.m

  8. Scaling the I(t) Function • A(t) and I(t) are normalized by the WOODWENV function • I(t) must be scaled in order to produce a clarinet note • scale.m

  9. Synthesizing a Note • Now have most of the pieces of x(t): x(t) = A(t)*cos(2Π*fc*t + I(t)*cos(2Π*fm*t + Φm) + Φc) • fc and fm: ratio is 2:3 for the clarinet • f0: frequency of the note – will be greatest common divisor of fc and fm

  10. Clarinet Function • clarinet.m

  11. Playing a 440 Hz note • Play the A note • Limitations of the equation

  12. Conclusion • Modeling instrument signals • Generating a clarinet note • Problems with modeling an instrument using a mathematical equation

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