Electronic Music

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Electronic Music

• Dr Ian Drumm

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Building Timbres

• Aims
• Extend concept of additive synthesis for the
  optimal creation of realistic timbres
• Wavetable techniques
• Learning Outcomes
• Partial synthesis, time varying partial synthesis
  and wave-table synthesis
• Cost and optimisation
• Advantages and disadvantages of additive
  synthesis technique

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Recap Fourier Series

• Summation of sinusoids to build complex waveforms
  
• If periodic
• hence
• However most realistic timbres are at best quasi
  periodic hence will have an-harmonic content
  (partials)

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Examples of additive synthesisers

• Hammond Organ
• Fairlight CMI, Kawai K5.

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Partials

• Fourier series pertains to complex waveforms that
  are periodic, being the summing of harmonics
  f,2f,3f, etc
• An-harmonic components are referred to as
  partials (or overtones)
• DFTs (and FFTs) can reveal an-harmonic content in
  signals that arent periodic
• Given real musical notes are time varying
  emulating partials is important for realistic
  sounds

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Time Varying Partial Additive Synthesis (TVPAS)

• Drops the harmonic assumption (include Partials)
• Takes account of temporal behaviour of frequency
  content
• Where

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Amplitude Envelopes

• There are two basic amplitude envelopes
• Continuous excitation instruments (woodwinds,
  bowed strings, voices, etc
• Momentary excitation instruments (plucked
  strings, pianos, percussion).

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Control Parameters

• Attack, Decay, Sustain, Release

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Computational Efficiency

• If we have p partials, the computer has to
  calculate
• for each sample point in the output.
• The time in which to do this is

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So for 100 partials at CD quality with 10 note
polyphony we need 4410027010010 1.19GHz of
processing
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Assessment of additive synthesis

• Pros
• Very fine control over output sound
• Well understood analysis stage to match synthesis
• Good for emulative synthesis
• Cons
• Realism (TVPS) implies a huge requirement for
  control data and considerable processing power
• Storing only a finite number of harmonics results
  in a finite error in synthesis
• Analogue implementation not sensible

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Linear Algorithmic Synthesis

• Classic D50
• ROM-sampled attack transients added to
  conventionally synthesised timbres

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Wavetable Synthesis

• PPG Wave, Waldorf Microwave, Korg Wavestation
• Table of basic wave functions
• Waveform chosen on cycle by cycle basis
• Pointer steps through a sequence of memory
  locations
• Hence interpolating between complex wave shapes
  over time as we play the musical note

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Wavetable - From PPG Wave Rom
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Wavetable Changing cycles

• Swept
• Sweeping through successive cycles
• Similar waveforms close together
• Random Access
• A specific sequence of cycles
• Dynamically changing sequence gives type of
  modulation

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Wavetable Storage

• Single cycle waveforms
• Multi-cycle waveforms
• Samples (with variable start and end points)
• Sequence lists
• Loops (for user with ASDR)
• Vector synthesis (dynamically mapping out a path
  or vector from one waveform to another)

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Advantage of Wavetable Synthesis

• A key advantage of wave table synthesis over more
  traditional additive synthesis is that it
  exploits the quasi periodic nature of real
  timbres. With additive synthesis the synthesiser
  effectively tries to compute the DFT of the
  timbre in real time where as wave table
  synthesis employs pre-computed elements.