Synthesis Concepts

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Synthesis Concepts
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• Depending on your age, you might think the first
  synthesizer looked something like this

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• However, it looked more like this

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Synthesis Definition

• The OCD defines synthesis as
• Combination, composition, putting together
• Building up of separate elements into connected
  whole

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Synthesis Definition

• Generally, most people associate synthesis purely
  with subtractive synthesis
• Very limiting way to look at sound synthesis by
  electronic means

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The Bigger Picture
Subtractive
Sampling
Analogue

• Theoretically sound divisions, but practically
  limiting
• Techniques of different types applicable to others

Granular
FM
Additive
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In the beginning

• Additive synthesis
• Principle first utilised in cathedral organs

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Additive Synthesis

• Mathematical basis
• 1822 Jean Baptiste Joseph, Baron de Fourier
  published theory
• Any arbitrarily complicated periodic waveform can
  be deconstructed into combinations of sine waves
  of different amplitudes, frequencies and phases
• This is accomplished by the Fast Fourier
  Transform FFT

• Any arbitrarily complicated periodic waveform can
  be deconstructed into combinations of sine waves
  of different amplitudes, frequencies and phases

• This is accomplished by the Fast Fourier
  Transform FFT

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Additive Synthesis

• Sine wave simplest possible waveform
• Contains only the fundamental

Amplitude
Frequency
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Additive Synthesis

• A more complex waveform will be composed of any
  number of sines of varying frequencies and
  amplitudes

• Each line represents a sine at a specific
  frequency and amplitude

Amplitude
Frequency
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Additive Synthesis

• But this simple approach hides many difficulties
• Theory shown so far deals with a single moment in
  a sounds duration
• Most sounds are complex and evolving

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Sawtooth Wave
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Complex Wave
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Additive Synthesis

• Thus, will have multiple slices depending on
• Length of waveform
• Rate of change of waveform
• Control data therefore massive
• Very hard to create sounds using additive
  synthesis
• Holy Grail Resynthesis

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FM Synthesis

• Nothing more than an extreme form of vibrato

• When the modulation is fast enough, we no longer
  hear the rise and fall of the vibrato
• Instead, we perceive the changes in pitch as
  changes in the timbre of the sound

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FM Synthesis

• Basic Approach

Oscillator
Carrier
Modulator
Frequency

• Mathematical techniques behind this are extremely
  complex, but revolve around the notion of
  sidebands

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FM Synthesis

• Sidebands are frequencies generated above and
  below the frequency of the carrier by the
  modulation process
• Above carrier frequency modulator frequency
  (CM)
• Below carrier frequency modulator frequency
  (C-M)
• With FM, this is actually a series
• C n M
• C-4M, C-3M, C-2M, C-M, C, CM, C2M, C3M, C4M
  
• Although the number of FM sidebands is infinite,
  there is a finite number of significant sidebands

Amplitude

• Useful rule
• If the ratio of CM is an integer one, the
  modulation spectrum will be harmonic. Otherwise,
  the spectrum will be inharmonic.

Frequency
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FM Synthesis

• The really tricky bit, though, involves working
  out the amplitudes of each sideband
• Far too complex to concern ourselves with here
  (Bessel Functions)
• Important concept the Modulation Index
• i.e. the amount of FM to be applied
• Simply, it is the amplitude of the modulator that
  determines the amplitude of the various sidebands

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FM Synthesis

• Unfortunately, the relationship between these is
  not predictable without experience
• as the Index changes, the amplitude of each
  sideband pair evolves in a different pattern
• some sidebands gain amplitude, others lose
  amplitude
• there may also be cancellation effects caused by
  phase-inverted sidebands.
• This remains the most significant barrier to
  learning FM synthesis
• Nevertheless a powerful technique for creating
  complex sounds

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FM Synthesis

• Two variants
• Exponential associated with Analogue Synthesis
• Linear associated with Yamaha DX-series
• Only real difference has to do with ability of
  modulator to track carrier frequency
• Exponential based on V/octave asymmetrical
• Linear based on Hz/V proportional changes in
  pitch

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Granular Synthesis

• Attempt to deal with the shortcomings of additive
  synthesis to deal with changes in the sound over
  time
• 1947 Dennis Gabor, physicist formulated theory
• sound is perceived as a series of short, discrete
  bursts of energy, each slightly changed in
  character from the last
• Rooted in quantum physics coexistence of the
  wave and photon in light
• Sonic equivalent of the photon is the grain

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Granular Synthesis

• Definition generation of thousands of short
  sonic grains which are combined linearly to form
  large scale audio events
• Grain tiny piece of sonic data, duration 10 to
  50 ms.

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Granular Synthesis

• Two components
• Envelope
• Contents

• NB Grain Density number of grains per second
• Low density leads to rhythmic effects

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Granular Synthesis

• Subject to same fundamental problem as additive
  synthesis, though
• Tension between precision and control
• Massive number of grain events
• Basic unit -gt grain cloud rather than grain
  itself
• Set of rules for generating and controlling
  grains
• It has some of the drawbacks of FM synthesis as
  well
• Unpredictable results
• But capable of creating sound textures that no
  other form of synthesis can

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Subtractive Synthesis

• Well understood and widely employed
• Basis for rest of presentation
• Begin with a harmonically rich sound source and
  remove frequencies by means of filtering
• While any sound source can be employed,
  traditionally associated with certain waveshapes

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Subtractive Synthesis
Modulators / Shapers

• Basic Approach

Sources
Filters
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Subtractive Synthesis

• Sawtooth contains all harmonics, with amplitude
  1/n

Amplitude
Frequency
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Subtractive Synthesis

• Not all sawtooth waves created equal

Perfect Saw
Andromeda Saw
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Subtractive Synthesis

• Circuit

• Fourier Series

phase phase phaseIncrement if( phase gt 1.0
) phase phase - 2.0

• Code

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Subtractive Synthesis

• Square only odd harmonics present, also with
  amplitude 1/n

Amplitude
Frequency
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Subtractive Synthesis

• Triangle only odd harmonics present, but with
  amplitude 1/n2

Amplitude
Frequency
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Subtractive Synthesis

• Basic Filters

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Subtractive Synthesis

• Esoteric filters comb filters
• Regular series of peaks and dips in spectrum of
  input signal
• Achieved by adding signal with delayed copy
• Comb results from phase cancellation and
  reinforcement between delayed and undelayed signal

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Subtractive Synthesis

• Esoteric filters all-pass filters
• Definition unity gain at each frequency
• Amplitudes of frequencies not changed
• Instead, changes time that it takes for different
  frequencies to get through filter
• Therefore frequency dependent phase shift

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Subtractive Synthesis

• Oscillator Sync waveform of one oscillator
  (slave) locked to the waveform of another
  (master)
• Alters waveform by resetting the slaves phase
  when pulse from master is received

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Subtractive Synthesis

• If master frequency gt slave frequency, slave
  locked to master frequency

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Subtractive Synthesis

• If master frequency lt slave frequency, slave will
  gain harmonic components corresponding to master
  frequency
• These are harmonic sidebands

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Subtractive Synthesis

• Soft sync here slaves frequency is increased
  to become an exact multiple of masters
• No change in slaves waveform
• Mainly used for locking oscillators into harmonic
  relationships

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Subtractive Synthesis

• Waveshaping
• Sound of a waveform determined primarily by its
  harmonic content
• Can create new harmonics by passing waveform
  through non-linear element waveshaper
• Form of waveform distortion

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Subtractive Synthesis

• Waveshaping any signal with time-variant
  amplitude will produce time-varied spectrum at
  the output
• Purpose of non-linear elements is to modify shape
  of waveform, not its amplitude

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Subtractive Synthesis

• Amplitude Modulation
• To tremolo as FM is to vibrato
• Not a series just CM and C-M

Amplitude
Frequency
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Subtractive Synthesis

• Ring Modulation form of AM except C and M
  removed from the resulting signal

Amplitude
Frequency
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Subtractive Synthesis

• Filter FM audio rate modulation of cutoff
  frequency. Extreme form of wah-wah
• Amplitude of frequencies in the range of
  variation of cutoff frequency will appear to be
  periodically AMed

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Subtractive Synthesis

• AM will have pulse shape, but with rounded
  corners. The more gradual the cutoff, the more
  rounded the amplitude modulation shape.

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Resources

• Synthesis
• http//www.soundonsound.com/search?sessiond824339
  68bb2b69eb88f4501a6d9d6ceurl2FsearchKeywordsy
  nthsecretsWordsAllSection8SubjectMonth
  YearSummaryNoArticlesSearchArticles
• http//eamusic.dartmouth.edu/book/MATCpages/table
  ofcontents.html
• http//www2.sfu.ca/sonic-studio/handbook/Sound_Syn
  thesis.html
• http//www.ipo.tue.nl/homepages/dhermes/lectures/S
  D/index.html
• http//ccrma.stanford.edu/jos/pasp/
• General
• www.soundonsound.com
• www.computermusic.co.uk
• http//www.emusician.com/
• Plug ins
• http//www.kvr-vst.com/

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The End