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Sound Synthesis. Part I: Introduction & Fundamentals Nicolas Pugeault [email protected] Introduction. Instruments can be made in a variety of ways: think guitar, piano, organs, etc.

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Sound synthesis

Sound Synthesis

Part I: Introduction & Fundamentals

Nicolas Pugeault

[email protected]



  • Instruments can be made in a variety of ways: think guitar, piano, organs, etc.

  • Use electronic devices to create sounds: synthesisers.

  • Can either

    • Recreate an existing timbre

    • … or something different.



  • Producing a sound by sending an electrical signal to a speaker is trivial.

  • The question is what are the relevant and desirable properties of the signal to ensure that the resulting sound is as desired (eg, similar to a real instrument).



  • Musical instruments

  • Computer games

  • Sound effects for films

  • Multimedia, computer system sounds

  • Mobile phones

  • Speech synthesis

  • Toys

  • Effects

Sound synthesis plan

Sound Synthesis Plan

  • Synthesis I: Fundamentals

  • Synthesis II: Additive

  • Synthesis III: Filtering and distortion

  • Synthesis IV: Other approaches

  • Post-processing, pitch correction (autotunes)

  • Sound perception

Sound synthesis1

Sound Synthesis

Part I: Fundamentals

Nicolas Pugeault

[email protected]

Lecture plan

Lecture Plan

  • Introduction to sound synthesis

  • Perception of sound

    • Loudness

    • Pitch

    • Timbre

  • Sound synthesis – Fundamentals

  • Summary

Sound cont d

Sound (cont’d)

  • Sound is a pattern of compression and depression of the air

    • Record it using microphones

    • Perceive it from our ears

    • Generate it by speaking or using speakers

  • Energy per m2 decreases with the square of distance...

Sound is a waveform

Sound is a waveform

  • Sound is a waveform,

  • Can be reflected when hitting a non-transmissive surface

  • If the surface is flat, reflected in cohesive way

  • Otherwise depends on frequency and surface texture

Sound proof studio wall, for

absorbing high frequencies

Attributes of sound

Attributes of sound

The simplest sound pure tone

The simplest sound: Pure tone

  • Sinusoidal wave (440Hz)

Periode p=1/f0

Reminder fourier transform

Reminder: Fourier Transform

  • Idea: “All functions can be decomposed in a (possibly infinite) sum of sinusoidal functions of varying frequencies.”

  • Transforms a function from time domain to frequency domain.

  • Eg, right, for a square wave.



First two


First three


First four




  • Often measured in decibels (dB) R=20*log10(A/A0)

  • A0 is a reference amplitude, often taken as the threshold of audibility.

  • Logarithmicperception of loudness.

  •  A change in 6dB means a doublingof amplitude!

  • Range of audibility: ~120dB (1 to 1million)

Perception of loudness

Perception of Loudness

  • Correlated with amplitude.

  • Here:

    • constant frequency (f0=440Hz)

    • Varying amplitude (A = 0.2, 0.5 or 1.0)

Loudness cont d

Loudness (cont’d)

  • However

    • Perception of Loudness is frequency dependent.

    • Sound X and Y have the same amplitude, which is louder, X or Y?

      • X (100 Hz, A=1)

      • Y (3,500Hz, A=1)

  • Considering only amplitudes, sound Y should be the same loudness as sound X.

  • However, Y is louderthan X. Why?

Loudness cont d1

Loudness (cont’d)

  • Fletcher Munson (1933)

    • Subjects listen to pure tones

      • Various frequencies

      • amplitude inc. per 10dB

  • Robinson & Dadson (1956)

    • more accurate

    • Basis for standard ISO-226

  • Perceived Loudness (Phons)

    • 1 Phon = 1dB SPL @ 1kHz

  • British Standard BS ISO 226 (2003) (source wikipedia)

Loudness cont d2

Loudness (cont’d)

  • There is a difference between sensory loudness and perceptual loudness! (Emmet, 1992)

  • For the design of a synthesiser with large dynamical range, changing only amplitude is a poor choice since signal may clip.

  • Solution: use spectral variation:

    • Broad spectrum will likely result in a loud sound.

    • Narrow spectrum will be perceived as quiet.

Perception of pitch

Perception of Pitch

  • Frequency correlated with pitch

  • Here: 3 examples of pure tones.

  • What if sounds are more complex?

  • Range: 20Hz-20kHz

  • Best acuity: 200Hz-2kHz

Pitch fundamental harmonics

Pitch: Fundamental & Harmonics

  • Real sounds are not pure – more complex!

  • The ear assumes that multiple frequency components form one sound.

  • Harmonically related -> fuse into single pitch at Fundamental Frequency (f0largest common divisor)

  • Each sinusoid is called a Harmonic partial of the sound (fk = N*f0)

Fundamental harmonics 2

Fundamental & Harmonics (2)

Fundamental f0

First harmonic f1 = 2*f0

Second harmonic f2 = 3*f0

Third harmonic f3 = 4*f0


Seventh harmonic f7 = 7*f0

Fundamental harmonics 3

Fundamental & Harmonics (3)

  • The pitch is correlated with the Fundamental frequency.

  • Although in this example the fundamental is missing, the pitch is the same. The timbre is different.



  • All those sounds have the same pitch (A4, 440Hz)

    • Flute A4

    • Tuning fork A4

    • Violin A4

    • Singer A4

  • They differ in timbre.

Defining timbre

Defining Timbre

  • Definition (American Standard Association):“That attribute of sensation in terms of which a listener can judge that two sounds having the same loudness and pitch are dissimilar.”(ASA, 1960 ; Wikipedia, 2011)

  • Has a “wastebasket” quality (Dixon Ward, 1965):

    • What is neither loudness nor pitch...

  • Synonyms:Tone quality or colour, texture...

  • Affected by a sound’s envelope.

Timbre cont d

Timbre (cont’d)

  • What physical parameters relate to timbre?

    • Static spectrum (transient)

    • Envelope of spectrum (transient)

    • Dynamic spectrum (time-evolving)

    • Phase

  • This list is not exhaustive.

    • cf “wastebasket” quality!

Timbre static spectrum

Timbre: Static Spectrum


Timbre envelope of spectrum

Timbre: Envelope of Spectrum

Timbre envelope cont d

Timbre: Envelope (cont’d)


  • Difference in envelope (same note, 440Hz fundamental)

    • Top: Flute

    • Bottom: Violin

  •  Envelope differs!

  • Conclusion:Envelope is instrument-specific.


Timbre envelope cont d1

Timbre: Envelope (cont’d)

  • Arrows indicate formants.

  • This slide indicates two speech vowels (i and u)

  • Formants not only determine timbre but helps distinguishing vowels.

  • (used in speech recognition)

Timbre dynamic spectrum

Timbre: Dynamic Spectrum


  • Will those two sounds have the same timbre?

  • No, same average spectrum, but different timbre!

  • Difference:

    • Top: original sound

    • Bottom: time reversed.

  • Conclusion: Temporal variation of spectrum impacts timbre!


Timbre dynamic spectrum cont d

Timbre: Dynamic Spectrum (cont’d)

Timbre spectrogram

Timbre: spectrogram

Frequency (Hz)

Time (s.)

Timbre dynamic spectrum cont d1

Timbre: Dynamic Spectrum (cont’d)

A) Normal

  • This slides shows the long term (average) spectrum for two sounds (top: original and bottom: time reversed)

  • Spectrum is identical; timbre is totally different  very misleading!

  • Conclusion:it is important to know how the spectrum evolves in time.

  • The timbre does not only depends on the harmonic structure but on the way spectrum varies in time.

B) Time reversed

Time envelope adsr

Time envelope (ADSR)

  • Time Envelope (ADSR)

    • Attackis the time from nil to peak.

    • Decayis the time from peak to the sustain level.

    • Sustainis the level during the main sequence of the sound’s duration, until key is released.

    • Releaseis the time to decay from sustain level to zero.

Time envelope example

Time Envelope (example)

Time envelope example1

Time Envelope (example)

  • Example of the same sound with and without attack

    • Attack cut at 0.7s.

    • With (blue+green):

    • Without (green):

Timbre phase

Timbre: Phase?

  • Sound A

  • Sound B

Are A and B of different timbres?

Timbre phase1

Timbre: Phase?

Sound A: Square wave, fundamental 500Hz, 9 harmonics.

  • Timbre depends (weakly) on phase relationship between harmonics.

  • BUT waveforms are totally different, magnitude spectra identical, and timbre are (almost) identical!

  • Conclusion:Human hearing is not sensitive to phase differences.

Sound B: Square wave, fundamental 500Hz, 9 harmonics,

every second harmonic phase shifted by 90 degrees.

Summary 1 loudness control

Summary 1: Loudness Control

  • In order to control loudness in synthetic sounds:

    • Modify the spectral content:

    • more energy at high frequency  louder(see right).

    • Modify the amplitude

    • Higher amplitude  louder

Summary 2 pitch control

Summary 2: Pitch Control

Fundamental frequency

  • In order to control pitch in synthetics sounds:

    • Modify the fundamental frequency.

    • High fundamental frequency  high pitch.

Summary 3 timbre control

Summary 3: Timbre Control

  • In order to control timbre in synthetic sounds, modify

    • Spectral content

    • Spectral envelope

    • Spectrum in time

    • Spectrum evolution during transient states

Sound synthesis


  • Introduction to sound synthesis

  • Perception of sound

    • Loudness

    • Pitch

    • Timbre

  • Sound synthesis – Fundamentals

  • Summary

Fundamental definitions

Fundamental Definitions

  • Computer Instrument: An algorithm that realizes (performs) a musical event.

  • Unit Generator: A high-level “building block” in an instrument.

Important terms

Important Terms

Two types of synthesisers



You can only play onenote at a time. If you play several keys together, only one note will be generated  no chords!

You can play several notes at the same time  can play chords!

Types of synthesis

Types of synthesis

Sound synthesis


  • Introduction to sound synthesis

  • Perception of sound

    • Loudness

    • Pitch

    • Timbre

  • Sound synthesis – Fundamentals

  • Summary

Additional reading

Additional Reading

  • C. Dodge, C., & Jerse, T. A. (1997). Computer Music: Synthesis, Composition, and Performance.Schrimer, UK.(see chapters 2 and 4)

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