Synthesis: Additive, AM, and FM

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Synthesis Additive, AM, and FM         

• Week 11
• IAT-204, Spring 2007SFU Surrey

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Todays topics

• Fundamentals of Sound Theory
• Additive Synthesis
• Amplitude Modulation (AM)
• Frequency Modulation (FM)

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Learning Objectives

• Explain harmonic tones and inharmonic tones
• Describe how to synthesize new complex tones by
  adding tones together
• Explain how to modulate the amplitude of carrier
  by modulator
• Describe how to emulate acoustic instrumental
  sounds with FM

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Fundamentals of Sound Theory

• The sounds we hear are fluctuations in air
  pressure caused by vibrating objects
• This continuous rise and fall in pressure creates
  a wave of sound

• frequency the number of cycles that occur in one
  second of the vibration

• phase an offset in time by some fraction of a
  cycle

• amplitude ? the greatest change in pressure
  achieved by the wave

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Frequency Sound vs. Light

• Light of a particular frequency, perceived as a
  particular color

• Sound of a particular frequency, perceived as a
  particular pitch

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Amplitude Loudness vs. Brightness

• Brightness intensity of color, independent of
  frequency (color)

• Loudness intensity of sound, independent of
  frequency (pitch)

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Complex Tones

• Harmonic motion a single sine wave vibration
• Complex tone any sound that contains more than a
  single frequency
• Spectrum the combination of frequencies that are
  present in a sound
• Partial each individual frequency that goes into
  the makeup of a complex tone

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Harmonic Tones

• Harmonic tones partials in a complex tone are
  all multiples of a fundamental frequency
• Fundamental frequency the lowest frequency of a
  harmonic tone
• Harmonics the exact multiples of the fundamental
  frequency
• E.g. if the fundamental is 440 Hz ? the 1st, 2nd,
  and 3rd harmonics are 440, 880, 1320 Hz

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Addition of Frequency Components

• The sum of all those harmonically related
  frequencies repeats at fundamental frequency ?
  Harmonic fusion

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Harmonic Tones (2)

• Fourier theorem
• Any periodic wave, no matter how complex, can be
  demonstrated to be the sum of different
  harmonically related frequencies (sinusoidal
  waves)
• Whenever youre hearing a chord, youre actually
  hearing a harmonic complex tone!
• E.g. ---------------------------------------------
  --?

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Harmonic Tones (3)

• C Major Triad
• simultaneously play sine waves whose frequencies
  are 100, 300 and 500 Hz (135)

Wave Diagram of C Major Triad (1 Period) Red
C 1   Green G 3   Blue E 5
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Inharmonic Tones and Noise

• If frequencies in a tone not multiples of a
  fundamental ? inharmonic tones
• E.g., a bell ? not a harmonically related set of
  partials
• Many different frequencies with no apparent
  mathematical relationship ? noise
• completely random frequencies and amplitudes ?
  white noise

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Additive Synthesis

• Combining tones
• Complex tones are composed of energy at several
  different frequencies ?
• One obvious way to synthesize complex tones ? add
  together multiple sine wave oscillators (cycle)

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Additive Synthesis (2)

• Sinusoids added together to make a complex tone

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Additive Synthesis (3)

• add cosine oscillators with independent control
  over frequency, phase, amplitude

• partial objects receiving fundamental from the
  same source, and integer partial ? their
  harmonic relations will be maintained

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Envelope generator function

• function object ? generate amplitude
  envelopes(allow you to draw the shape you want)

• When function receives a bang ? sends a list of
  value-time pairs out its 2nd outlet

• line ? produces a changing signal corresponding
  to the shape drawn

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Amplitude Modulation (AM)

• AM changing the amplitude of one signal
  (carrier) using that of another signal (modulator)

• In the general case, the modulator is used to
  alter the carriers amplitude ? cause fluctuation
  of amplitude around some value other than 0

• Ring modulation a specific case of AM ? the
  two signals are simply multiplied

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Difference Ring vs. AM

• The two main differences
• The modulator in AM has a DC offset (a constant
  amplitude value at frequency 0 Hz )
• The AM normally doesnt go all the way to 0,
  whereas the ring mode does

• 100 Hz tone multiplied by 4 Hz cosine with
  amplitude of 0.25, which is used to vary the
  amplitude around a DC offset ? 0.75 (0.51.0)

• 100 Hz cosine multiplied by a 4 Hz cosine the
  amplitude of both cosines is 1

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Frequency Modulation (FM)

• Modulating the frequency of one wave with another
  wave ? sidebands (output tone)
• Why FM?
• Very effective and efficient means of
  synthesizing a wide variety of musical tones

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Controls of FM Synthesis

• Harmonicity ratio Fm/Fc ? frequencies of output
  tone and harmonic/inharmonic relationship
• Fc, FcFm, Fc-Fm, Fc2Fm, Fc-2Fm, Fc3Fm, Fc-3Fm,
  etc
• Modulation index Am/Fm ? timbre of sidebands
• Timbre the quality of a sound that distinguishes
  it from other sounds of the same pitch and volume
• (Music) The distinctive tone of an instrument or
  singing voice
• The greater the index, the brighter the timbre
  (more sidebands of significant energy)

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Implementing Harmonicity Ratio Modulation Index

• The setting enables us to specify the carrier
  frequency, harmonicity ratio, and modulation index

• It then calculates the modulator frequency and
  modulator amplitude to generate the FM signal

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Summary of Todays Topics

• Harmonic tones and inharmonic tones
• Synthesize new complex tones by adding tones
  together
• Modulate the amplitude of a signal (carrier) by
  another signal (modulator)
• Emulate acoustic instrumental sounds / generate
  unusual new sounds with FM