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PH 105. Dr. Cecilia Vogel Lecture 13. OUTLINE. Timbre and graphs: Time graph Spectrum graph Spectrogram Envelope scales units interval factors. Fourier Analysis. Fourier Synthesis meant from the spectrum, build the Fourier Analysis means from the waveform, find the

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ph 105
PH 105

Dr. Cecilia Vogel

Lecture 13

slide2

OUTLINE

  • Timbre and graphs:
    • Time graph
    • Spectrum graph
    • Spectrogram
  • Envelope
  • scales
    • units
    • interval factors
fourier analysis
Fourier Analysis
  • Fourier Synthesis meant from the spectrum, build the
  • Fourier Analysis means
    • from the waveform, find the
    • Let’s let the computer do it.
  • This yields a spectrum graph
    • or ____ graph
    • Amplitude vs
pitch and timbre graphs
Pitch and Timbre —Graphs
  • Dominant influences on pitch and timbre:

*f1 might be lowest freq, but might not

*Often overtones are nf1.

envelope
Envelope
  • Envelope is the time variation of the sound
    • Often divided into:
    • attack = initial building up of sound
    • decay = decrease to sustained level
      • or to zero, if the sound is not sustained
    • sustain = sound held fairly steady
    • release = final decrease of sound to zero

A

D

S

R

slide6
ADSR
  • Attack, decay, and release
    • Are usually described by the time they last
  • Sustain
    • is usually described by the level (amplitude)
  • But all four may have their own
    • frequency, spectrum, amplitude, and duration
spectrograms
Spectrograms
  • time graphs
    • show time variation (x-axis is time)
  • spectrum graphs
    • show frequencies in spectrum (x-axis is frequency)
  • Spectrograms
    • show both
    • x-axis is time
    • y-axis is frequency
    • Amplitude is shown by heaviness of graphing
bird song spectrograms
Bird Song Spectrograms
  • Top one (a)
    • three trills
    • many freq’s — noise-like
  • Bottom one (b)
    • first a low tone with many harmonics
      • rises and falls slightly
    • then higher, purer tone
      • falls slightly
  • finally lower, more noise-like tone
octave
Octave
  • If two pitches
    • the frequency of one is
    • fundamental similarity in
    • often leads to
  • Octaves are further divided
    • into cents, semitones, whole tones
cents
Cents
  • One cent interval has a ratio of 1.0006
    • 1 cent above 440Hz is
    • Can you tell the difference between 440 Hz and 440.25 Hz?
  • a jnd is a ratio of 1.005
    • about 8-9 cents
    • 10 cent above 440Hz is
    • Can you tell the difference between 440 Hz and 442.55 Hz? (10 cents)
cents calculation
Cents Calculation
  • Interval, I, in cents is related to the
  • Example, an octave has a ratio of
semitone
Semitone
  • An octave is often
    • each semitone is a factor of
    • multiply 440 Hz (an A) by
      • you’ll get about 880 Hz
  • Keys on a piano are separated by
  • 12 semitones in order is a
musical staff
Musical Staff
  • Musical notes are
    • the x-axis is
    • the y-axis is
    • Fig 8.9
      • Only the notes in spaces are written in.
      • Notes on lines are letters between.
      • Short lines indicate where sharp/flat would be , graphically.
major diatonic scale
Major Diatonic Scale
  • Western music uses a ____________ instead.
  • A major diatonic scale has
    • (the 8th would be an
    • The intervals are not all semitones
    • some are
      • whole tone is about a factor of (1.06)2 = 1.12
    • The intervals in major diatonic scale are
    • Start with any key on the keyboard.
      • You’ve played a major diatonic scale.
example
Example
  • Key of C (major diatonic scale)
  • play
  • CDEFGAB
  • C to D is a
    • C#/Db is between
    • similarly with
  • E to F is a
scale on piano
Scale on Piano
  • one octave on keyboard
    • ignore the gray for now
slide18

Summary

  • Envelope — ADSR
  • equal pitch intervals are equal frequency factors
    • jnd, cents, semitone, whole tone, octaves
  • Scales
    • chromatic, 12 notes, 1 semitone apart
    • major diatonic, 7 notes, whole and semitone intervals
  • Staff