Harmonic Analysis with CoolEdit2000

1
Harmonic Analysis with CoolEdit2000

• Phys 332W
• Lab 4
• Sept 23, 2004

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• Goals
• To familiarize yourself with the tools of
  harmonic analysis in CoolEdit2000.
• To analyse the harmonic structure of several
  tones from a single real sound source.
• Equipment
• Musical instrument Voice, Recorder, Guitar,
  Keyboard, CD recording,
• Computer with CoolEdit
• Initialization
• Launch CoolEdit
• From the Options menu, select Monitor Record
  Level
• From the Options menu, select Windows Mixer

• From the View menu, select Show CD Player

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• CoolEdit Initialization, contd
• In Windows Mixer, select source for recording
• In Volume Control, select Options, Properties,
  Recording
• Select your sound source
• Microphone
• Line-in (keyboard, etc)
• CD Recorder

4
Recording

• Record several seconds of music.
• Use sample rate44100
• Mono or Stereo, 16 bit
• Select a single note, and highlight it with the
  cursor.
• In the Analyze menu, select Frequency Analysis.
• Select FFT size 32768, Blackman-Harris, and hit
  Scan
• Use the cursor in Frequency window to get exact
  frequencies and amplitudes (dB) of major
  intensity maxima

Find the peak frequencies by matching the db
reading in the cursor window with the value on
the vertical axis.
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Here are sample frequency data from the downbeat
of the second movement of the J.S. Bach 1st
Violin Concerto
If you open the exel file, on Sheet-1 you can see
the excel formula for computing the trendline
(straight-line fit). The magenta points are 10
times the difference between the data and
trendline (simple integer multiples of
fundamental.
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J.S. Bach 1st Violin Concerto, 1st Movement
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Here are sample frequency data from the downbeat
of the first movement of the J.S. Bach 1st Violin
Concerto
This is the same exel file. On Sheet-2 you can
see the excel formula for computing the trendline
(straight-line fit). Notice that is is a chord,
the first few harmonics are not multiples 1,2,3
of the funadamental but 5/4, 3/2, 4/2, 5/2
multiples. The magenta points are 10 times the
difference between the data and trendline
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Proceedures

• Record 2 different notes from 2 different
  instruments.
• Make a note (on paper or in excel spreadsheet if
  you have a disk) of the frequencies and
  intensities of the first 5 strong harmonics you
  observe.
• Comment on any changes you observe in the spectra
  if you change the filter type (Gauss, Welsh,
  Blackman-Harris), or FFT size (2048-32768).
• Are the frequency peaks narrower or broader?
• Is there more or less noise?
• Comment on any difference you observe from
  different sound sources
• Harmonics more/less well defined.
• Pitch/frequency peak sharper or broader.

9
Write-up

• Make a plot of your frequency values first simple
  integer or rational estimates of the
  overtone/chord frequencies
• Compute and tabulate the difference between each
  of your overtone frequencies, and some simple
  integer or rational (5/4, 3/2,) multiples of the
  fundamental.
• Comment on how closely in tune these overtones
  are.
• One musical half step is a 6 change in frequency
• Two pitches f1 and f2 (including a phantom
  overtone) will beat (oscillate in amplitude) with
  frequency f1-f2.
• If (f1-f2)/(f1f2) lt 0.02 this produces tremulo
• If (f1-f2)/(f1f2) gt 0.02 this produces a
  clashing dissonant sound.
• A more sophisticated way of doing this is
  calculating residuals in excel.