PowerPoint Presentation
Harmonic Series and SpectrogramsBy Jordan Kearns (W&L
14)& Jon Erickson (still here )220 Hz (A3)
Why do they sound different?Instrument 1Instrument 2Sine
WaveWaveform
Piano GuitarSine WaveOvertones and Music PerceptionOvertones
occur at integer multiples of the fundamental frequency when an
object vibrates. The addition of these tones at regular intervals
is musical to the human ear.Example: Fundamental (1st Harmonic):
220Hz1st Overtone (2nd Harmonic): 440Hz2nd Overtone (3rd Harmonic):
660Hz
Video produced by Brandon Pletsch Univ. of Georgia Medical
SchoolURL: https://www.youtube.com/watch?v=PeTriGTENoc
PianoGuitarFrequency SpectrumModes of Vibration: Standing
Waves
Harmonic Motion in Guitar
Frequency Decomposition: Pure Sine Wave
T = 2ms
f = 1/Tf = 500HzFrequency Decomposition: Pure Sine WaveT =
1ms
f = 1/Tf = 1000Hz
Composite Wave I
Composite Wave II
Waveform
Piano GuitarSine WaveSpectrogram: Piano
Piano: Component Sine Waves
TimeMicrophone Signal Amplitude Piano: Component Sine Waves
Composite Wave(From Previous Slide)Original Piano WaveLook how
close with only three sine waves!!!Fourier Series and
Superposition
Why you should change stringsA quick experiment with a
spectrogram
OldNewC major chordPiano C chord (2nd inversion)
G4 (388) C5E5 (657)G5 (775)117113141564
Frequency Spectra for Different InstrumentsSame pitch played,
but TIMBRE is entirely unique
Chart71000000
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*500*t)
Sheet1150012100003150004200005250006300007350008400009450001050000base
freq500
Sheet1
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*500*f*t)
Sheet2
Sheet3
Chart80100000
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*1000*t)
Sheet1150002100013150004200005250006300007350008400009450001050000base
freq500
Sheet1
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*1000*f*t)
Sheet2
Sheet3
Chart51100000
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*500*t) + sin(2pi*1000*t)
Sheet1150012100013150004200005250006300007350008400009450001050000base
freq500
Sheet1
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*500*f*t) + sin(2pi*1000*f*t)
Sheet2
Sheet3
Chart610.500000
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*500*t) + 0.5sin(2pi*1000*t)
Sheet115001210000.53150004200005250006300007350008400009450001050000base
freq500
Sheet1
Frequency (Hz)Amplitude (arbitrary units)Frequency Spectra for
x(t) = sin(2pi*500*f*t) + 0.5sin(2pi*1000*f*t)
Sheet2
Sheet3
