The Effects of the Una Corda Pedal on Harmonic Structure

1
The Effects of the Una Corda Pedal on Harmonic
Structure

• Danielle Castens
• Southern Illinois University Edwardsville

2
Why This Study?

• The una corda pedal is used by pianists for a
  softened tone, not only in volume but also in
  sound quality.
• The harmonic structure of a musical note is
  strongly related to the sound quality.

3
Fundamentals of Music and Sound

• The pitch of a musical note is determined by its
  frequency.
• Pitches are named by a set of letters known as
  the musical alphabet.
• The eight-note span between pitches of the same
  letter name is referred to as an octave.

4
Structure and Function of the Piano

• Sound is produced on the piano by striking the
  strings with felt-covered wooden hammers.
• Energy is transmitted into the strings, producing
  a sound wave.
• The strings alone are too small to provide
  sufficient volume, so a wooden soundboard is
  built into the piano.
• Higher pitches have multiple strings to provide
  volume equal to that of the lower pitches. The
  three strings of a pitch are slightly mistuned to
  produce a warmer sound and to counter the tripled
  sound decay that would otherwise occur.

5
Structure of the Piano cont.
6
Harmonic Structure

• Sounds are actually made up of a combination of
  frequencies, referred to as the harmonic
  structure of a sound.
• Each string has natural modes of vibration, in
  which a certain number of standing waves form.
  These modes occur simultaneously when the string
  is set in motion, interfering with each other.

7
Harmonic Structure cont.

• Fundamental frequency
• The harmonic series

1st Harmonic (Fundamental Frequency)
2nd Harmonic
3rd Harmonic
4th Harmonic
Multiple standing waves on a string.
8
The Una Corda Pedal and Sound Decay

• The una corda pedal, which is the left pedal on
  the piano, functions by shifting the hammers
  slightly to the right, causing them to strike two
  of the three strings of a pitch.
• This causes a less intense initial sound and less
  rapid sound decay.
• The third string begins vibrating in sympathy to
  the other two strings, creating a more sustained
  sound after the initial sound.

9
Methodology

• We measured the harmonic structure of notes in
  octaves (C2-C6, D2-D6) and successive notes
  within the same octave (C3, D3, E3, F3, G3). Ten
  trials of each note were taken, with and without
  the pedal.
• Data was taken during the initial 0.5s and at a
  later 0.5s interval, selected by locating a
  qualitative change in the waveform of each note.
• A computer software program, Audacity, was used
  to record and produce a Fourier analysis of each
  note.

10
Methodology cont.

• Sets of data were taken using the same grand
  piano within a short time frame to minimize the
  effects of temperature and humidity change as
  well as structural differences and tuning.
• To ensure that the amount of pressure applied to
  the key was identical during each trial, I placed
  a 47mm tube over the key and dropped a 78g weight
  through the tube to strike the key.

11
Data Analysis

• The overall pattern throughout the data indicates
  that the harmonic structures with and without the
  pedal of the initial sound follow a similar
  trend, while data taken at a later point in time
  indicate that the harmonic structures grow
  increasingly different as time passes.
• This may be an effect of the third string
  beginning to resonate later in the sound when the
  una corda pedal is used.

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Data Analysis C3
C3 C4 G4 C5 E5 G5 A5 C6 D6 E6 F6 G6 A6 A6
B6 C7
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Data Analysis C3
C3 C4 G4 C5 E5 G5 A5 C6 D6 E6 F6 G6 A6 A6
B6 C7
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Data Analysis D3
D3 D4 A4 D5 F5 A5 C6 D6 E6 F6 G6 A6
B6 C7 C7 D7
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Data Analysis D3
D3 D4 A4 D5 F5 A5 C6 D6 E6 F6 G6 A6
B6 C7 C7 D7
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Data Analysis, cont.

• Both C and D seem to have fairly different
  behaviors, however the overall effect is the
  samedifferences between the harmonic structures
  of notes with and without the pedal become
  magnified as time passes, although in different
  ways.
• This effect is consistent throughout the data,
  however no two notes behave in exactly the same
  manner.

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Conclusions and Implications

• Although effects are not consistent from pitch to
  pitch, there were significant differences in
  harmonic structure when the pedal was used,
  indicating an overall qualitative effect in the
  sound.
• The harmonic structure is always altered when the
  pedal is used, but specifically which harmonics
  are higher or lower varies from note to note.

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References

• Berg, Richard E., Stork, David G. (1995). The
  Physics of Sound. Englewood Cliffs, New Jersey
  Prentice Hall.
• Blackham, E. D. (1965). The physics of the piano.
  Scientific American. Online. Available
  http//www.concertpitchpiano.com/PhysicsOfPiano.h
  tml
• Hall, Donald E. (2002). Musical Acoustics.
  Pacific Grove, CA Brooks/Cole.
• Henderson, George A. (2002 Preliminary Edition).
  Musical Acoustics with Minimal Math.
  Edwardsville, IL Southern Illinois University
  Edwardsville.
• Horner, Lenore. (Creator). (2006). Multiple
  standing waves on the same string. Graph.
  Edwardsville, IL Southern Illinois University
  Edwardsville.
• Musical pitches. (n.d.). Retrieved October 15,
  2005 from http//www.people.virginia.edu/pdr4h/p
  itch-freq.html
• Tillery, Bill W., Enger, Eldon D., Ross,
  Frederick C. (2004). Integrated Science. New
  York McGraw-Hill.

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Acknowledgements

• I would like to sincerely thank Drs. Lindell and
  Horner of the Physics department for their
  knowledge, guidance and generosity of time. I
  would also like to thank Richard Murphy, the
  piano technician at SIUE, for explaining some of
  the details of harmonic structure and piano
  function, allowing the use of his equipment, and
  training me to do so.

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Contact Information

• Danielle Castens
• dcasten_at_siue.edu

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Data Analysis C3

• This pattern is evident in C3, as the harmonic
  structures recorded initially follow an almost
  identical trend, and the later sample shows no
  smooth shape to the harmonic curve.
• Many of the harmonics indicate a greater relative
  intensity when the pedal is used, indicating a
  slower decay with the pedal.

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D3 Data Analysis

• Again, in the initial data taken of D3 we see a
  very similar trend in the initial data, this time
  with many of the harmonics having less intensity
  when the pedal was used.
• The data taken later in the sound indicate a
  considerable difference in the harmonic structure
  when the pedal was used, some harmonics being
  relatively more intense and some being relatively
  less intense when the pedal was used.

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Structure of the Piano cont.