Transcript PowerPoint Presentation - The Effects of the Una Corda

The Effects of the Una Corda Pedal
on Harmonic Structure
Danielle Castens
Southern Illinois University
Edwardsville
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.
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.
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.
Structure of the Piano cont.
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.
Harmonic Structure cont.


Fundamental
frequency
The harmonic series
1st Harmonic (Fundamental Frequency)
2nd Harmonic
3rd Harmonic
4th Harmonic
Multiple standing waves on a string.
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.
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.
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.
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.
Data Analysis: C3
C3 (initial)
20
10
0
Intensity
0
2
4
6
8
10
12
14
16
-10
Without pedal
With pedal
-20
-30
-40
-50
C3 C4 G4 C5 E5 G5 A#5 C6 D6 E6 F6 G6 A6 A#6 B6 C7
Harmonic
Data Analysis: C3
C3 (later)
20
10
Intensity
0
-10
0
2
4
6
8
10
12
14
16
Without pedal
With pedal
-20
-30
-40
-50
C3 C4 G4 C5 E5 G5 A#5 C6 D6 E6 F6 G6 A6 A#6 B6 C7
Harmonic
Data Analysis: D3
D3 (initial)
20
10
Intensity
0
-10 0
2
4
6
8
10
12
14
16
With pedal
-20
-30
-40
-50
Without pedal
D3 D4 A4 D5 F#5 A5 C6 D6 E6 F#6 G#6 A6 B6 C7 C#7 D7
Harmonic
Data Analysis: D3
D3 (later)
20
10
Intensity
0
0
2
4
6
8
10
12
14
16
-10
Without pedal
-20
With pedal
-30
-40
-50
D3 D4 A4 D5 F#5 A5 C6 D6 E6 F#6 G#6 A6 B6 C7 C#7 D7
Harmonic
Data Analysis, cont.


Both C and D seem to have fairly different
behaviors, however the overall effect is the
same—differences 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.
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.
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.html
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/pitch-freq.html
Tillery, Bill W., Enger, Eldon D., & Ross, Frederick C. (2004).
Integrated Science. New York: McGraw-Hill.
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.
Contact Information
 Danielle
Castens
[email protected]
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.
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.
Structure of the Piano cont.