Transcript Student project - Jacobs University Mathematics

Musical Instruments
Howard & Angus, Chapter 4
www.phys.unsw.edu.au
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Any acoustic instrument has two main components:
 a sound source, and
 sound modifiers.
e.g., echo, reflection, absorption
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Student project
Student project
Hearing music in different environments
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Stringed instruments
The string family of musical instruments
includes the
 violin, viola, violoncello, double bass and all
their predecessors
 keyboard instruments use of strings, such as
the piano, harpsichord, clavichord and spinet
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 All stringed instruments consist of one or more strings
stretched between two points.
 The fundamental frequency produced by the string is
dependent on its mass per unit length, length and tension.
 The mass per unit length of an individual string is constant and
changes are made to the tension and/or length to enable
different notes to be played.
bridge
A.Diederich – International University Bremen – USC – MMM – Spring 2005
variable mass
 The string is set into vibration to provide the
sound source to the instrument.
 A vibrating string on its own is extremely quiet
because …?
 All practical stringed instruments have a body
which is set motion by the vibrations of the
string(s) of the instrument.
 The body of the instrument is the sound
modifier.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Three main methods by which energy is
provided to a stringed instrument:
 plucked (e.g., violin family, guitar lute)
 bowed (e.g., violin family)
 struck (e.g., piano)
(A vibrating string fixed at both ends has a
unique set of standing waves.)
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Sound modifiers in stringed
instruments
 The sound source provided by a plucked of
bowed string is coupled to the sound modifiers
of the instrument via a bridge.
 The vibrational properties of all elements of
the body of the instrument play a part in
determining the sound modification that takes
place.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Example: Violin family
 top plate ( the plate under the string which the
bridge stands on and which has the f holes)
 back plate
 the air contained within the main body of the
instrument
 Less:
 glues, varnish, choice of wood, wood
treatment
A.Diederich – International University Bremen – USC – MMM – Spring 2005
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Wind instruments
A.Diederich – International University Bremen – USC – MMM – Spring 2005
The main parts of flue (open metal and
stopped wood) and reed organ pipes
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Sound source in organ flue pipes
The important features
of a flue sound source
are a narrow slit (the
flue) through which air
flows, and a wedgeshaped obstacle placed
in the airstream from the
slit.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Sound modifiers in organ pipes
 The sound modifier in a flue organ pipe is the
main body of the pipe itself, or its "resonator".
 The most straightforward are resonators whose
dimensions do not vary along their length.
 Two basic types: open or stopped at the end
 The fundamental frequency of air reed
vibration is entirely controlled by:
 the length of the resonator
 whether the pipe is open or stopped
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Recorder and flute
 The length of the resonator is changed by
means of finger holes.
 To play a second octave the flue is overblown.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Brass instruments
The sound source in brass instruments is the vibrating
lips of the player in the mouthpiece
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 The basic valve combinations used on brass instruments to
enable seven semitones to be fingered.
 Black circle = valve depresses
 White circle = valve not depressed
 On a trumpet, first valve is nearest the mouthpiece, second in
the middle, and third nearest the bell
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Percussion instruments
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Sound source and sound modifiers
 The sound source in percussion instruments
usually involves some kind of striking.
(Impulse, all frequency components, nonperiodic)
 Three classes of percussion instruments, using
 bars (e.g., xylophone, glockenspiel, céleste,
triangle)
 membranes (e.g., drums)
 plates (e.g., cymbals)
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Two categories regarding pitch
 Those with a definite pitch, on which a
melody can be played.
 Those with an indefinite pitch, on which a
melody cannot be played.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Definite Pitch
Timpani
Celesta
Xylophone
Glockenspiel
Tubular Bells
Indefinite Pitch
Bass Drum
Side Drum
Cymbal
Gong
Triangle
Tambourine
Castanets
Wooden Block
A.Diederich – International University Bremen – USC – MMM – Spring 2005
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Student Project
A truly psychological question:
Musicians and instruments: Are there any
personality characteristics? or
Are trombone players different from
violinists?
A.Diederich – International University Bremen – USC – MMM – Spring 2005