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BTEC Level 5 HND Diploma in Music (Production)
Acoustics Assignment 1
Scott Probert HND 2 A
28/12/85
138951
07/12/12
The objective of this assignment is to analyse the frequency
content and
harmonics of one note produced by a musical instrument. There is
no specified
instrument for this assignment although it must fall under the
Sachs Hornbostel
classification of either an aerophone or chordophone.
To evaluate the frequency response of the fundamental frequency
and its
harmonics fairly, three sustained notes will be recorded at
different pitches to
gain an insight into how the instruments harmonics change
relative to the
fundamental frequency at different pitches. The analysis of the
frequency
content will be carried out using a frequency analyser such as
the one found inSteinbergs Wavelab software that allows a detailed
picture of the frequencycontent to be taken and examined in
detail.
The conclusion to the analysis will be written up in a report
along with any
supporting evidence and handed in via Moodle by 3pm on the
7thDecember
2012.
For the purpose of this investigation three instruments will be
chosen to
compare the frequency content and see if there is a pattern to
the harmonic
content of the instruments. For the analysis to be fair, two of
the instruments
will be from the same classification of the Sachs Hornbostel
system and one
instrument will be an un-pitched instrument from a different
classification toanalyse if there is a pattern to its harmonic
content as is expected with pitched
instruments.
For the experiment to remain un-biased microphone choice will be
of upmost
importance. The microphones chosen should be able to capture the
sounds
created by the instruments in terms of frequency and have as
little influence on
the frequency content as possible. For these reasons the first
decision will be
choosing what instruments to record.
After referring to the Sachs Hornbostel classification system it
was decided
that the two instruments from the same classification would be
the flute and the
Bb clarinet. As they both fall under the same classification of
an aerophoneaccording to the Sachs Hornbostel classification system
but are made from
different material (the flute being metal based and the clarinet
being wood), and
produce a different range of frequencies. This should allow an
adequate
comparison to be made between the two instruments and also allow
the
candidate to see if the different structure of an instrument can
have an effect on
the frequency content and harmonics produced by an
instrument.
The third un-pitched instrument chosen was a snare drum as
according to Jon
Fox of the Singapore Symphony Orchestra the snare drum has an
indefinite
pitch (Fox. 2006). Also by choosing a snare drum, although being
un-pitched,will allow the player to produce three different sounds
using different playing
techniques (basic hit, rim shot and a basic hit without its
rattle attached). Thisshould in theory produce three different
tones and allow an insight into how its
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frequency content changes through different playing techniques
and allow
analysis to take place to decipher if there is a connection
between the harmonic
content of a pitched and un-pitched instrument through Fourier
analysis.
Sachs Hornbostel.
Created by Erich Moritz von Hornbostel and Curt Sachs the Sachs
Hornbostel
classification system was devised to categorise instruments into
groups
depending on how they produced sound. First published in
Zeitschrift furEthnologie in 1914 the system wasbased around four
main catergories ofinstruments, idiophones, membranophones,
chordophones and aerophones.
Idiophones are described as instruments that produce sound
through its
resonating body such as the cymbal, xylophone, marimba and glass
harmonica.
The sound created when any of these instruments are struck
causes the
instruments main body (the cymbal itself, the wooden bars of the
marimba) to
vibrate and disperse sound waves through the air.Membranophones
are instruments that produce their primary sound through
a tightly stretched membrane stretched over or between a body of
material. This
includes instruments like the snare drum, bass drum and
kettledrum where the
membrane is struck and the membrane vibrates causing the air
around it to
fluctuate and produce sound waves that travel through the
air.
Chordophones are catergorised as instruments that produce their
sound by a
vibrating string that has been stretched between two points.
Instruments such
as the violin, piano, harp and guitar fall into this category as
when struck, (either
by the finger in the case of the harp, or a wooden mallet in the
case of the piano)
the strings of the instrument vibrate the air around them to
produce the sound
waves heard by the listener.The category of aerophones includes
instruments such as the flute, clarinet
and recorder whose sounds are produced by a vibrating column of
air that is
usually forced through the instrument by the player, covering
different air holes
on the instrument can produce different notes and timbres.
Although these are the four main groups that the Sachs
Hornbostel system
uses for instrument classification there are several
subcategories for each group
that allow the system to become a little more precise.
Idiophones can be
subcategorized into directly struck idiophones such as the
cymbal andindirectly struck idiophones such as the ratchet or
maracas. Membranophones
can be subcategorised into friction membranophones like a drum
that is rubbedto produce sound and singing membranophones like the
kazoo. Chordophonescan be split into categories such as the simple
chordophone (piano), or
composite chordophone (guitar). Aerophones also has its own
subcategories
such as the non-free aerophone like a flute or the reed
aerophone like a
clarinet that uses a reed to help the air vibrate through the
instrument.
The timbre of the sound produced by the instruments in the Sachs
Hornbostel
system can altered by the material that the instrument is made
from and is the
reason why some instruments are more expensive than others. The
size of the
instrument can also change its sound and frequency output like
the difference in
size between the toms on a drum kit and the size and shape of a
bass clarinet and
Bb clarinet. Although they fall under the same classification of
directly struck
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idiophones and reed aerophones the size, material and shape of
the instrumentallows the them to be used to produce different tones
and frequencies.
Bb Clarinet.
The Bb clarinet is labeled as a soprano woodwind instrument that
falls under thereed aerophone category of the Sachs Hornbostel
classification system. The Bb
clarinet is one part of the clarinet family that also includes
the alto clarinet that is
one fourth lower in pitch range than the Bb clarinet and the
bass clarinet that is a
whole octave below the Bb clarinet. According to the Vienna
SymphonicLibrary the clarinet was introduced into the symphonic
orchestra during the
period of Vinesse classicism during the second half of the
18thcentury(Unknown. 2012). This made it one of the newest members
of the woodwind
instruments to be introduced into the orchestra and has quickly
established
itself as one of the most important instruments in the woodwind
section.
The clarinet generally produces quite a warm full sound when
played howeverwhen played using different techniques it can also
sound quite harsh and shrill
compared to the more mellow sound it is known for, this makes it
quite a
versatile instrument that can fit in many musical outfits from
an orchestra to a
marching band and for its wide range of notes through variations
of the
instrument (bass clarinet, alto clarinet and contrabass
clarinet) it has been
known that there are many clarinet only (Unknown. 2012)
orchestras based inthe USA (United States of America).
Most clarinets available are constructed from hardwoods such as
the mpingoAfrican Blackwood or the Honduran rosewoodnative to their
namesakes andare fitted with keyholes made from metal that are
usually nickel-plated.
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Flute.
The word flute comes from the Latin word flare which means to
flow (Miller.
2002). This is a simple explanation as to how the instrument
produces its sound.
The player provides the source power for the instrument through
blowing into
the lip plate which forces air through the column of the
instrument and out of thefinger holes. This, depending on which
finger holes are open causes air to
vibrate the air around the instrument at a certain frequency
creating the pitch of
the note heard by the listener.
The flute falls into the aerophone category of the Sachs
Hornbostel classification
system and belongs to the woodwind section of an orchestra,
although only the
piccolo flute is actually constructed from wood while the more
common concert
flute is made from a mixture of silver and nickel. The reason
for it belonging in
the woodwind section of an orchestra is mainly due to the fact
that its an
aerophone and has a light and airy sound similar to other
instruments in thewoodwind section. Often an airy breath can be
heard from the instrument
especially in soft passages that is provided by the player
providing the source
power that drives the instruments sound. This makes it easier to
record an
orchestra and not be overpowered by the other sections.
The flute is split into three main sections, the head joint,
middle joint (body)and the foot joint. All three sections of a
concert flute are constructed from thissilver nickel mixture and
being made from this material can leave the instrument
susceptible to the elements such as heat and humidity. High
temperatures and
humidity can make the instrument and keys swell and will change
the timbre of
the instrument and in some cases can even affect the pitch.
Being so
temperamental makes the instrument harder to control in certain
conditions andrequires special attention from the player to control
the sound of the instrument
to avoid any unwanted errors in pitch and consistency. The keys
on the flute are
made from the same material and are used to cover the air holes
to allow the
player and instrument to produce notes of different pitches.
Another main
component of the flute is the lip plate rested on an embouchure
that the player
blows into to provide the source power for the instrument.
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Originating in the Stone Age and regarded as the first ever
woodwindinstrument (Unknown. 2012), the flute has over gone many
changes over the
years. Originally used by the Sumerians who used bamboo flutes
with only fourholes gave it a very limited range. However years of
evolution means that todays
flute has a range of D4-D6 on the modern western scale making
the flute a
versatile instrument that is capable of producing different
fluctuating tones
(depending on the players experience of course).
The flute usually has quite a soft attack and decays to a
sustained level
depending on the source power provided by the player. It also
has quite a quick
but soft release as the flute isnt very long in length, as soon
as the source power
has ceased it doesnt take long for the air to empty out of the
instrument thatproduces the sound waves. However the attack of the
sound produced by the
flute can become quicker by elevating the embouchure to become
what is knownas a reform embouchure. This along with different
playing techniques allowsthe instrument to be played with different
styles such as legato, staccato and the
commonly known flutter style associated with the flute. Vibrato
can be addedto the sound by movement of the playerslips or small
movements of the
instrument, while the flutter technique is produced by special
tonguingtechniques.
Snare Drum.
The snare drum, sometimes referred to as the side drum,
whichcomes from its
use in the military where the drum was held at the side of the
player by a strap,is the smallest drum in a modern drum kit.
However military snares are usually
larger from having a thicker casing than the more common snare
drums found in
most musical genres. It falls into the category of a directly
struck
membranaphone in the Sachs Hornbostel classification system
because of the
way in which its sound is produced. The snare drum is a staple
in most musical
genres from jazz music to dance music and along with the bass
drum usually
keeps the timing of a musical piece to a predetermined tempo.
The snare drum
can also be found in the percussion section of most symphony
orchestras and is
described by the Vienna Symphonic Library as having no
definitive pitch
(Unknown. 2012). However even though it has no definitive pitch
and is knownfor producing a sound that occupies the treble (higher)
range of the frequency
spectrum, it can be tuned to produce a different sound that
changes its presence
in the frequency spectrum and allows the instrument to fit more
suitable with
other instruments in musical pieces.
Formed in the middle ages and referred to as a frame drum
(perhaps as adescription of its construction), it was later given
the Latin name tympanum
and why it is associated with the timpani section of an
orchestra.
Constructed mainly of wood or metal with only plastic being used
in the
construction of cheaper models, the timbre of the instrument can
be affected by
the type of wood or metal used as its resonating body. The snare
drum often hasa sharp abrasive sound and gets its distinctive sound
from the wire rattle
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otherwise known as the snare that is attached to the underside
of the drum andvibrates against the bottom skin of the drum when
struck. The skin of the
instrument is the part that is directly struck and is usually
made from calfskin or
plastic and struck with a wooden stick, wire brush or timpani
stick. Usually the
snare drum is known for its sharp attack and fairly long release
that can be
shortened by tightening the wire rattle and using different
playing techniques.
The character of the sound can be changed by using playing
techniques like the
stroke, often used when playing with a wire brush. A rim-shot is
used to
reduce the amount of snare rattle and produce a sharper attack
with ashorter
release and is achieved by striking the edge of the metal frame
that holds the
construction of the snare drum together. Another popular
technique used when
playing the snare drum is the grace note that involves a softer
strike of thedrum before the main strike that adds movement and
rhythm to a drum pattern.
These different playing techniques and construction materials
allow the snare
drum to become more versatile when used in different styles of
music and why
modern snare drums can range from 50 - 5000 to buy and why many
people
consider it to be the most important percussion instrument
available.
Constructing a fair test.
The next task was to decide which microphones to use to record
the three
instruments. As the test would need to be kept as neutral as
possible, the samethree microphones should be used to record all
three instruments while catering
to the characteristics of the instruments frequencies. The first
microphone
chosen was the Studio Projects C3 condenser microphone as it has
a frequencyresponse of 30Hz-20,000Hz which was more than adequate
to capture the subtle
vibrations produced by sound waves travelling through the finger
holes of the
clarinet and the flute while also being able to handle the
higher SPLs (soundpressure levels) produced by striking the snare
drum.
The next microphone chosen was the Sennheiser E604dynamic
microphone.
Having a frequency response of 40Hz-18,00Hz would allow the
sound produced
through the clarinets bell to be captured while also being able
to capture the
lower frequencies produced by a flute for comparison and again
will be able tohandle the high SPLs produced by the snare drum.
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The last microphone chosen was the Behringer ECM8000
condensermicrophone which according to the manufacturers website
has a flat frequencyresponse from 15Hz to 20kHz (Unknown. 2011).
This would be a perfect
microphone for comparing the three instruments harmonic content
as it
shouldnt enhance any frequencies produced by the instruments and
form a solid
base for Fourier analysis. However from looking at the frequency
response chartprovided on the box of the microphone, several small
peaks of up to 3dB can be
seen at around 80-100Hz, 450Hz, 1500Hz, 4kHz, 10kHz and
18-20kHz. This will
have to be taken into account when using Fourier analysis to
analyse the
frequency content of the instruments but shouldnt cause too much
trouble asthe same effects that the microphone has on the frequency
content will be placed
on all three instruments and will still allow an adequate
comparison to be made.
Although the three microphones chosen may not be the ideal
choice for the
recording each instrument, using these three microphones will
produce a much
fairer experiment and allow the conclusions made from the
Fourier analysis to
represent a fair experiment unbiased to any one instrument.If
recording these instruments in a normal recording environment for
musicalreproduction and general distribution, different microphones
would be used to
allow a more musical recording to be made and possibly even
enhance the
frequencies produced to produce a recording that is more
pleasing to the ears. A
closely placed Shure SM57 dynamic microphone would probably be
used torecord the snare drum while a large diaphragm condenser
microphone such as
an AKG C414XLS placed around one foot away from the finger holes
could beused to mic the clarinet and the flute (separately) in
order to capture a more
aesthetically pleasing sound for listening. However this
experiment is based on
recording three sustained notes at three different pitches and
analyzing their
frequency content so a nice sounding musical recording is not
necessary.Instead a fair equal recording of the three instruments
is the key to a fair
analysis, and by using the same three microphones placed at the
same distance
away from the sound source at the same angle will result in a
fair experiment
with more accurate results.
Fourier analysis.
French mathematician and physicist Jean Baptiste Joseph Fourier
determined
that any periodic motion, nomatter how complex, could be broken
down into
its harmonic components (Reid. 1999). This procedure was given
the nameFourier analysis and allowed people to understand that no
matter how complex
a waveform, it is always made up of simply sine waves, known as
partials, each of
different pitches, phase and amplitudes. Of course different
pitches equal
different frequencies, and different frequencies complete one
full wave cycle
over a different time period. For example, here is a picture of
two different
pitched sine waves, and for the purpose of this example imagine
that the two
waves have an x axis representing time, and the x axis for both
sine waves
represents the same amount of time.
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So from the example we can determine that the second wave
completes more full
cycles in the same amount of time as the first wave, and knowing
that the faster
the cycles the higher the pitch (and frequency) we now know that
adding the two
sine waves together would alter the resulting wave producing a
more complex
waveform as they are affecting each other. As the two waves are
completing
their cycles at different times, we can see that the peaks and
troughs of the
waves will not line up, so the waveform produced will not be a
simple case of
additive synthesis where the pitch of the wave form would stay
the same but theamplitude would simply double increasing its
perceived loudness. Instead the
two differently pitched sine waves would affect each other when
played
simultaneously and would create a much more complex waveform.
Having
different amplitudes would also affect the waveform and
represent a closer
relationship to how real instruments produce their sound and
timbre and would
appear to look like this:
As can be seen from the image above, the constructed waveform
appears to be a
lot more complex than simply adding two sine waves with the same
pitch
together. The key to these complex waveforms is time. The time
in which the
added waveforms perform their cycles relate to the pitch of the
sound waves and
by adding them together the sound produced is not simply the two
pitches of the
two waves but is a complex wave of various pitches and this
where the
harmonics of a waveform are produced. These are what are known
as Fourier
series coefficients.
So as you can see from the image above you can see that a
complex noise such
as the sound of an exhaust (which the image represents), when
analysed using
the algorithm fast Fourier transform (FFT) can be broken down
into itscomponents which show a complex repeating waveform over
small increments
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of time usually shown in milliseconds. Although most tuned
instruments like
flutes and clarinets produce these repeating waveforms that form
the periodic
tones that we recognise, some un-pitched instruments such as
cymbals and
drums produce non periodic tones or noises that dont conform to
the Fouriertheory of repeating waveforms.
Real sounds also arent perfect sinewaves, and any distortion of
a sinewave
results in the production of a harmonic series (Corben. 2011).
The harmonicseries of a sound are known as the sounds harmonics and
have a direct
relationship to the sounds fundamental frequency (the lowest
frequency of a
sound). According to the world of physics the additional
harmonics of a sound
are exact multiples of the first harmonic (the fundamental
frequency). So if thefundamental frequency were 1Hz the frequency
of the second harmonic would
be 2Hz, the third harmonic would be 3Hz, the fourth 4Hz, and so
on (Unknown.2012). So from this theory it should be relatively easy
to find the harmonic
series of a musical note, so long as we can determine the
fundamental frequency.However as musical instruments have many
factors that affect their sound
production, like construction material, shape, humidity,
temperature and source
power (fingering, tonguing, plucking techniques and even how
hard you blow)
when providing the power source for an instruments sound
production, the
overall harmonics of a sound can vary and not collate to the
theory behind the
mathematical equation for a harmonic series.
According to the University of New South Wales in Sydney
Australia the
seventh and eleventh harmonics of a stringed instrument actually
fall halfway
between notes on the equal tempered scale (Wolfe. 2005). This
means that the
frequency of these harmonics dont correspond with the frequency
of any notes
on the modern western musical scale. Instead these two harmonic
frequenciesfall in between two notes on the modern western scale
and so we have no actual
way of communicating the pitch of these frequencies in terms of
a musical scale
and no way of producing these notes frequencies by themselves on
a traditional
instrument. They could be created in the digital world using a
sine wave
generator and maybe a parametric EQ (equaliser), but these
harmonics do not
represent a musical pitch that we recognise as a musical
interval. This makes an
instruments harmonic content even more complex and is what gives
an
instrument its own individual sound, as if each different
instrument had the
same harmonic series for each note than each instrument would
sound the same.
So for this reason fast Fourier transform will be used to
analyse the frequencycontent and harmonic series of the three
instruments used for this assignment.
This will be achieved by using the FFT analyser provided in
Steinbergs
Wavelab software and will allow an insight into whether the
harmonic series ofa real instrument does stick to the theory that
each harmonic will be a multiple
of the fundamental, or whether the results will show that there
is no relationship
between the theory and fact. Along with this, analysis will also
show if there is a
connection between the different instruments and their harmonic
series.
The FFT analyser provided with Steinbergs Wavelab software
provides asnapshot of a sounds frequency content at any given time
during a sound wave.
It also features a camera button that allows the user to take a
screenshot of thefrequency analysis provided by the FFT analyser.
While the imported sound
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wave is shown as a whole wave by its length and how long the
sound wave lasts
over time in a linear manner. The FFT analyser simply provides a
snapshot ofthe sound waves frequency content at any given point in
time during the sound
waves linear movement. This will need to be taken into account
when analyzing
the sound waves of the chosen instruments as in order to perform
an accurate
analysis of the frequency content of the sound a snapshot will
need to be takenduring the sounds repeating waveform during the
sounds sustain period rather
than during the instruments attack, decay or release stages
where the sound, and
its frequency content may be affected by the power source of the
instrument (the
player).
The peaks in the frequency analysis will be examined using the
FFT analyser
that also gives the user the actual frequency that the peak is
present in. This is
achieved by simply holding the cursor of the mouse over the peak
of the
frequency snapshot. This process will be continued for the first
seven harmonics
provided by the FFT snapshot and will be determined by the size
of the peak as
the frequency spectrum is discrete, and only defined at the
harmonicfrequencies (Smith. 2011). This means that although there
will be small peaksand troughs in-between the main harmonic
frequency peaks, that the
frequencies between the harmonics can be thought of as having a
value of zero,
or simply not existing (Smith. 2011). This applies only when
analysing the
harmonics of a sound as these extra frequencies obviously
contribute to the
overall sound and timbre of the instrument. So although they may
not be very
important when analyzing the harmonic content of a sound, they
are still integral
to an instruments sound production.
Analysing the sounds.
A table showing the frequency of each note in the modern western
scale will be
used as a reference for the FFT analysis of the chosen three
instruments and can
be found
herehttp://www.phy.mtu.edu/~suits/notefreqs.htmlprovided by the
Michigan technology website.
The first instrument that will be analysed using the FFT
analyser will be theFlute playing a C note. This first FFT snapshot
is from the repeating wave of the
flute recorded using the Studio Projects C3 condenser
microphone.
FFT snapshot of the note C played on a flute and recorded using
a Studio Projects C3 microphone.
http://www.phy.mtu.edu/~suits/notefreqs.htmlhttp://www.phy.mtu.edu/~suits/notefreqs.htmlhttp://www.phy.mtu.edu/~suits/notefreqs.htmlhttp://www.phy.mtu.edu/~suits/notefreqs.html
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As can be seen from the screenshot of the snapshot of the FFT
analyser thereare many frequencies present in the frequency content
of a repeating waveform
of one note produced by the flute. For the purpose of this
assignment the
frequencies of the first seven harmonics will be written into a
table similar the
table used as a reference from the Michigan technology website.
This will allow
a direct comparison to the harmonics found in the FFT analysis
to thefrequencies of the notes provided by the Michigan technology
website to be
made and assessed to analyse any anomalies found in the theory
of the
instruments harmonic content. However as found out earlier,
although all sound
waves can be deconstructed using Fourier analysis to be seen to
be made up of
simple sine waves, real instruments consist of more complex
waveforms and
may not produce harmonics that can be compared to notes found in
the modern
western scale. For this reason the musical note that is
represented by the
harmonics will be taken by finding the closest frequency of the
note represented
by the modern western scale found in the table provided by the
Michigan
technology website.
FFT snapshot of a C note played on a flute and recorded using a
Behringer ECM8000 microphone.
Flute playing the note C.
Fundamentalfrequencies
(Harmonics) in Hz.
Musical noterepresented by the
frequency found using
the modern western
scale.
Actual frequency of thenote using the table
found on the Michigan
technology website.
256.1 C4 261.63
516.0 C5 523.25
796.7 G5 783.99
1054.3 C6 1046.50
1337.9 E6 1318.51
1594.0 G6 1567.981846.6 Bb6 1864.66
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Recording the same sound source with three different microphones
was a way of
constructing a fair test and allowed analysis of how different
microphones could
affect the results found. However as can be seen from the
screenshots of the
different microphones used, it is clear to see that although the
microphones can
affect the overall sound of the instrument by attenuating and
boosting certainparts of the frequency spectrum. It is obvious that
the choice of microphones
doesnt affect the fundamental frequencies, except for maybe a
slight gain orreduction in amplitude. So for this reason for the
rest of this investigation the
only microphone that will be used for analysis will be the
Behringer ECM8000condenser microphone as this seems to have the
smallest effect on the overall
frequency spectrum of all the microphones used.
Flute playing the note D.
Fundamentalfrequencies
(Harmonics) in Hz.
Musical noterepresented by the
frequency found using
the modern western
scale.
Actual frequency of thenote using the table
found on the Michigan
technology website.
602.0 D5 587.33
1204.0 D6 1174.66
1808.2 A6 1760.00
2409.8 D7 2349.32
2994.3 Gb7 2959.96
3617.8 A7 3520.00
4191.2 C8 4186.01
Flute playing the note G.
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern western
scale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
387.2 G4 392.00
796.7 G5 783.991196.0 D6 1174.66
1594.0 G6 1567.98
1980.6 B6 1975.53
2376.3 D7 2349.32
2772.3 F7 2793.83
After comparing the three tables showing the results for the
flute instrument and
using the modern western musical scale to determine the
difference between the
harmonics, it is clear to see that there is a very solid pattern
shared for all three
notes played.
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Analysing the difference between the harmonic series
sequentially, the
findings share the same difference between the different
fundamentals all the
way up to the sixth fundamental. However the seventh fundamental
for each
note does not share the same pattern and seems at this point to
be completely
random. The table below shows the pattern that occurs between
each notes
fundamental frequencies (with exception to the seventh) and will
allow furtheranalysis into why or how these patterns occur.
Table showing the musical difference between the fundamental
frequencies.
Fundamental. C
note.
Difference
from
previous
note.
D
note.
Difference
from
previous
note.
G
note.
Difference
from
previous
note.
1st C4 D5 G42nd C5 1 octave D6 1 octave G5 1 octave
3rd G5 3 tones 1
semitone
A6 3 tones 1
semitone
D6 3 tones 1
semitone
4th C6 2 tones 1
semitone
D7 2 tones 1
semitone
G6 2 tones 1
semitone
5th E6 2 tones Gb7 2 tones B6 2 tones
6th G6 1 tone 1
semitone
A7 1 tone 1
semitone
D7 1 tone 1
semitone
7th Bb6 1 tone 1
semitone
C8 3 tones F7 1 tone 1
semitone
As can be seen from the table above, the first six fundamentals
of the three notes
played on the flute share the same difference in musical tone.
This could
attribute to the timbre of a note played by the instrument and
may explain why
the note sounds pleasing to the listener. It doesnt have any
fundamental
frequencies that fall in between notes from the modern western
scale, and that
means that they are notes that are recognisable to the modern
western listener.
It could be said that when producing a single note from an
instrument the fact
that there are other frequencies present at the same time that
represent other
notes from the modern western musical scale, that this is a
fault and that the
only frequency that should be present when playing one note is
that notesfrequency. However as 1stfundamental frequency is the
most prominent
frequency with the highest amplitude, the other fundamentals
simply provide
harmony for the note and as their amplitudes are lower it isnt
the same as just
playing several notes together. Even using synthesis and
layering several sine
waves together at these fundamental frequencies wouldnt produce
the samesound as when the note is played by a flute. Obviously by
changing the
amplitude of each sine wave to replicate the fundamentals of the
flute note may
produce a closer emulation of a flute but other factors such as
the instruments
construction, playing techniques and the subtle frequency
content found
between the fundamental frequencies all contribute to the sound
and timbre of
the instrument making the instrument sound unique and providing
it with its
place in the musical world.
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
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Bb clarinet playing the note C.
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern westernscale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
257.9 C4 261.63
516.0 C5 523.25
796.7 G5 783.99
1054.3 C6 1046.50
1310.0 E6 1318.51
1571.8 G6 1567.98
1846.6 Bb6 1864.66
Bb clarinet playing the note D.
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern western
scale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
523.3 C5 523.25
1061.7 C6 1046.50
1594.0 G6 1567.98
2094.8 C7 2093.002639.6 E7 2637.02
3166.9 G7 3135.96
3720.6 Bb7 3729.31
Bb clarinet playing the note G.
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern western
scale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
346.1 F4 349.23
712.2 F5 698.46
1054.3 C6 1046.50
1424.9 F6 1396.91
1783.0 A6 1760.00
2139.2 C7 2093.00
2478.3 Eb7 2489.02
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As can be seen from the tables above the clarinet notes were not
as would be
expected after analysing the results from the flute. After some
research into why
this may have happened it appears that the Bb clarinet has a
different
transposition for its notes when using the modern western music
scale. The Bb
clarinet is in the key of B flat. If you play the pitch C on
your clarinet, it will
register as a B flat on your tuner (Coughlin. 2009). For this
reason all the noteswritten for a clarinet are actually a whole
tone lower than what is actually
written. This means that C note analysed was actually the note
of D on the
clarinet, the D note analysed had the fundamental frequency of a
C note and the
G note played by the clarinet actually had the frequency of a F
note. This actually
jeopardises the fairness of the test as the fundamental
frequencies of the notes
will not have the same frequencies and will therefore not allow
a comparison
between the patterns produced within the harmonic series.
Fundamental. C
note.
Difference
fromprevious
note.
D
note.
Difference
fromprevious
note.
G
note.
Difference
fromprevious
note.
1st C4 C5 F4
2nd C5 1 octave C6 1 octave F5 1 octave
3rd G5 3 tones 1
semitone
G6 3 tones 1
semitone
C6 3 tones 1
semitone
4th C6 2 tones 1
semitone
C7 2 tones 1
semitone
F6 2 tones 1
semitone
5th E6 2 tones E7 2 tones A6 2 tones
6th G6 1 tone 1
semitone
G7 1 tone 1
semitone
C7 1 tone 1
semitone
7th Bb6 1 tone 1
semitone
Bb7 3 tones Eb7 1 tone 1
semitone
After analysing the fundamental frequencies and the patterns
between the
frequencies when represented by their individual musical notes,
it is clear that
although the instruments are playing different notes in terms of
pitch, they have
the same patterns in terms of difference between their
fundamental frequencies.
This means that even though the test wasnt as fair as was
initially intended, thefact that different notes of different
pitches also show a pattern in the harmonic
series that it actually further solidifies the results found
when analysing the fluteand its fundamental frequencies. However
unlike the flute there also seems to
be a pattern when reaching the seventh fundamental, in that they
all have a
difference of 1 tone and 1 semitone from the previous note. But,
as the test is
flawed due to the transposition of the Bb clarinet which caused
the two first
notes to be the same note (C) only an octave different. The fact
that the seventh
fundamentals of each note are the same can only seen as
coincidence and not
taken as a given due to other notes seventh fundamentals not
being tested and
could be different. We can say however that the clarinets
fundamental
frequencies contain the same fundamentals as the flutes when a C
note is played.
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
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FFT snapshot of a C note played on a Bb clarinet recorded with
the Behringer ECM8000
microphone.
This shows a pattern between the two instruments when playing
the same note
however as can be seen from the FFT snapshot the frequency
content inbetween the fundamentals have slight differences and the
amplitudes of the
fundamentals themselves are also different. This is an expected
result as from
earlier research performed explained that if the frequency
content of both
instruments playing the same note were exactly the same then
both would soundexactly the same, but due to their different
construction and playing methods
they both produce different timbres unique to the individual
instrument.
Snare drum (standard hit).
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern western
scale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
128.0 C3 130.81
194.9 G3 196.00
371.2 Gb4 369.99
474.4 Bb4 466.16
712.2 F5 698.46
842.6 Ab5 830.61
998.0 B5 987.77
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
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Snare drum (rim shot).
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern westernscale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
128.0 C3 130.81
194.9 G3 196.00
282.5 Db4 277.18
366.1 Gb4 369.99
516.0 C5 523.25
602.0 D5 587.33
687.7 F5 698.46
Snare drum (held snare).
Fundamental
frequencies
(Harmonics) in Hz.
Musical note
represented by the
frequency found using
the modern western
scale.
Actual frequency of the
note using the table
found on the Michigan
technology website.
193.5 G3 196.00
300.9 D4 293.66
363.5 Gb4 369.99
451.7 A4 440.00593.6 D5 587.33
682.9 F5 698.46
774.6 G5 783.99
From looking at the tables above of the different playing
techniques of a snare
drum it is clear that the patterns found in in the harmonic
content of the flute
and the Bb clarinet do not apply with the harmonic series found
with the snare
drum. This could be due to the snare drum not being a pitched
instrument, but
further analysis will need to be performed to obtain a more
comprehensive
conclusion for the harmonic series of the snare drum.
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
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Fundamental. Snare
drum
(Standard
hit).
Difference
from
previous
note.
Snare
drum
(Rim
shot).
Difference
from
previous
note.
Snare
drum
(Held
snare).
Difference
from
previous
note.
1st C3 C3 G3
2nd G3 3 tones 1semitone
G3 3 tones 1semitone
D4 3 tones 1semitone
3rd Gb4 5 tones 1
semitone
Db4 3 tones Gb4 2 tones
4th Bb4 2 tones Gb4 2 tones 1
semitone
A4 1 tones 1
semitone
5th F5 3 tones 1
semitone
C5 3 tones D5 2 tones 1
semitone
6th Ab5 1 tone 1
semitone
D5 1 tone F5 1 tone 1
semitone
7th B5 1 tone 1semitone
F5 1 tone 1semitone
G5 1 tone
From analysing the results found in the table above it is clear
to see that the
patterns of the fundamentals in the harmonic series of the
different playing
techniques of the snare drum dont follow the same pattern as the
flute and theBb clarinet. In fact the only pattern that appears
between the three different
playing techniques of the snare drum are between the first and
second
fundamentals and show that they are all 1 tone and 1 semitone
apart. The rest of
the fundamentals show no pattern when compared to the other
instruments or
the different playing techniques used when striking the drum.
This could simply
be because the snare drum is known as having no definitive pitch
(Unknown.2012). This means that although snare drums can be tuned
by changing the
tension of the skin of the snare, it does not produce a
definitive note that can be
found using the modern western music scale.
FFT snapshot of a snare drum being struck (standard hit) and
recorded using a Behringer
ECM8000 microphone.
From looking at the FFT snapshot of the snare drum it is clear
why the results
turned out the way that they did. The fundamentals of the snare
drum are
clearly not as prominent as they are with the flute and the Bb
clarinet and it ishard to distinguish the difference between the
fundamentals and the rest of the
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
19
frequency content. This means that this could be the cause of
the snare drum
appearing to sound more like a burst of noise rather than a note
of definitive
pitch with a musical harmonic series, as was the case with the
flute and the Bb
clarinet. However as can be seen from the FFT snapshot there is
stillfundamental frequencies especially the first, there is no
frequency content lower
than the first fundamental which means that although it doesnt
follow thepattern of pitched instrument in terms of harmonics,
there is still some form of
pitch in terms of a fundamental frequency. This is due to the
tension of the skin
and the resonating chamber (body) of the instrument and means
that by
changing the body of the instrument and the tension of the skin
that a different
fundamental frequency can be produced. This is why there are so
many different
snare drums available to consumers and why different snare drums
appear to
work better with different types of music. Obviously it is up to
the player to
decide which snare drum to buy but it actually has the advantage
being able to
work with other instruments in a way that pitched instruments
cannot. A snare
drum can be played with any pitched instrument playing any note
in the modernwestern scale and due to the fact that it has no
definitive harmonic series, it can
gel with them without having to play in the same key as its
accompanying
instruments.
Evaluation.
Although from analysing the results of the investigation it has
been determined
that there is a pattern in the fundamental frequencies of
different instruments
and that they produce a musically pleasing sound for the
listener. The
experiment shows from the experiment with the snare drum that
this pattern
doesnt apply to all instruments found in the Sachs Hornbostel
classificationsystem. Also as only three notes were chosen for
analysis and two of the Bb
clarinet notes were transposed differently, it cannot be said
definitively that the
same pattern would occur in all the different pitched
instruments found in the
Sachs Hornbostel classification system. Nor can it be determined
that the same
pattern would apply to all the different notes in the modern
western music scale
as only three were tested. So to get a more precise
understanding of the
harmonic series of instruments, more instruments would need to
be analysed as
well as more notes and more un-pitched instruments.
The experiment was also flawed in other ways as the microphone
used for
analysis was the Behringer ECM8000 condenser microphone, and
although themicrophone is described by Behringer as having a
ruler-flat frequency
response (Behringer. 2011), it is clear to see from the
frequency response
diagram provided by Behringerthat the microphone does have small
peaks andtroughs in certain areas of the frequency spectrum.
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
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Frequency response chart for the Behringer ECM800 condenser
microphone.
This, although it should only affect the amplitude of the
frequencies, proves that
the microphone is not actually a flat frequency microphone as
described byBehringer.
Not only was the experiment flawed by the limited testing of the
instruments
and influential microphone, it was also flawed by the FFT
analysis software notbeing as accurate as it could be. With a
larger screen for analysis and a more
detailed image of the frequency content, a more accurate
analysis could be
performed. This, along with the different materials and
construction techniques
used when creating instruments could affect the results and
produce a differentoutcome. As it has been found from the research
conducted that the quality of
the material used can affect the instruments timbre and is what
affects their
pricing, it can only be assumed that this could also have
affected the results
found. Perhaps if a higher quality flute or clarinet was used
than the
fundamental frequencies found would not have fallen between the
pitches
frequencies on a note that doesnt correspond with a pitched note
found in the
modern western scale.
However despite these flaws the fundamental frequencies found in
the
instruments notes all fell very close to the frequencies of
notes found in the
modern western scale and allowed comparisons to be made as
fairly as possible.
The difference in the frequencies of the fundamentals were so
close to the
frequencies of notes found in the modern western scale that the
difference
would only be detected by FFT analysis and they would be
extremely difficult todetect by even the most distinguished music
listener. So we can conclude that
the patterns found in the fundamentals are close enough to use
as evidence for a
harmonic series and that the results show a very musical pattern
that may
explain why pitched instruments sound pleasing to listeners.
As the results show that all the fundamentals of a single note
contain
frequencies that correspond with the major triad of the
fundamental frequency
(for the chord of C the notes used are C, E and G), it is easy
to see why the notesof a pitched instrument work well with other
instruments and are capable of
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5/28/2018 Acoustics Harmonic Content Assignment Level 5
21
producing a very musically rich and pleasing melody. This is
proven with all the
instruments and notes used, except the un-pitched snare drum.
The major triad
of a D chord is D, Gb and A and the major triad of a G chord
contain the notes G, B
and D. This shows a very musical connection between the
frequency content of a
single note and the notes used in a major chord scale and from
this we can
predict that the fundamental frequencies of other notes that
were not testedwould follow the same pattern. So an E note played
on a pitched instrument
should contain fundamental frequencies that correspond to the
notes E, Ab and B
and an A note should contain frequencies that correspond to the
notes A, Db and
E. This would obviously need to be tested and confirmed with
another
experiment and would allow the flaws from this experiment to be
reassessed and
catered for to create more accurate results that could be used
in academic
studies.
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