Acoustics Harmonic Content Assignment Level 5

5/28/2018 Acoustics Harmonic Content Assignment Level 5

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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


the modern western

scale.

Actual frequency of thenote using the table


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


the modern western

scale.

Actual frequency of the

note using the table


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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Bb clarinet playing the note C.

Fundamental

frequencies

(Harmonics) in Hz.

Musical note

represented by the


the modern westernscale.




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


the modern western

scale.




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


the modern western

scale.




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


15

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.


16

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


the modern western

scale.




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


17

Snare drum (rim shot).

Fundamental

frequencies

(Harmonics) in Hz.

Musical note

represented by the


the modern westernscale.




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


the modern western

scale.




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.


18/

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


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.


20

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


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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Acoustics Harmonic Content Assignment Level 5

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