David da Silva

DIG4154 Acoustic Fundamentals UG1

Acoustic Fundamentals:
Introduction

The aim of this report is to detail the classification of three acoustically similar instruments using
various tests based on analytical recordings taken. In this report, I will be looking to:

Identify whether or not materials have an effect on an instrument’s timbre and dynamics.

Establish the effect that room modes have on the sound of the various instruments.

I will be conducting tests including: single note audio analysis in order to establish distinct

and individual differences between these acoustically similar instruments.

I will be using Mirtoolbox to conduct more advanced audio analysis such as:

spectral analysis of Individual notes

Testing the brightness of a note

Attempting to distinguish the differences in spectral centroid

Comparison of note harmonics

For my report, I have chosen to use two different types of guitars and a Mandolin

Instrument

For this report, the instruments of choice were the Harley Benton D-120BK, the Yamaha APX500
MKIII and a Mandolin. For starters, a distinct characteristic to note between the two guitars is the
fact that the Yamaha is an electro acoustic guitar. In regard to the Harley Benton D-120BK its back
and sides are made of Mahogany /Catalpa wood, whilst its neck is made of mahogany. Mahogany is
a wood that is most known for its durability and its attractive finish. The Yamaha on the other hand:
its back and sides are made of Nato/okume wood.

This particular electro acoustic guitar is best known for its non-scalloped X-type bracing which allows
the guitar’s top to sing and maximizes the resonance. Another distinct characteristic to note, is the
size of the two guitars. The Harley Benton in noticeably larger than the Yamaha although they both
have a scale of 650mm. With the nut width of the Harley Benton being 42.5 mm and the Yamaha
being 43mm. As well as this the Yamaha has a System 66 preamp.

In regard to the Mandolin it is believed to of come from the Mandolino and was first developed in
the mid 18th century. The mandolin varies on design but usually has 8 strings in pairs of two. The
most popular combination of metals used for mandolin strings is phosphor bronze.

Fig 1 Fig 2

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Fig 3
(Mandolin.Digital image.Strumenti Musicali.Web.11 January 2018.)

Testing Methodology

Before any data was collated and any recordings done I had to put in place a series of measures to
ensure that my test was deemed fair. In regard to a fair test: in all recordings and tests, the same
instruments were used and the recordings were conducted using the same rooms: Live room 2,
drum tank and mix 2. Furthermore, all instruments were played and recorded in the same position in
each of the rooms. This was in an attempt to cancel out any effects that room modes may have on
the recording. As well as this, I ensured that the same microphone was used for all recordings.
Following research on analytical recordings and microphones I found that: “Microphones differ in
the way in which they respond to different frequencies. They might boost a frequency or reduce it
depending on the purpose for which the microphone was designed” (Huff, 2010).

It was this that led me to my decision to seek a microphone which wouldn’t alter any frequencies:
“They might not alter the frequency at all, in which case the microphone has a flat response to that
frequency. A flat response microphone is one that is equally sensitive to all frequencies” (Huff,
2010).

The DPA4090 in my opinion was the best mic for this test. This is because when one is carrying out
an analytical recording of this nature, it is crucial that a microphone with a flat-unbiased frequency
range is used. This is because microphones with flat response frequencies essentially help to avoid
frequency boosting and attenuation (which is also known as the measure of the energy loss of sound
prorogation). Furthermore, the fact that the DPA4090 microphone has a linear frequency response
in the 2oHz to 20khz range means that it is able to capture all the frequencies within the human
hearing range. This can be illustrated below in the frequency response chart for the DPA4090:

(Typical on and off-axis response of a d:screetTM 4090 taken from DPA microphone website)

As well as this in order to ensure a fair test I ensured that the same skilled musician played both
guitars, whilst another trained musician played the mandolin.

David da Silva

Methodology

In regard to how I conducted my experiment I started by recording the three instruments in various
rooms, which I then measured and took room EQ sweeps. This was done in order to test the room
modes and to see how/whether or not it would have an effect on the sound of the instruments and
how they were perceived. I conducted my recordings by first collecting the instruments, once I had
decided on my sample. The recordings were taken in various rooms in millennium point: drum tank,
Mix 2, and live room 2. The equipment used to record the various instruments were as follows:

Mac book with Logic pro x

Audient ID14

DPA4090 (microphone)

XLR Male to female

Microphone stand
The equipment was set up as followed, which can also be seen below:

Set up mic stand to desired height, which in this case was intended to be aligned to the
middle of the instruments sound hole

Connect Microphone to cradle and then attach to stand.

Connect Audient ID14 to MacBook via USB

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4. Once connected, set up logic project file and set up recording track and begin to record

In regard to recordings: take a sample of scale C played on the various instruments and then
record a melody on each.

Then proceed to repeat this in the various rooms in order to develop a sample for analysis.

Once recordings are taken export files to ‘.wav’ format.

In terms of analysis I initially planned on using a Mat lab add-on Mirtoolbox’ Mir onsets function.
This was to help with the detection of successive notes within the C scale. However, from the
diagram below we can see that there is in fact room for error when using automated algorithm
systems for note detection. As we can see below the Mir onsets function has detected numerous
points within the c scale that are not actually there.

For this reason, I decided to Individually detect the notes/ sort them by chopping them up in
audacity and plotting a spectrum graph.

David da Silva

Results and Findings

I conducted the first test by taking the recordings I had obtained of the c scale played on the various
instruments, and comparing individual notes. I first started with the two guitars. Using audacity, I
was able to ‘chop up’ the individual notes which I then used to plot a spectrum analysis. The plot
spectrum feature in audacity enables one to convert a selected region of audio and takes the
selected audio (which is a set of sound pressures values at points in time) and converts it to a graph
of frequencies (the horizontal scale in Hz against amplitudes (the vertical scale in dB) (Audacity
Manual). Below is an example:

From the ‘Plot spectrum’ graph we can see that the fundamental frequency (the one with the
highest peak) is recognised as C4 at 266 Hz.

The figure above is another example of how I was able to acquire the notes for my sample, in this
case the fundamental frequency is G4 at 393Hz. Once I had done this for all the notes I wished to use
in my sample, I then exported the audio files as ‘.wav’ and began my analysis MATLAB.

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Mirspectrum

From the plot spectrum, I was able to compare the different fundamental frequencies of the notes
which in this case was D. The Yamaha played D at a frequency of 20.7 Hz while the Harley Benton
was -46.6 Hz.

After this I then proceeded to conduct further tests in MATLAB in order to delve deeper into the
reasoning behind the differences between these two instruments. Using MATLAB’s toolbox, Mir
toolbox I first used the ‘mirspectrum’ function. This function allows the user to display the
repartition of energy along the different frequencies. I decided to start this analysis with a different
note than the one above, in order to see if these differences in frequency were still prevalent. As we
can see from Fig 4 (Yamaha C note) and Fig 5(Harley Benton C note) whilst there are differences
between the notes such as: the Harley Benton having more of its lower frequencies bunched
together. Overall differences between the two are relatively small on first appearance.

Fig 4

Fig 5

My initial plan was to test each single note, by getting the spectral representation for each of the
notes and comparing them. However, on the scale of 10^4 very little difference could be shown
between notes. Although, once I lowered the frequency region of the spectrum to 2khz I was able to
see more of a difference which can be shown below.

Fig
7

Fig 6

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From fig 6 (Yamaha C note) and Fig 7 (Harley Benton C note) we can now see that both the Yamaha
and Harley Benton produce its strongest frequencies within the 0-200 Hz range, which would be
expected as when I compared the frequencies to a note frequency table C4 was registered at
261.6Hz. From the graphs, we can also see that the Yamaha’s C note (fig 6) generally produces
frequencies of a higher frequency with some reaching 800 Hz to even 1.3 kHz. Following my tests
with the two guitars I then decided to compare the same C note on the mandolin (fig 8), and my
observations are as follows:

Fig8

As we can see from the spectral analysis of the mandolin (fig 8), the mandolin has a much broader
frequency range than both the guitars. With its highest frequency reaching 2k Hz.

I decided to repeat this procedure below using the note G, below are the results: Fig 9 is the Harley
Benton. Fig 10 is the Yamaha. Fig 11 Is the mandolin.

Fig 9 Fig 10

Fig11

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Brightness

After comparing and analysing the spectral representations of the guitars and mandolin I then
decided to test the differences in brightness between the instruments. Brightness is concerned with
showing the evolution of brightness throughout the piece of music-high values usually indicate
moments in the music where most of the sound energy is on the high frequency register. Using
Mirtoolbox’ Mirbrightness I was able to analyse the individual notes and plot a graph which
illustrates the differences.

Fig 12

Fig 13

fig14

From Fig 12 and Fig13 we can see that the two guitars show clear differences. We can see from Fig
12 that at 0.2 S there is a sharp dip in brightness, while in Fig 13 shows a more gradual decrease in
brightness before finally hitting a dip at 0.3 S. These differences can be seen in a number of points:
0.6 S where we can see that in Fig 12 it appears to be the start of a gradual decline in brightness
while at Fig 13 at 0.6 S we can see that it is the bottom of a peak.

The Mandolin on the other hand gives a more peculiar data set. From Fig 14 we can see that the
mandolin has its highest amount of sound energy located on the high frequency register, this can be
shown by the fact we can see the mandolin fluctuates from a high brightness of 0.8 to as low as 0.2
in 0.33 S.

I decided in order to expand my sample/ scale of comparison I did the same for the G note.

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Mir centroid

In addition to plotting a brightness curve I decided to plot the spectral centroid curve which further
shows around which frequencies the sound energy is centred.

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Once again, we notice quite a distinct difference between the two guitars and the mandolin. With
the mandolin appearing to show a smooth decline.

The G note sample is below:

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Room modes

Room modes are resonance in a room. The frequency of the resonance is dependent on the shape
and characteristics of the room. There are three main types of room modes for room acoustics
which are: Axial, Tangential and oblique. It is usually the case that the Axial room modes are the
ones that researchers are usually most concerned with. This is because Axial Modes are the most
prominent and usually have the largest affect. As rooms have several surfaces room modes occur
between the width, height and length. “A room mode can cause both peaks and nulls (dips) in
frequency response. When two or more waves meet and are in phase with each other at a specific
frequency, you will have a peak in response. When they meet and are out of phase with each other,
they cancel and you end up with a dip or null in response” (Williams, 2009).

Below are pictures of one of the rooms (live room 2) I tested using the Room EQ sweep. Before I
began testing I took the dimensions of the room which include: width 2.41m, length 3.49m and
height 2.71m which I acquired with the intention of using it later in a programme called Amroc,
which is a room mode calculator.

As we can see from below the room is carpeted and the room is treated with various isolation pads.
As a result of this, one would presume that this would have some effect on the recordings. This can
be supported by the fact that: “Products that have absorptive properties include foam and rigid
mineral-wool, and they ‘soak up’ the sound energy, turning it into heat, through friction. Most
effective on high?frequencies, absorption is essential for reducing flutter echoes and for taming
bright?sounding or ‘ringy’ rooms” (Mayes-Wright, 2009).

David da Silva

David da Silva

Method

In regard to my method for testing the room modes, I first conducted a series of room sweeps in
various rooms around Millennium point using Room EQ Wizard (REW). Within the rooms, I tested
several points in order to obtain the ‘sweet spot’ which would be the spot where I would do my
recording.

REW is a free room acoustics analysis software for measuring and analysing room and loudspeaker
responses. “The audio analysis features of REW help you optimise the acoustics of your listening
room, studio or home theater and find the best locations for your speakers, subwoofers and
listening position.(https://www.roomeqwizard.com/). Which is why I thought that REW would be
the most appropriate programme to use.

This was

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done by:

Collecting equipment:

Pa Speaker
Audient ID14 (audio interface)
XLR to jack lead
Kettle lead (for speaker)
DPA4090 (microphone)
Microphone stand
XLR male to female

David da Silva
The room testing was done by:

Testing the rooms:

1. Open REW

2. Place speaker in a corner of the room.

3. Connect the kettle lead into the speaker and then plug into wall socket.

4. Set up microphone stand in chosen position of analysis, then screw in cradle, then place

microphone in holder.

5. Connect ID14 audio interface into your computer

6. Connect microphone into the ID14 via the XLR male to female lead

7. Then connect the speakers into to ID14 via XLR to Jack lead

8. Once connected set preferences in REW ensuring ID14 is selected in “output device”

9. Run sweep on your chosen spots of the room

Room EQ Wizard Results

Below we can see an example of results of one of the room Sweeps I conducted using REW. I
conducted a room sweep in 4 points of the room and applied 1/6 smoothing to the results. These
were the: middle of the room (Fig A), far left corner (Fig B), front left corner (Fig C) and front right
corner (Fig D).

Fig A

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(Fig B)

(Fig C)

(Fig D)

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From the figures above we can see the various differences across the tested room (live room 2).
Once I had acquired this data, I then compared the graphs to look for the spot of the room which
frequency deviated the least (Fig E), which would give me the ideal recording spot.

(Fig E)

I came to a conclusion that the middle of the room was the ideal spot for recording. Although I
would have to be mindful of where I recorded it. This is because From Fig A we can see that the
room struggles at certain frequencies. Which are due to the various modes, which are represented
by the dips and peaks in the graph. For example: from the graph, we can see that from 100Hz to
150Hz there is a 10dB drop and is followed by a dip. Although we can see that the modes have an
effect on the room and in turn, will affect the way we hear frequencies depending on where we are
in the room. We do not know where they are located nor the true extent of the effect on our
recording. For this reason, I used a room mode calculator called Amroc.

Amroc Room mode calculator

Amroc is a room mode calculator which allows the user to input the dimensions of the room being
tested, and see a visual representation of the room modes.

Below we can see examples of a visual representations of the tested room and how the modes are
spread out over a range of frequencies, represented by a notes on a piano. From this we can see
that as the frequency increases so does the mode density.

David da Silva

Reflection and Conclusion

In reflection, I was able to test most of my concepts. I was able to establish the difference room
modes have on a frequency by testing different rooms from different positions and seeing how given
frequencies respond.

Looking back, I would have wished to of changed:

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The number of recordings I took as I had to discard my earlier samples and re-record due
to inaccuracies within the recording.
The rooms I tested, this is due to the fact that many of the rooms I tested were similar in
the way they were acoustically treated. Which no doubt would have an effect on the
recording.

The way I recorded the notes. In that I wished that I would have recorded notes with the
same set time limit for each note.
Instruments used, as I would have wanted to of used another acoustic guitar rather than
an electro acoustic. This is for the simple fact that due to the Yamaha’s Installed pre-amp
and other electrical components, I was not able to fully distinguish whether or not the
differences were due to the difference in wood, body shape or the fact that the Yamaha
contains a 3 band EQ system.

The tests I conducted. While I have been able to establish valuable data, I would have
wanted to do a broader range of tests such as mapping to human auditory system using
MFCC analysis for example or even looking at the polar pattern

The musician. I would have preferred to of used the same skilled musician for the guitar
playing and the mandolin. This is because it would have helped to eliminate any individual
differences between the players, such as playing style and even the ‘Strength’ of the pluck.
Which may all of in turn had an effect on the recordings.

David da Silva

In conclusion, it can be said:

That differences between the two guitars are slight, but significant nonetheless. In regard

to the tests which showed the greatest difference between the guitars and the mandolin I

would say these were brightness and the spectral centroid.

In terms of the test which showed the least difference between the guitars I would say

this would have been the initial spectrum analysis.

David da Silva

Bibliography

https://www.roomeqwizard.com/
http://www.guitarcenter.com/Yamaha/APX500III-Thinline-Cutaway-Acoustic-Electric-Guitar.gc