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Guitars are extremely liked and well used instruments in the modern day. They have been loved in homes due to their ease of use and characteristic sound. This report will look at some of the main acoustical characteristics of three different guitars and try to understand how they truly differ from one another. This will be done using software to analyse a set of recordings made in a controlled environment. Such analyses will look at the brightnesses of chosen notes played on each guitar and onset detection algorithms. For the purpose of this report, a ukulele, mini acoustic piccolo guitar and a full sized acoustic guitar will be used to classify the three instruments in a way that shows clear differences between them.

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For the purposes of this report, three differently sized guitars were chosen. A full sized steel string guitar, a small steel string piccolo guitar and a nylon string ukulele. This was done so as to ensure a wide variety of tests and comparisons could be made and as to ensure that a wide variety from the guitar family had been tested, within our limits. All the guitars used had a figure 8 shape to them and were made of various wood. The piccolo guitar was an Ibanez EWP15LTD-OPN, made from mahogany and spruce. Mahogany is one of the hardest woods used in guitar making, and, when used for the back and sides, produces a very bright sound. It is also known for accented lows and clear highs (Schmitt, 2007). The material the ukulele was made from is unsure of, but would probably have been made from laminated wood or spruce as opposed to more expensive versions being made with mahogany. This would affect the sound the instrument makes drastically and so the tests will be more interesting.

In order to gain a clear idea of the sounds the chosen guitars made, a microphone with a flat frequency would work best, meaning that frequencies will not be attenuated and the resulting recordings will be as close to what it should be as possible. Room measurements will also be made, so a flat response microphone will work best in all of the tests. An ideal microphone for this would be the DPA 4090 or the Behringer ECM8000 (H. Robjohns, 2009) due to their responses, as is shown in fig 1 and 2.
As can be seen in Fig 1 and 2, the DPA clearly has a flatter frequency response than its counterpart and so for the purpose of this experiment, will be ideal. However, there is clearly some large smoothing applied to the curves in both of these images and so the accuracy may be lower than expected.

The 4090 was used in conjunction with an Audient iD14 and a Mackie top speaker to take room measurements using Room EQ Wizard(Fig 4 and 5). This allows for identifying possible issues with recordings such as null points in the room and overreactive room modes. The result of these readings are shown in Fig 3a and b. This is an average of 5 recordings, one in each of the four corners and one in the centre (Fig 4 and 5). The microphone was placed at about head height and the speaker was placed off axis in order to achieve clearer readings. 1/12 octave smoothing was applied on the resulting graph in order to get a clearer idea of the data.

There are some obvious disagreements between Fig 2 and 3a. The roll off below 80Hz in Fig 3a would be caused by the room modes, the result of sound reflecting off various room surfaces which are directly related to the dimensions of the room (GIK acoustics, 2009). Other differences can be explained by the equipment not properly being able to replicate the frequencies being measured. From this graph, it can be seen that there may be possible issues in the lower frequency register as there seems to be a large roll off. Judging by this graph, the Schroeder frequency of the room is around 90-100Hz, this denotes approximately the boundary between reverberant room behaviour and discrete room modes (S. Linkwitz, 2017), meaning that anything below about 100Hz is subject to the room modes and anything above is subject to the reverberation of the room.

For best results, an acoustically treated room would work best. Live room 2 and mix room 2 were used in this case as they were out of the way of the general traffic of the university, so as clear a recording as possible could be achieved. 

Two DPA 4090 microphones were set up 30cm and 60cm away from the sound hole of the first guitar (Fig 6), pointing at a slight angle into the hole. The microphones are omnidirectional so precise positioning doesn’t matter too much in this case. A static chair was used so as to avoid unwanted movement from the player so the experiment could be kept as fair as possible. The two microphones were then connected via XLR to an Audient ASP  4816 in a different room via a patch       
bay. The gain and volumes were all kept the same throughout the recording and there was no EQ added to the recordings to keep the sound as pure and controlled as possible. This was then sent to a Pro Tools session, with 2 tracks recording at 44.1KHz, 32 bit. The player was kept the same throughout all recordings and was encouraged to play equally over the 3 guitars. The microphones were adjusted with every guitar to ensure they kept the same distance of 30cm and 60cm apart(Fig 7-10). 

The player then played a scale of CEGABC twice, first allowing the notes to ring out fully, and then playing them in quick progression one after the other. A final recording was taken of a melody in order to be able to test ADSR (Attack, delay, sustain and release). This was done three times on each guitar for each of the members of the group to receive a unique copy. During analysis, it was noted that there were no discernible differences between the two microphone placements, and that analysis would be done on the 30cm microphone only.

All of the waveforms and spectrums for the recorded data can be seen in the Appendix. Keeping in mind the fact that the channel gains and microphone placements were kept the same throughout all recordings, there are some large deviances between the amplitudes of the waveforms from the same guitar. This can be caused by error on the players part, the acoustics of the room or the differences of the guitars.

The first test carried out was to determine how well the software (MATLAB, MirToolBox) can detect the onset of different notes. To do this, the onset curve was found, along with its attacks and releases(Fig 11d, e and f), and then the original waveform was segmented into these phases(Fig 11a, b and c). This was done to see whether any obvious differences between how sound leaves the instrument could be seen. Looking at fig 11a, it is clear that there is a lot more going on harmonically as there are more detected onsets in the waveform than in Fig 11b and 11c. This could be because the body is a lot larger than the others, and as the body serves to transmit the vibration of the bridge into vibration of the air around it, it needs to have a relatively large surface area so that it can push a reasonable amount of air backwards and forwards (J.Wolfe), therefore a larger body would have a clearer and more defined sound and would amplify the harmonics more, possible leading to the results in Fig 11a-f.

It could also be suggested that the mini guitar had the cleanest recording, or that that guitar sounded clearer overall because the onsets are far more accurate, however the hammer-ons aren’t counted as individual notes by the onset detector, so it isn’t as accurate as at first glance. It is worth noting here that the ASDR plots are not accurate in that they are very sensitive and have picked up on something other than the actual notes that were played. This could be the harmonics or background noise that wasn’t controlled. 

It is also worth mentioning that all six of the figures show the software recognising the final two notes played perfectly, with even Fig 11d and 11f recognising the hammer-ons in the melody that was recorded. Looking at Fig 11e, it jumps out as being the most accurate of the six graphs as almost all off the notes have been detected, with some exception, which is also the case in its segmented waveform, Fig 11b. The differences between the three guitars this test highlights are clear. They are all playing the same melody with relatively equal power and amplitude under the same test conditions, yet there are different results when the data is run through the same set of tests. This shows that the different guitars have different qualities to them, such as some being more articulate than the others or some producing a more accurate sound than others may, which could boil down to the different materials used.

The brightnesses of the three guitars were also tested in this experiment, utilising MirToolBox. For this, note 2 was again selected from the scale as it was the clearest overall throughout the recordings. The brightness test investigates the amount of harmonics involved in the recordings, the more harmonics that are in the recording, the higher the note sounds. Mir-brightness was used on the second note of the scale. This was done to see whether there would be any major differences between the three guitars and their registers.

Fig 12a and b are fairly similar, however there are minor differences between the two. The full sized guitar is much brighter as the note is played, but towards the end, the brightness levels off. This is shadowed by the mini guitar, but with a few differences. The note is not as bright as in the full sized guitar, but it does stay in the brighter register towards the end more than the full sized guitar does. 

The ukulele is vastly different however. It peaks much higher as the noise is played but drops rapidly to lower than any of the other two guitars did. Later on as the note dies out, it becomes more and more bright, peaking almost as high as the other two guitars’ first note. As this guitar has nylon strings, it will have a softer or sweeter sound, whereas the steel stringed guitars will have a louder and therefore more pronounced sound. “Because of the smaller body size and high pitch of the strings (compared with a guitar), ukuleles produce tones in the upper range – commonly called bright. You don’t get the kind of tonal resonance and depth you get with larger-bodied instruments. Many luthiers try to balance this by using woods that dampen the higher range a bit and offer more mid- to low-end tones.” – Ian Chadwick

The roughness curve shows the amount of sensory dissonance at each successive moment throughout the piece of music. This sensory dissonance corresponds to when several sounds are heard with nearly the same frequency, but with just a small difference. When roughness is high, the sounds feels more harsh, containing more strange oscillations (O. Lartillot, 2014). The full sized guitars original note has the highest value for ‘roughness’. This shows that there are more frequencies occurring at the same time, whereas the ukulele has the least amount. There could be a possible link between roughness and size of the guitar as there seems to be a correlation. The full size guitar also has more moments in its note where roughness increases, for example, directly after the original note is played, there is a ripple effect not seen in the other two guitars. There is a small ripple in the ukulele at around 7.4 seconds and at further points in the section. This doesn’t happen in the other two guitars. This is either due to multiple harmonics playing at similar frequencies or a problematic recording. This test clearly shows differences between the three guitars because they are all playing the same note, yet their brightnesses and spectral make ups are different. They all have the same shapes, but all have different values which show clear differences.

The fast Fourier transform is a computational tool which facilitates signal analysis by means of digital computers. It is a method for efficiently computing the discrete Fourier transform of a series of data samples (W.T Cochran et al,1967, Pg 1664 – 1674). The plots (in Audacity), are made using a Fast Fourier Transform, giving a value for each narrow band of frequencies that represents how much of those frequencies are present. All the values are then interpolated to create the graph (audacityteam.org). For this, note 2 was again selected, the note E in the scale that was recorded. This was imported in to Audacity and the spectrum was plotted. This shows harmonic makeup for all of the guitars and allows all of the frequencies and their respective value to be seen easily. The plots are shown in Fig 14a-c, and their harmonic data is shown in Table 1. As can be seen by Table 1, all of the three guitars follow the same harmonic path, with only a few Hz of difference. This also shows that the guitars’ notes are easy to recognise by software, as Audacity accurately determined that the note was E4 in all of the tests. Fig 14a-c depict the logarithmic scale of the FFT functions for all of the guitars. It can be seen in Fig 14a, depicting the full sized guitar, that its harmonics decay evenly, aside from the subharmonic between F1 and F2, which has a larger value than F1. This is a similar occurrence in Fig 14b where a subharmonic appears larger than F1 and F2. Fig 14b shows the frequencies get messier in the higher frequency region as there are no dominant frequencies that relate to any harmonics. This is similar with all three of the guitars. This may be because the frequencies involved in the harmonics don’t appear any stronger than any other 

frequencies. Fig 14c shows a much clearer image of the spectrum than 14a or b. This shows more dominant harmonics, only getting messy towards the F4. This test shows clear differences between the three instruments as, even though they are all playing the same note and all have similar harmonics, different harmonics are stronger in all of the three instruments and they all have fundamentally different harmonic make ups. It is easy to recognise that they are all in the same family of instruments, but there are some visual differences in the spectrums that shows that they are different to one another. The FFT function used here has many different parts to it. The size controls how many frequency divisions are used for the spectrum. In Spectrum, a larger size gives more accurate frequency resolution but averages the result over a longer period of time (audacityteam.org). The size was left at 1024 bins because this was accurate enough for the purposes of the report and it kept the data easy enough to read. The window was also kept as the Hanning window because it was the most suited to the needs of the report. All other windows give the same results, just display it differently (audacityteam.org).

The aim of this report was to classify three similar instruments in ways that would show clear differences between them, incorporating room acoustic measurements. Three different guitars were chosen; A full sized acoustic guitar, a small piccolo guitar and a ukulele. All were played by the same player and recorded in a controlled environment. Three different analyses were carried out on the resulting recordings, an onset detection, a harmonic spectrum analysis, and a fast Fourier transform. All of these tests show clear similarities between the three instruments. They all show roughly the same harmonics for the same notes. However, there are some differences between the three instruments, for example, the brightnesses and roughness was different over all three of the instruments, mainly coming down to their size and mechanical build, and also the physical properties of the instruments. The tests carried out may not have been an adequate way of properly classifying these instruments differently, but they have gone a way to make a start that could be built upon in future work.

There were issues in the recording stages of this report however, and so any future work would have to involve the re-recording of some data to ensure nothing was overlooked and possibly using more microphones in different places around the rooms. Related to this, other future work could involve analysing how sound propagates from each of the three guitars and how they differ to one another. It would also be interesting to see how more instruments from the guitar family differ to the three discusses in this report. For example a mandolin or a sitar could be an interesting addition to these results.