David repartition of energy along the different frequencies.

David da SilvaMirspectrumFrom 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 4Fig 5My 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 6David da SilvaFrom 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:Fig8As 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 10Fig11    David da SilvaBrightnessAfter 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 12Fig 13 fig14From 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. David da Silva  Mir centroidIn 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.  David da Silva  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:   David da SilvaRoom modesRoom 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 SilvaMethodIn 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• • • • • • • •done by:Collecting equipment:Pa SpeakerAudient ID14 (audio interface) XLR to jack leadKettle lead (for speaker) DPA4090 (microphone) Microphone standXLR male to female  David da SilvaThe 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 placemicrophone 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 roomRoom EQ Wizard ResultsBelow 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 ADavid da Silva (Fig B) (Fig C) (Fig D)David da SilvaFrom 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 calculatorAmroc 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 ConclusionIn 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: • •• •• •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 patternThe 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 SilvaIn conclusion, it can be said:• That differences between the two guitars are slight, but significant nonetheless. In regardto the tests which showed the greatest difference between the guitars and the mandolin Iwould say these were brightness and the spectral centroid.• In terms of the test which showed the least difference between the guitars I would saythis would have been the initial spectrum analysis.David da SilvaBibliographyhttps://www.roomeqwizard.com/ http://www.guitarcenter.com/Yamaha/APX500III-Thinline-Cutaway-Acoustic-Electric-Guitar.gchttp://manual.audacityteam.org/man/plot_spectrum.htmlhttp://www.dpamicrophones.com/microphones/dscreet/4090-omnidirectional-microphone-hi-sens- p48http://www.behindthemixer.com/importance-microphone-frequency-response/http://www.gikacoustics.com/what-are-room-modes/ https://www.soundonsound.com/sound-advice/beginners-guide-acoustic-treatment#para3 https://www.guitarplayer.com/miscellaneous/5-things-about-scale-length