report 1.2

Fraser Birchenall - S15100664

Acoustic Analysis of a Hand Built Native American Drone Flute Fraser Birchenall S15100664 Recipient: Islah MacLachlan

Word count: 2439 Submitted: Thursday 26th May 2016

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Abstract This report will explore the methods needed to record audio data from a Native American Drone Flute to produce an array of results to determine the Sound Pressure Level (SPL) of each note produced by the flute, the constancy and harmonic content of each note, and the polar pattern that the flute produces around a 2πrad surrounding area. These results will be compiled and put into suitable visual formats for a reader to easily interpret, and will be critiqued and assessed to determine any good points to discuss and/or any flaws to amend. After evaluation the results will be concluded and compiled before determining that the Native American Drone Flute is a success and a viable and functioning music instrument.

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Table of Contents 1.1 Introduction ……………………..………………………………..……………….……………………. 5 1.2 Aims ……………………………………………………………………….…..….……………. 5 1.3 Objectives ………………………………………………………………..………………….… 5

2.1 Background Information ………………………………………………………………………………. 6

3.1 Experimentation ……………………………………………………………….………………………. 6 3.1.1 Methodology ……………………………………………………….…………..………….… 6 3.1.2 Note Accuracy Compared to Concert Pitch ……………………………………………… 7 3.1.3 Consistencies of the Notes ………………………………………………..…………….… 8 3.1.4 Polar Plot of the Flute …………………………………………………………………….… 9

4.1 Evaluation ……………………………………………………………………………..…………….… 11 4.1.1 SPL Readings ……………………………………………………..……………….……… 11 4.1.2 Accuracy of Pitch ……………………………………………….……………………….… 11 4.1.3 Consistency Evaluation ………………………………………………………..……….… 11 4.1.4 Polar Plot Evaluation ………………………………………………..………………….… 12

5.1 Conclusion ………………………………………………………..………………..………………… 13

6.1 References …………………………………………………………………………………………… 14

7.1 Appendix ……………………………………………….…………………………..………………… 15

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Table of Figures Figure 1: Chart showing the average SPL readings …………………………………………………… 6 Figure 2: Diagram showing harmonic content ………………………………………………………..… 7 Figure 3: Detailed diagram of fundamental peak ……………………………………………………… 15 Figure 4: Equation to work out the number of cents between two frequencies a and b ….….…… 15 Figure 5: Chart showing distance of each note from concert pitch …………………………………… 8 Figure 6: Note consistency diagram …………………………………………………………..….……… 8 Figure 7: Diagram showing harmonic content of the drone chamber ………………………….…….. 9 Figure 8: Table of RMS values …………….……………..……………………….…………………..… 10 Figure 9: Polar graph of the flute ….……………………….…………………………………………… 10 Figure 10: Diagram showing decrease in brightness when recording behind player …………...… 16

Plate 1: Recording the SPL of the flute …………………………………….……………….…………… 6 Plate 2: Microphone setup whilst recording data to plot the polar graph …………………………… 16

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1.1 Introduction This report examines the data recorded from the analysis of the Native American Drone Flute through various methods, including the processed data developed in MatLab using MirToolbox. This data will then be collected, evaluated and critiqued, considering the reliability of the results before compiling them into a format suitable for presenting within this report. A number of tests conducted will be discussed, including the processes of obtaining the average decibel output of the instrument and its polar shape - indicating which direction a majority of the instrument’s sound is projected. All of the found data will determine the level of success the project achieved and show how well the instrument produces sounds, including the analysis of said sound.

1.1 AIMS The aims of this report are as follows:

- Examine the raw data and determine its meaning(s)

- Develop a useable format for the collected data

- Interpret these results and construct a visual representation of them

- Take these visual representations to evaluate the quality of the instrument

- Act upon this evaluation to improve the instrument

1.2 OBJECTIVES The objectives of this report are to achieve out the following:

- Detail the methods of testing used on the instrument

- Collect all of the data produced by the tests carried out and compile them into a usable format through the use of MatLab

- Analyse and critique said data to produces average values that can then be used to produce various graphs and tables

- Evaluate the final data produced and determine the characteristics of the sonic quality of the instrument

- Devise methods of finding the flaws in the data and improve the instrument further

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2.1 Background Information in terms of constructing the flute, a number of techniques had to be used in order to correctly model the acoustic chambers of the flute and the locations of the finger holes and fast air chamber (where the air blown directly into the slow air chamber would be forced through a considerably smaller space, increasing its speed drastically enough that when it hits the leading edge of the flute it will vibrate and create a sound). These included using a tin whistle modelling software called TWCalc to calculate the sizes and positioning of the holes making it as ergonomic to play as possible, and a boring technique to accurately carve out the chambers of the flute from a solid piece of wood. However flaws were created whilst using these techniques, such as the bore holes created not being quite straight and the splitting edges not being at quite the right angle, will create artefacts in the sound and reduce the instrument’s sonic quality.

3.1 Experimentation 3.1.1 METHODOLOGY USED IN TESTING Throughout the four tests conducted there was different methodology used to record the different results needed. Recording the decibel level of the instrument involved the use of a single decibel meter held about a meter away from the splitting edge of the instrument just below the bird[plate 1] (where a majority of the instruments sound comes out from). The average SPL of the room was recorded first to compare to the combined SPL of the ambient room noise and the flute which can

then be used to extract the true SPL for the flute by itself[fig.1]. This was repeated twice, playing

each note both quietly and loudly to generate an average SPL level for each dynamic, which shows where the instrument is louder and therefore more resonant. This could cause problems with the consistency of the overall dynamic level of the flute, but the graph shows a clear consistency between the sets of results so this is most likely to just be to do with the actual design of the flute rather than a fault such as a narrowing of the tube which would create a faster airflow and alter the notes. To create a fair and consistent set of results, the same length note was used when playing and recorded in groups of loud notes followed by groups of quiet notes to try and keep the dynamic levels used as consistent as possible. The decibel meter was held in the exact

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Plate 1: Recording the SPL of the flute Figure 1: Chart showing the average SPL readings in decibels


same position for the entire experiment to ensure that the ambient noise level of the remained the same and the flute remained within a 1 metre proximity of the recorder[plate 1].

3.1.2 RECORDING THE NOTE ACCURACY (WHEN COMPARED TO MODERN CONCERT PITCH) To record the note accuracy, the recordings from the decibel test were imported into MatLab and their frequencies were calculated using MirToolbox’s command MirSpectrum which shows the harmonic content of the sound as shown in the figure below[fig. 2] as a frequency-amplitude chart (using limits to narrow the scale and produce a more detailed image).

This shows that there is relatively little harmonic content to the instrument’s sound, giving it a very pure tone with little in the way of overtones to produce a richer sound. The higher and relatively quiet frequencies come from mainly air noise from the player, which creates the ‘woody’ sound these flutes are famous for. This data was then taken to find the fundamental (the highest peak in this case) by reducing the range between the upper and lower limits to get an accurate frequency for the note[fig. 3 in appendix] which concluded to be 732Hz. The concert pitch in hertz for an F#5 is 739.99Hz which shows the instrument is 0.187946 semitones flat for this particular note (calculated using the equation listed in the appendix[fig. 4 in appendix]). This process was repeated for three other notes and the drone chamber and charted to show the tuning consistency[fig. 5] .

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Figure 2: Diagram showing harmonic content of the flute playing an F#5 with the code used to create upper and lower limits for the data


This shows that the tuning for the lower notes is flat and the tuning gets progressively sharper as the flute plays higher up the scale, this could be due to any slight inaccuracies in the placement and sizing of the finger holes or the shape, size and positioning of the flue which will be discussed in detail within the evaluation.

3.1.3 NOTE CONSISTENCIES WITHIN THE TUNING OF THE FLUTE

Notes produced by the flute are fairly pure in tone and quality as shown by the previous tests, but the consistency required yet more testing to be conducted in order to be found, done by using MirToolbox’s command MirSpectrum (as used earlier[fig.2]) and modifying it to show the consistency of the frequencies[fig. 6] over time rather than their amplitudes.

As the diagram above shows, the note barely wavers over the 6 seconds it was recorded for which shows that the flute produces a very pure and consistent (yet slightly out of tune) sound. This diagram also provides a visual representation of the harmonics and overtones of the note where the brighter the line, the louder the frequency. Some of the notes such as the one above[fig. 6] had a

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Figure 5: Chart showing the amount each note is sharp or flat of concert pitch

Figure 6: Diagram showing note consistency of the flute playing an F#5 with the code used to create upper and lower limits for the data


few overtones in them, whereas others such as the one below[fig. 7] (which shows the consistency of the drone) show barely any harmonics and create a very pure sound.

3.1.4 POLAR PLOT OF THE FLUTE Producing a polar plot of the flute to show how much of its sound is projected in which direction involved using four identical measurement mics placed perpendicular to each other on the four walls of a soundproofed, acoustically treated room[plate 2 in appendix]. An F#5 was played on the flute in the centre of this arrangement and recorded, turning as close as possible to 18˚ each time being picked up by the four mics. This produced four recordings with each of the takes 90˚ apart from each other and reduced the number of takes needed from 20 to just 5. This process was done twice in order to calculate an average SPL for each position around the instrument, which was then imported into MatLab for further processing. Using the command…

mirrms ‘filename.extension’

…gave the root mean squared value of each note which is the perceived loudness a listener would interpret - this gave an output of a coefficient between 0 and 1 in MatLab. This was then converted into decibels and then in turn had the room noise (which was measured at an average -50dB) removed - which is useful when using a program such as MatLab to create a polar pattern graph as negative numbers don’t work. For example, a reading of -25dB - - 50dB would give a reading of + 25dB which would fit nicely on the polar plot.

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Figure 7: Diagram showing the drone and its lack of overtones and wavering in pitch

Figure 8: Variable table in MatLab showing a list of coefficients ready to be converted into decibels


Each of the readings was plotted onto a variable table within MatLab[fig. 8] along with another row increasing in value with increments of 2*pi/16 (which calculates the amount of radians that was travelled through over 18˚) ready to be plotted into a polar graph. Once plotted and converted, the string of code…

polar(variable_table_name(2,:),variable_table_name(4,:))

…was used in order to read the data from the variable table and input it into a polar graph showing the stereo imaging of the instrument[fig. 9].

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Figure 9: Polar graph of the flute


4.1 Evaluation of Collected Data 4.1.1 SPL READINGS All of the four separate sets of data constructed out of this test were consistent with each other and showed the same shapes and correlation, hinting that the end result obtained[fig. 1] is most likely reliable and true to the actual sound of the instrument. Each test showed that the note E5 was the most resonant on this instrument and that the loud and quiet notes remained true to this. Due to the design of the flue however, the drone and bottom C# of the primary chamber over blow an octave above what they should be, producing a louder sound.

In terms of accuracy of the test itself, most of the actions that took place were in line with what could be called a fair test. That being said, a few aspects of the process could be slightly changed in order to produce even more consistent and accurate results, including:

- Placing the decibel meter on a stand rather than having someone hold it as steadily as possible. This will ensure that any natural movement of a person would be eliminated and keep the source of the recording at a constant distance.

- Playing the flute in the exact middle of the room rather than estimating its position. This will produce as equal sonic reflections each side of the flute as possible and give a more accurate reading on the decibel meter.

- Placing the flute on a stand so to keep it a constant distance away from the decibel meter.

4.1.2 ACCURACY OF THE PITCH For these readings, the amplitude of the recordings was not important, it was the actual frequencies and their partials themselves, so the recordings from the SPL test were used. After the processing in MatLab, the results showed that the lower notes were flat and the higher notes were sharp[fig. 5] - almost as if the finger holes had been scaled up but the body of the instrument had remained the same. However, on further analysis of the physical properties of the flute it was found that the flue was the problem as it had been crafted too shallow. This forced air through the rest of the instrument at a faster rate than was originally modelled, pushing the amount of air further past any open holes, creating a deeper tone for the lower notes and a higher tone for the upper notes. However, all but one of the notes are only a fraction of a semitone out of tune from concert pitch, with the A note being an outlier in this data at almost a semitone flat. However, the flute is in tune with itself and produces a consistent note without any fluctuations or artefacts.

4.1.3 CONSISTENCY OF THE TONE OF THE FLUTE As with the previous test, the frequency was what was important for these results not the amplitude of them, so the recordings from the SPL test were used to produce a consistency diagram. These showed that the flute plays a very consistent and pure sound over a considerable amount of time,

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with very few partials and harmonics to add any overtones and very little in terms of variation of pitch. The results from this test also showed a similar pattern to those of the SPL readings, where the most resonant[fig. 1] note E showed the least harmonics and the most pure, sinusoidal like tone[fig. 7], and the quieter and less resonant the note became the more partials and artefacts appeared in the sound[fig. 6].

4.1.4 POLAR GRAPH EVALUATION The polar graph generated from the results recorded is near enough symmetrical, showing that a majority of the sound comes from directly in front of the flute at 0˚ and directly from the sides at both 90˚ and 270˚[fig. 9]. This is most likely due to the combination of the sound immediately beginning to travel outwards in a steep cone shape as soon as it leaves the end of the instrument and what little reverberations reflect around the room (although many of them will be absorbed as the room was acoustically treated). The graph produced shows that the instrument is well audible from which ever angle you hear it from (including from behind the player, although there is a slight decrease in amplitude and brightness[fig. 10, 11 in appendix]). The slight asymmetrical appearance of the graph could be down to a number of reasons, the most likely of which is down to the design of the instrument itself. Looking at the results shown in the SPL test[fig. 1] the lower notes are quieter (taking note that the drone was overblown to the octave above during this test). In the polar graph test the drone played the lower octave making it significantly quieter than the primary chamber, so the left hand side of the instrument is louder than the right hand side - which is evident in the polar graph[fig. 9] (270˚ being left and 90˚ being right).

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5.1 Conclusion Considering the results collected and evaluated in this report and the flaws discovered and corrected, the flute is capable of producing a near sonically symmetrical and pure sound to within at least a semitone of a note at concert pitch. The tests conducted have lead to reliable results that can easily be replicated to produce and obtain similar values, showing that the design of the flute works well. All in all, this report concludes that the flute was a success despite some minor flaws in its functionality made apparent through this selection of tests and is a competent working musical instrument.

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6.1 References Lartillot, Olivier. Mir Toolbox 1.5 User's Manual. 1st ed. 2013. Web. 25 May 2016.

MTU,. "Frequencies Of Musical Notes, A4 = 440 Hz". Phy.mtu.edu. N.p., 2016. Web. 25 May 2016.

Wikipedia,. "Cent (Music)". Wikipedia. N.p., 2016. Web. 25 May 2016.

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7.1 Appendix Below[fig. 4] is the equation used for calculating the amount of cents between two frequencies, which was used when determining how far away the pitches played on the flute were from true concert pitch.

For example:

This equation was used to calculate the amount that each note was out of tune by to create fig. 5.

In order to obtain these frequencies, a very detailed image was developed in MatLab for each frequency which zoomed in on the fundamental note to see the frequency of said fundamental to within a tenth of a hertz accuracy[fig. 3].

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Figure 4: Equation for calculating the difference between two frequencies in cents

Figure 3: Detailed view of a fundamental frequency


Whilst the player was stood playing the flute during the polar graph test, they will have blocked some of the sound from reaching the microphone behind them. This is apparent from two places, one being the polar graph itself[fig. 9] where there is a visible dip in amplitude over by the 180˚ area that would be behind the player. Secondly, if a recording from in front of the instrument and a recording from the same session from behind the instrument (180˚ on the polar graph) are taken and run through the mirbrightness command in MatLab, two coefficients will be outputted to represent the brightness or dullness of the signals. The data shows that the audio captured from directly in front of the instrument at 0˚ is roughly twice as bright as the data captured at 180˚, backing up the reasoning given earlier for the decrease in amplitude on the polar graph.

Below is a plate showing the set up for recording data to produce a polar graph of the flute[plate 2].

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Figure 10: Data showing the duck in brightness and amplitude between the microphone placed at 0˚ and the microphone placed at 180˚

Plate 2: Microphone set up for recording polar pattern data.

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