the effecect of a lacquer finish on the timbre … · 1 2.671 go forth and measure 2.671...

1 2.671 Go Forth and Measure

2.671 Measurement and Instrumentation Monday PM

Ashin Modak 12/20/15

THE EFFECECT OF A LACQUER FINISH ON THE TIMBRE OF THE FRENCH HORN

Thalia Estrella Massachusetts Institute of Technology

Cambridge, MA, USA

ABSTRACT When choosing a finish, French horn players have

many options, however, many players make a decision based on the finish’s impact to the sound before basing it on aesthetics. The theoretical resonant frequency of an open-closed cylindrical air column, such as the tubing of a French horn, depends on the length of the tube. The vibrational frequency of a flat plate—such as the bell of a brass instrument—depends on the thickness, dimensions and material properties, and it has been studied to impact the sound. In order to study whether a clear lacquer finish impacts the sound of a French horn, the sound frequency response of brass tubes of several lengths was measured by inputting a buzzing signal through a French horn mouthpiece. With an impact hammer, the sound frequency response of brass plates of several thicknesses at different impact points was measured. Both were measured before and after adding lacquer. Lacquer made the resonant frequency of brass significantly higher within 95% confidence, in the small and medium tubes and the thick plate diagonal impact point, which means the instrument plays a sharper pitch overall.

1. INTRODUCTION When choosing to a brass instrument to play on, a player has several options for the brass finish. According to Yamaha, a large-scale musical instrument manufacturer, the type of lacquer will make a difference to the sound and timbre of the instrument. Lacquer may produce a sharp and powerful tone. Gold lacquer (gold paint mixed in with the lacquer) produces a solid and dark tone and a clear forte. Clear lacquer (similar to regular lacquer painted by transparent lacquer) produces a similar sound, while silver-plated produces soft and bright tone. Silver-plated instruments “directly deliver the character of the instrument itself and are more expressive in subtle nuances”. Gold-plated instruments will produce a soft and relatively distinct sound, which is similar to silver-plated instruments, but with a darker tone.[1] Other options for a

brass instrument finish are satin silver, polished silver, and brushed finishes, but they do not have a definitive qualitative description of the sound.

For French horn players, choosing a finish is particularly important. Many professional players, who purchase custom or refurbished vintage instruments, choose anything but a lacquered finish. Choosing a lacquer finish alone opens another branch of decisions, as nitro-cellulose or urethane lacquers are available. A player may take into account the effort to upkeep a certain finish, the comfort of playing on a certain finish, a finish that complements the material of the instrument (brass and nickel silver are the most common) or, most importantly, the effect on the quality of the sound, often sacrificing aesthetic qualities, for an instrument that better suits personal preference of the sound. While there are claims that the differences in the finishes are minimal, and that in any blind study, a player would not necessarily prefer a certain finish over another, many professional players admit to a certain personal preference.

The addition of lacquer to brass could have two possible effects on the physical instrument that could consequently impact the sound. First, the overall thickness of the brass instrument could change significantly. Second, the material properties of lacquer could change the acoustic impedance of the brass and add a damping effect in the frequency response. Slight changes in frequency attribute to a characteristic of timbre called micro-intonation.

A Conn-6D yellow-brass, clear-lacquered horn was used as a reference brass instrument to measure both resonant frequency of the tubing and vibrational modes of a bell. Two types of experiments were conducted to model the physical way that sound is produced in a brass instrument. The first experiment was designed to emulate the sound produced by vibrating air in the wrapped tubing parts of the horn. A buzzing signal, similar to that of a brass player playing an actual brass instrument, was input through brass rods of different lengths both with and


without added lacquer. The second experiment was designed to emulate the effects on the sound caused by the horn bell. Brass plates of different thicknesses, with an area modeled after the French horn bell, were hit with an impact hammer at different impact points representing different vibrational modes, and the frequency of the sound produced was measured. The frequency at the resonant peaks was determined and compared for the lacquered and un-lacquered cases for both the tubes and the plates. For the plates, the transfer function between the input force and sound output was found for the plates and analyzed.

2. BACKGROUND 2.1 SOUND ANALYSIS AND MUSICAL QUALITIES 2.1.1WAVES AND SOUND FREQUENCY

Sound is a periodic complex waveform. According to Fourier, any periodic signal may be created from a sum of sinusoids. More specifically, these sinusoids are harmonics (integer multiples) of the fundamental frequency. A simple instrument, such as a cylindrical air column, has a series of natural resonances called modes. The lowest-frequency mode is called the fundamental mode, which corresponds to the fundamental frequency[2]. Resonances that are integer multiples of the fundamental are called harmonics. Subsequent modes are also called overtones. These are some of the components of the frequency spectrum and are often more useful to analyze sound. 2.1.2 TIMBRE, PITCH AND MICRO-INTONATION

In music and sound, timbre is the quality that distinguishes different types of sound production. Some subjective attributes and corresponding objective physical phenomena used to characterize timbre are pitched tonal character described by periodic sound, coloration described by spectral envelope, vibrato (frequency modulation) and tremolo (amplitude modulation). Micro-intonation describes small changes in frequency, usually intervals smaller than a semitone, which includes all the chromatic notes in the Western scale. Slight frequency changes in Western music are not desired. 2.2 FRENCH HORN CHARACTERISTICS AND SOUND PRODUCTION 2.2.1 FRENCH HORN CHARACTERISTICS The common double French horn has two sets of tubing tuned in B-flat and F with approximate total lengths of

2.7 m and 3.6 m, respectively. Double French horns (with both B-flat and F tubing) are designed with three rotary valves operated by valve levers with the fingers of the left hand. There is a fourth valve operated with the thumb which alternates between the F and B-flat pitched sides of the tubing. Figure 1 shows complete labeled parts.

Figure 1: Scheme of a double French horn from underneath. 1. Mouthpiece 2. Leadpipe, where the mouthpiece is placed 3. Handrest 4. Spit valve 5. Fourth valve 6. Valve levers 7. Rotary valves 8. Slides 9. Long tubing for F pitch with slide 10. General slide 11. Short tubing for B-flat pitch with slide 12. Bellpipe 13. Bell; the right hand is cupped inside this.

As a reference, a Conn-6D yellow-brass, clear-

lacquered horn was measured to determine both resonant frequency of the tubing and vibrational modes of a bell. The dimensions of the bore—the top of the leadpipe at the mouthpiece entrance—and the thickness of the flat part of the bell are shown in Figure 2.

Figure 2: A Conn-6D yellow brass clear lacquered French horn depicting the outer diameter of the bore at the mouthpiece entrance and the bell thickness.


2.2.2 SIMPLE BRASS INSTRUMENT MODEL A simple model of a brass instrument consists of a

length of straight, cylindrical tubing with a mouthpiece on one end and a funnel-shape bell at the other. This model has one end open (bell) and one end closed (the mouthpiece), as shown in Figure 3, and its fundamental frequency depends on its length. An even simpler model neglects the effect of the bell and consists of a brass tube length and a mouthpiece. The possible notes that can be played on this simple instrument are the integer modes—the overtone series.

Figure 3: A simple brass instrument modeled by the superposition of mouthpiece, tube and bell.

In an actual brass instrument, the frequency depends on the effective length of the wrapped tubing, including the effects of the mouthpiece the instrument bell. By pressing valves, the effective length of the instrument can be changed by opening and closing paths within the tubing of the instrument. A brass instrument is carefully designed to achieve the right effective lengths to achieve notes in a harmonic series. 2.2.3 HOW THE FRENCH HORN MAKES SOUND

French horn players place the lips on the mouthpiece to form an effectively airtight seal, holding the lips in tension, and creating a buzzing sound, or vibrating air sound signal. This air vibrates back to the opening of the lips and vibrates through the coiled tubing to produce a sound, essentially emulating a vibrating air column.[4] With the use of the rotary valves, tube paths are opened and closed, changing the length of the path the air travels to, creating different pitches.

2.3 PHYSICAL MODELS OF THE FRENCH HORN 2.4.2 RESONANT FREQUENCY OF CYLINDRICAL AIR COLUMNS

By neglecting the effect of the mouthpiece and the bell, the tubing of the French horn is modeled as an open-closed cylindrical column, as discussed in section 2.3.2. The resonant frequency of the cylindrical tube with one end closed given by Equation (1)[2], depends on the effective length, 𝐿, of the tube, the mode, 𝑛, and the speed of sound in air, 𝑐. While the main main assumption is that

tubing is modeled as an open-closed cylindrical column, the both ends open model will also be analyzed. The resonant frequency of the cylindrical tube with both ends open is given by Equation (2). Equations (1) and (2) will be used to compare the measured fundamental frequency of brass tubes to the theoretical fundamental frequency.

𝑓! =2𝑛 − 1 𝑐4𝐿

(1)

𝑓! =2𝑛 − 1 𝑐2𝐿

(2)

A diagram of the shape of the sound waves in a

cylindrical air column is shown in Figure 4. In an open-closed tube, only the odd harmonics are achieved, also as shown by Equation (1).

[3]

Figure 4: Standing sound waves in an open-closed tube. Only the odd harmonics are achieved.


Straight length brass tubes in these experiments were modeled as cylindrical air columns and the dimensions depicted in Figure 4 were measured. The inner and outer bore diameters, 2a and 2b, respectively, were chosen to be close to the dimensions of a Conn-6D horn. Several lengths, L, were also measured. Different lengths correspond to different fundamental frequencies as given by Equation (1).

Figure 4: The dimensions of brass tubes used in the experiment are defined by an inner radius a, and an outer radius, b and length, L.

2.3.2 EFFECT OF BELL WALL VIBRATION ON SOUND OF BRASS WIND INSTRUMENTS

The vibrations of the bells of brass instruments affects the sound produced during play. In a study of brass instruments with the same cylindrical parts, the resonant frequencies were measured with a damped and undamped bell, either allowing the bell to vibrate freely or constraining the vibrations of the bell. Their respective measured resonant frequencies found to be significantly different. Brass instruments vibrate while they are being played. These strain oscillations occur in the entire instruments but the effects are most pronounced when they occur in the bell and they interact with the air column of the instrument. [5]

2.3.3 FRENCH HORN BELL MODELED AS A FLAT SQUARE PLATE

A French horn has a significantly larger bell than other brass instruments. For simplicity, to measure the frequency modes of a French horn bell, it will be modeled as a flat square plate. This is an accurate model because the focus is to find the difference in the material or thickness vibrating, not the overall shape. Figure 5 shows the approximate dimensions used to determine the area the flat brass plates chosen for these experiments.

Figure 5: The approximate dimensions of a French horn bell modeled as a square plate. The area depicted is the approximate area of the flat plates measured in the experiment.

2.3.4 FREQUENCY MODES OF A SQUARE PLATE

The vibrational frequency of the mode (𝑚, 𝑛) of a square plate with simply supported edges is given by Equation (3)[6], where 𝑐! is the speed of longitudinal waves in the material, 𝑡 is the thickness of the plate, and 𝑙 is the side length the plate.

𝑓!" = 0.453𝑐!𝑡𝑚 + 1𝑙

!

+𝑛 + 1𝑙

!

(3)

The vibrational frequency of the (0, 0) mode of a

clamped square brass plate is given by Equation (4)[6]

𝑓!! =

1.654𝑐!𝑡𝑙!

(4)

Regardless of the boundary conditions, the

vibrational frequency of the same mode (same impact position) will only change by a factor of the change in the thickness of the plate if all other constants, material properties and length, remain the same. Equation (3) will be used to compare the theoretical vibrational frequency of brass plates to the measured vibrational frequency. An impact hammer will provide a measurable force to introduce vibrations to the plate, causing the fundamental frequencies in the plate to resonate. To measure the pure transfer function, the force must be measured.


3. EXPERIMENTAL DESIGN In order to measure the effect of lacquer on the

sound of brass instruments, the resonant frequency of several lengths of brass tubes were measured both before and after being lacquered. Using the dimensions and properties of a Conn-6D yellow-brass, clear-lacquered French horn as a model brass instrument, rods of similar dimensions as the horn were used. Using a French horn mouthpiece, a buzzing signal, similar to that of a brass player playing an actual brass instrument, was input through brass rods of different lengths both with and without added lacquer. The frequency of the output sound was measured with a microphone. The effect of the wall vibrations of the instrument bell on the sound was also taken into account, and vibrational modes modeled after the French. Brass plates of different thicknesses, with an area modeled after the French horn bell, were hit with an impact hammer at different points representing different nodes, and the frequency of the sound produced was measured to find the vibrational mode of the plate.

3.1 MEASURING THE FREQUENCY MODES OF A BRASS TUBE

The resonant frequencies of brass tubes were measured. First, for brass tubes of three different lengths, here on referred to as “small”, “medium”, and “long”, the dimensions depicted in Figure 4 were measured. The inner diameter was measured with Mitutoyo CD-S6"CT calipers and the outer diameter was measured with a Mitutoyo 293-340 micrometer, as seen in Table 1.

Each of the brass was marked and clamped in place in the center. A spirometer and a microphone were placed at one end. A Patterson Standard Model Mouthpiece was inserted into the tube on the other end. Figure 6 shows an overview the setup. Both the microphone and the spirometer were connected to a LabQuest Mini connected a computer. Data was collected at a 50 kHz sampling rate.

Figure 6: The final setup to measure the frequency of sound of the brass tubes, including the Small brass tube, mouthpiece, microphone and spirometer.

A player played into the brass tubes with a similar

technique to French horn playing, attempting to play a C6 note, which has a frequency of 261 Hz. The buzzing lips signal traveled through the tube. The sound response and airflow were recorded simultaneously. A block diagram of the entire setup is shown in Figure 7.

Figure 7: Block diagram of the brass tube system. The lips send a buzzing signal through the brass tube. The sound and airflow are recorded by the microphone and spirometer, respectively.

All the tubes were then cleaned with isopropyl

alcohol in preparation to the addition of lacquer. A generous coating of Nikolas 2105 Clear Lacquer was sprayed on the outer part of the brass rods and the lacquer was let to set overnight. The inner and outer diameters were measured again. The same experiments were repeated, five times for each length tube, for the lacquered rods. Table 1 shows the length and bore dimensions of the tubes as defined in Figure 4 before and after lacquer was added.


Table 1: The measurements of length, outer diameter and inner diameter of each of the different-size brass tubes before and after adding one layer of lacquer.

Length, L (cm) Outer Diameter before lacquer, 2b (mm)

Inner Diameter before lacquer, 2a (mm)

Outer Diameter, after lacquer 2b

(mm)

Inner Diameter, after lacquer 2a

(mm) Small 30.25 ± 0.16 9.53 ± 0.01 8.54 ± 0.25 9.5474 ± 0.0095 8.54± 0.28

Medium 61.15 ± 0.12 9.53 ± 0.01 8.51 ± 0.50 9.541 ± 0.0052 8.37 ± 0.34 Long 91.46 ± 0.29 9.53 ± 0.01 8.38 ± 0.28 9.564 ± 0.023 8.43 ± 0.26

3.2 MEASURING THE VIBRATIONAL FREQUENCY MODES OF A SQUARE BRASS PLATE

The resonant frequencies of square brass plates were measured. Two brass plates of two different thicknesses were used, here on referred to as “thick” and “thin” plates. The side length of both plates was 135 mm. The experimental procedure was repeated five times for each plate. Similar to the tube experiments; the plates were then cleaned with isopropyl alcohol in preparation to the addition of lacquer. A generous coating of Nikolas 2105 Clear Lacquer was sprayed on both sides of the plates. The lacquer was let to set overnight, the thicknesses of the plates were measured again, and the same experiments were repeated five times for the lacquered plates. Table 2 gives the thicknesses of both plates, before and after the addition of lacquer, measured with a Mitutoyo 293-340 micrometer.

Table 2: The measurements of the thickness of both

square plates, before and after the addition of lacquer. Thickness, before

lacquer (mm) Thickness, after

lacquer (mm) Thin 0.3058 ± 0.0047 0.3168 ± 0.0097 Thick 0.5122 ± 0.0042 0.5280 ± 0.0060 Three impact points were labeled on the plate as

follows: one in the center of the plate, here on referred to as “center”, one at the midpoint of the edge and the center point, here on referred to as “offset” and one diagonal to the center point aligned vertically with the offset point, here on referred to as “diagonal”. The plate was clamped in place. Figure 8 shows the positions of the impact points on the clamped plate.

Figure 8: The positions of the impact points labeled on the clamped brass plate as described: center, offset and diagonal.

A Vernier microphone connected to a LabQuest

Mini was clamped and positioned 37 mm above the clamped plate. An overview of this setup is shown in Figure 9.


Figure 9: The clamped brass plate setup with a Vernier microphone clamped in place 37 mm above the place.

An Impact Hammer was connected to a 480C02 ICP

Power unit, which was connected to a Vernier INA-BTA instrumentation amplifier, which was connected to another LabQuest Mini. The Impact Hammer was used to hit the brass plate to introduce vibrations at each location and the sound response was recorded with the microphone. Each location was hit five times on both plates. Data was collected at a sampling rate of 50 kHz. A block diagram of the entire setup is shown in Figure 10.

Figure 10: Block diagram of the brass plate and impact hammer system.

4. RESULTS AND DISCUSSION 4.1 THE VIBRATIONAL MODES OF A BRASS TUBE

The sound response for a single trial for the small tube no-lacquer experiment is shown in Figure 11. Sinusoids of different amplitudes can be depicted. The response is representative of the trials for all three lengths of tubes with and without lacquer.

Figure 11: The sound response for the small tube.

The frequency power spectrum was computed for each of the trials. The resonant peaks were determined to be the absolute highest peaks within 200 Hz intervals. The resonant peaks were consistently at higher frequencies than the small and medium non-lacquered tubes. Figures 12, 13, and 14 show the power spectrum of one representative trial of the frequency response of the small, medium and long tubes with and without lacquer, respectively. The harmonic peaks were consistently higher for the small and medium lacquered tubes. The harmonic peaks were consistently lower for the long lacquered tubes.

Figure 12: The Frequency Power Spectrum of the Small Tube. The peaks depict the resonant frequencies. The lacquered tubes are represented in red and the non-lacquered tubes are represented in blue.

0 0.05 0.1 0.15 0.2-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time (s)

Soun

d Pr

essu

re

Small Tube Sound Pressure Response


Figure 13: The Frequency Power Spectrum of the Medium Tube. The peaks depict the resonant frequencies. The lacquered tubes are represented in red and the non-lacquered tubes are represented in blue.

Figure 14: The Frequency Power Spectrum of the Long Tube. The peaks depict the resonant frequencies. The lacquered tubes are represented in red and the non-lacquered tubes are represented in blue.

Figure 15 shows the frequency and uncertainty of

the first resonant peak, the fundamental frequency, across all five trials for all three tubes. The frequency of the lacquered tubes was significantly higher than the non-lacquered tubes within a 95% interval for the small and medium tubes, with p-values of 0.001 and 0.003,

respectively. However, the frequency of the lacquered tubes was significantly lower than the non-lacquered tubes for the long tubes with a p-value of 0.0232. All the p-values were less than the significance value of 0.05.

Figure 15: The frequency and uncertainty of the first resonant peak, also known as the fundamental frequency, across all five trials for all three tubes. The red bars represent the lacquered tubes and the blue bars represent the non-lacquered tubes. The small and medium lacquered tubes were significantly higher in frequency than the non-lacquered tubes. The frequency for the non-lacquered long tube was significantly higher than the lacquered tubes.

The theoretical frequency for the first three modes,

including the fundamental, was calculated using Equation (1), assuming the open-closed cylinder model. The lengths of the rods as shown in Table 1 were increased by 5 cm to take the length of the mouthpiece into account. The speed of sound in air at 25 degrees Celsius was taken to be 343 m/s. The theoretical frequency, using both a closed and open model, is compared to the measured frequencies of the lacquered and un-lacquered tubes in Table 3. The comparisons of the theoretical frequencies to the measured frequencies show that not all the fundamental harmonics were captured in the data collection and power spectra analysis. The failure to capture all the fundamental frequencies can be attributed to the attempt of the player to emit a C4 pitch with their buzzing signal, which has a frequency of 261 Hz. Therefore the minimum frequency measured will be

Small Medium Long0

50

100

150

200

250

300

350

400

Freq

uenc

y (H

z)

Fundamental Frequency of Brass Tubes

No LacquerLacquer


Table 3: Comparing the theoretical frequency of the first modes to the un-lacquered and lacquered results for all three tube sizes Mode, n or

Peak number Theoretical Frequency Open-Open Model (Hz)

Theoretical Frequency

Open - Closed Model (Hz)

Average Un-Lacquered

Frequency (Hz)

Average Lacquered Frequency

(Hz) Small 1 422.2 211.7 238.3 ± 6.4 261 ± 10

2 1270.4 635.2 477 ± 10 524 ± 21 3 2117.2 1058.6 720 ± 14 785 ± 29

Medium 1 243.04 120.52 300 ± 20 335 ± 13 2 722.12 361.56 600 ± 36 669 ± 31 3 1205.2 602.60 891 ± 65 -

Long 1 168.96 84.48 259.6 ± 9.8 249.2 ± 6.6 2 306.90 253.45 518 ± 20 497 ± 12 3 844.84 422.42 779 ± 28 742 ± 15

limited by the frequency of the signal. Furthermore, while the main assumption was that the tubes were closely to be open-closed, but it is possible the modes of the open-open model were present.

The contribution of the air column micro-

intonation changes in a brass instrument can be fixed by adjusting the slide positions while tuning the instrument, so this is not a major contribution to slight changes in frequency. 4.2 THE VIBRATIONAL MODES OF A BRASS PLATE

The sound response for a single trial for the thick plate no-lacquer experiment, and the impact hammer impulse input is shown in Figure 16. The response is representative of the trials for both plates with and without lacquer.

Figure 16: The top plot shows sound response for the thick un-lacquered plate at the offset position for one trial. The bottom plot shows the impulse input force of the impact hammer for one trial.

The transfer function of the impact input, sound output

was computed for each of the trials. Figures 17, 18 and 19 show the transfer function for one representative trial of the thick plate at the offset, center and diagonal impact locations, respectively. Figures 20, 21 and 22 show the transfer function for one representative trial of the thin plate at the offset, center and diagonal impact locations, respectively.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.41

2

3

4

5

Time (s)

Soun

d Pr

essu

re

Thick Plate Offset Sound Pressure Response

0 0.05 0.1 0.15 0.2-5

0

5

10

Time (s)

Pote

ntia

l (m

V)

Impact Hammer Force


Figure 17: The transfer function of an impact hammer force input and sound output for the thick plate at the offset location. The blue line represents the non-lacquered plate and the red line represents the lacquered plate. The gain is similar across the frequencies but there is an apparent phase shift.

Figure 18: The transfer function of an impact hammer force input and sound output for the thick plate at the center location. The blue line represents the non-lacquered plate and the red line represents the lacquered plate. The gain is similar across the frequencies but there is an apparent phase shift.

Figure 19: The transfer function of an impact hammer force input and sound output for the thick plate at the diagonal location. The blue line represents the non-lacquered plate and the red line represents the lacquered plate.

Figure 20: The transfer function of an impact hammer force input and sound output for the thin plate at the offset location. The blue line represents the non-lacquered plate and the red line represents the lacquered plate.

Frequency (Hz)100 150 200 250 300 350 400

Gai

n (V

olts

-1)

10-3

10-2

10-1

100

101

102

103 Thick Plate Offset Transfer Function

No LacquerLacquer

Frequency (Hz)100 150 200 250 300 350 400

Gai

n (V

olts

-1)

10-4

10-3

10-2

10-1

100

101 Thick Plate Center Transfer Function

No LacquerLacquer

Frequency (Hz)100 150 200 250 300 350 400

Gai

n (V

olts

-1)

10-2

10-1

100

101

102 Thick Plate Diagonal Transfer Function

No LacquerLacquer

Frequency (Hz)100 150 200 250 300 350 400

Gai

n (V

olts

-1)

10-3

10-2

10-1

100

101

102

103 Thin Plate Offset Transfer Function

No LacquerLacquer


Figure 21: The transfer function of an impact hammer force input and sound output for the thin plate at the center location. The blue line represents the non-lacquered plate and the red line represents the lacquered plate.

Figure 22: The transfer function of an impact hammer force input and sound output for the thin plate at the diagonal location. The blue line represents the non-lacquered plate and the red line represents the lacquered plate.

Figure 23 shows the frequency and uncertainty of

the first resonant peak, the fundamental frequency, across all five trials for all impact locations in the thick plate. The diagonal location had a significant higher frequency in the lacquered case than the non-lacquered case within a 95% interval for the small and medium tubes, with a p-value of 0.002, which is less than the

significance value of 0.05. It is unknown if this is an experimental result or there is something significant about that impact location. Further analysis is necessary for the thin plate responses is necessary, but some of the data became corrupted in the process.

Figure 23: The frequency and uncertainty of the first resonant peak, also known as the fundamental frequency, across all five trials for each impact location of the thick plate. The red bars represent the lacquered tubes and the blue bars represent the non-lacquered tubes. The diagonal location had a significant higher frequency in the lacquered case than the non-lacquered case.

5. CONCLUSIONS For the small and medium tubes, and the thick plate

at the diagonal impact point, the sound frequency was significantly higher within a 95% confidence, all with p-values less than 0.05. The lacquer cases frequency in the music world this means a sharper pitch. However the sound frequency for long lacquered tubes was significantly higher than the non-lacquered tubes. Furthermore, the contribution of the air column tubing to micro-intonation changes in a brass instrument can be mitigated by the modular design of the French horn. By adjusting the slide positions to tune the instrument, slight changes in frequency can be changed. However, these changes may vary. Major contributions come from changes in the vibrational frequency of the bell, since this can especially not be adjusted.

The slight changes embouchure (lip pressure) of the player affects the frequency, however this does not explain why the frequency was consistently higher. The theoretical frequency for a cylindrical air column model

Frequency (Hz)100 150 200 250 300 350 400

Gai

n (V

olts

-1)

10-3

10-2

10-1

100

101

102 Thin Plate Center Transfer Function

No LacquerLacquer

Frequency (Hz)100 150 200 250 300 350 400

Gai

n (V

olts

-1)

10-3

10-2

10-1

100

101

102 Thin Plate Diagonal Transfer Function

No LacquerLacquer

Center Offset Diagonal0

100

200

300

400

500

600

Freq

uenc

y (Hz

)

Resonant Frequency of Flat Square Brass Plate

No LacquerLacquer


for the tube experiments does not take the effect of the mouthpiece into account.

In the plate experiments, the impact location accuracy varied slightly with each trial, which may affect the overall frequency response. For the thick plate experiments, the frequency response was only significantly higher in the diagonal location. Within trials, the frequency was not consistently higher for any of the locations in either plate.

Recommendations for further data analysis include comparing the theoretical frequency models to the measured frequencies. For the plate experiments this includes which changes in frequency can be attributed to a change in thickness, and which were due to additional material property damping.

Some recommendations for future work include designing an experiment to measure the physical vibrational modes of brass plates with strain gauges and comparing those frequencies with the theoretical frequencies. Similar experiments could be carried out to measure the sound frequencies with thicker lacquer layers or distinct finish options as mentioned in the introduction, and a lacquer option that more closely resembles the lacquer finish of a brass instrument.

ACKNOWLEDGMENTS I would like thank Ashin Modak for his extensive

guidance and patience during the background research and designing of the experiment, his assistance during data collection and data analysis and his overall enthusiasm and support. I would also like to thank Dr. Barbara Hughey for her input in the design of the experiments, her help in my understanding of the theory and analysis, as well as her relentless support throughout this project. Special thanks to all the 2.671 staff for their positive feedback and input into the development of this project, from the brainstorming process to completion.

REFERENCES [1] “What is the difference between lacquer and plated finishes? - Trumpets - Brass/Woodwinds - Musical Instruments” [Online]. Available: http://faq.yamaha.com/us/en/article/musical-instruments/winds/trumpets/905/2979/What_is_the_difference_between_lacquer_and_plated_finishes. [Accessed: 07-Dec-2015]. [2] Thompson, A., 2010, “A Study of French Horn Harmonics,” Institute of Acoustics.

[3] Fuchs, J., “Ultrasonics - Sound - Harmonics,” CTG Tech. Blog. [4] Berg, R. E., and Stork, D. G., 2005, The Physics of Sound, Pearson Prentice Hall, Upper Saddle Rive, New Jersey. [5] Kausel, W., Zietlow, D. W., and Moore, T. R., 2010, “Influence of wall vibrations on the sound of brass wind instruments,” J. Acoust. Soc. Am., (128). [6] Principles of Vibration and Sound.

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