Tonal Analysis of Different Materials for Trumpet Mouthpieces

Transcription

1 Greg Formosa PHYS 199 POM Project Write-up Tonal Analysis of Different Materials for Trumpet Mouthpieces INTRODUCTION: Trumpets have been noted as one of the oldest instruments in the world, and ever since the time they were created they included some type of mouthpiece structure. The trumpet itself has evolved greatly in its time of existence, but so have its mouthpieces. Every great player knows that the mouthpiece is the instrument, meaning that different mouthpieces make for better types of music and tone. But what about the same mouthpiece, but made with different materials? Aside from physical playing differences, are there differences that an untrained listener might notice? I decided to find out just what the differences between mouthpieces of different materials (essentially different densities) really were. While playing in my high school symphony band, I used a Blessing 5C mouthpiece, a very general and simple mouthpiece usable by most any player for most any music. During a

2 high school Science Olympiad competition, I created a French horn-type instrument and crafted an oak hard wood mouthpiece, replicated off of my Blessing 5C mouthpiece, by using a lathe and some precise sanding techniques. This year while in ME 170 class, I designed a mouthpiece to replicate my Blessing 5C using Pro-Engineer CAD software (seen below). After designing it and using precise measurements found from various mouthpiece websites, it was made in a rapid-prototyping machine out of Accura SI 40, a strong plastic material. As seen in the picture above of the metal (brass), plastic (accura), and wood (oak) mouthpieces, they are all very similar, made to the best of my ability to do so. The density of the metal mouthpiece, made of a 67% copper and 33% zinc Yellow brass mixture [1], is around g/cm 3, while the plastic is 1.1 g/cm 3 and the wood is g/cm 3 [2]. As you can tell, their densities are quite different, so even if the design is not exactly the same for each mouthpiece, I should see some noticeable data if there is any. HYPOTHESIS: A rule of thumb that I first tried to imagine was that the lower the density of each mouthpiece, the more sound might be absorbed by it and not transferred into sound coming out of the bell. Therefore I assume that as the density decreases, from metal to plastic to wood, the amplitude/energy of the sound would decrease due to more being absorbed by the mouthpiece. I

3 also then assumed that the harmonics would change significantly, the less dense having less higher end harmonics or being less bright than one with a higher density. Frequency did not seem to be something that might change significantly, but maybe (assuming that the metal is the norm) the softer materials (mainly wood) would absorb some of the sound and reflect the vibrations less, slowing down the air and creating a slightly lower frequency, causing the note to be slightly flat. As far as phase shifts go for each mouthpiece, I assume that the plastic would be similar to the metal because of the rigidity of the surface, allowing the waves to bounce similarly off of the insides of the mouthpiece and following the same basic path. The wood might be quite different, because not only is it the most absorptive, but it is the softest of the three. EXPERIMENT: I used a Bach Stradivarius, silver plated Model 37 trumpet for each mouthpiece. I played a C5 tuning note for trumpet, a concert Bb (about Hz), a few times on each note and each mouthpiece, and picked out the best sounding and most similar recordings for each trial. During testing, I used as similar of a pressure, force, and playing technique on each mouthpiece, so if there was a difference in amplitude, it was due to the mouthpiece and not how loud I was trying to play. First things I noticed were the differences in the physical textures of the mouthpieces. The metal was easy to play on, being very smooth and rigid, and precisely manufactured. The plastic was a bit harder because of the uneven surface of the plastic due to the rapid-prototyping machining. The plastic also transferred heat much less than the metal one, so it stayed about room temperature no matter how long I played on it. I noticed that it was harder to hit higher

4 notes on this mouthpiece for some reason, possibly because of the slight inaccuracies in design. The wood mouthpiece was the most different, because even though the rim and cup were more similar to the metal than the plastic was, the material made the rim stick more to my lips, making it harder to control and change notes. It seemed smooth to the touch of the finger, but when saturated lips were playing on it, it seemed that the material softened up and made buzzing more of a chore to get out a better sound. Audibly, the metal mouthpiece had a bright and full sound, like I expected. The plastic sounded very similar to the metal, but with slightly less power until played on higher notes like the C5 that I was testing. While playing this note, the mouthpiece seemed to project more so than it did for lower tones. The wood mouthpiece gave a much weaker sound that might have been less bright. Because the human ear is not flawless, this physical data is only based on what I personally heard and not on any type of recorded analysis. After recording, I used a program named wav_analysis from the UIUC Physics Department to analysis the sound. After clipping out the attack and release of the note to reveal a consistent and solid tone, I analyzed the amplitudes of the first 6 harmonics of each note on each mouthpiece. What I found was that the metal mouthpiece seemed to have the lowest fundamental amplitude, which I found strange. Although it had the lowest fundamental, all the other 5 harmonics relative to this had a much greater difference than the other mouthpieces, having a maximum of three times the amplitude of the fundamental for some harmonics. All the mouthpieces were similar in having a high 3 rd harmonic, but only the wood and the metal ones had this as the highest amplitude. The plastic one showed a significantly higher 2 nd harmonic, meaning that the harmonic that we hear most predominantly on that mouthpiece would be the 2 nd. On the other two mouthpieces, the 3 rd was the highest, so we would hear that one the most

5 predominantly. All three mouthpieces also were similar in having the fundamental being lower than most of the harmonics, with the 6 th harmonic being the lowest for each and every one. I can imagine that any later harmonics beyond 6 were just as low or lower than the 6 th compared to the rest of the amplitudes, but my data only shows the first 6 harmonics. 2nd 3rd 4th 5th 6th Metal Plastic Wood

6 Next, I analyzed the relative phase differences between the three mouthpieces. I noticed greatly that the metal and plastic mouthpieces had very similar relative phases, probably close enough to be undetected by the human ear. The very slight differences were that the 4 th and 6 th harmonics for the plastic mouthpiece were slightly more skewed and out of phase compared to the metal one. Also, the plastic s 3 rd and 5 th harmonics were slightly more in phase than that of the metal one. This also struck me as strange. However, the 6 th harmonic was almost dead-on accurate for both the plastic and metal mouthpieces. The wood mouthpiece was quite different in relative phase though. The relative phase vs. time graph showed a VERY skewed and seemingly exploded view of the harmonics in order. I was not sure how to interpret this data. Just in case it was a computer error, I analyzed the relative phase of the sound file twice, from differently cut threads of time of the recording. The same basic graph resulted, showing a very high degree of phase shifting (around 25,000 degrees) for most of the harmonics. This did not look anything similar to the other mouthpieces graphs, not even to the order of the harmonics based on positive or negative phase shifting. *** The wood mouthpiece s graph is shown here first, the metal and plastic graphs of relative phase are on the next page to show better comparison

7 Because I only got data to relate the metal and plastic mouthpieces, I continued to use the program s abilities to analyze the normalized amplitudes and phase. This showed MUCH greater results for comparison, because it allowed me to view the harmonic amplitude and the phase shift with respect to a polar graph, so that even the skewed wood mouthpiece s relative phase graph would be represented in the form of what degrees the phases of each harmonic were at. The metal and plastic were similar as I expected from the relative phase graphs, with the exception that the second harmonic was significantly bigger for the plastic mouthpiece, as seen in the analysis of harmonic amplitudes. Between these two mouthpieces though, the phase was very similar. The metal mouthpiece had very definite phase shifts, with the 3 rd at 90 degrees, the 2 nd around 240 degrees, and the 4 th close to 300 degrees. The plastic had the 3 rd shifted a bit more towards the x axis, resulting in about 60 degrees, while the 2 nd moved to 225 degrees and the 4 th to about 270 degrees. The wood mouthpiece amplitudes were the same, as seen in the analysis of harmonic amplitudes, but now I had a chance to see its phase represented on a 360 degree scale. The graph was very different, showing that the fundamental, 3 rd, 4 th and 5 th (most predominant) harmonics were shifted between -30 and 30 degrees of the fundamental. The 2 nd was the

8 exception however, but it was a high amplitude near the highest of the 3 rd, so it is worth mentioning that it was almost IDENTICAL to the 2 nd harmonics of the metal and wood mouthpieces, being around 220 degrees out of phase.

9 Lastly, I was particular about analyzing the frequency to see if I could notice any big differences in tuning, such as the different mouthpieces being sharper or flatter than the others. Looking at their graphs of frequency vs. time of individual harmonics, I clearly see no visible difference in each mouthpieces graph. Each mouthpiece showed little variation (if any) between mouthpieces, so this did not seem to be a factor in differences between them. If there was a miniscule difference in being sharp or flat, the human ear would probably not easily detect it, unless very well trained (that of a piano tuner) or with comparison to a fundamental pitch. CONCLUSION: By feeling, hearing, and investigating through use of a sophisticated wave analyzing software, I came to a few conclusions about the differences between mouthpieces of different

10 materials. Because of their different densities, the mouthpieces should each show a distinct characteristic or trend in some sort of explicable way, but I only found a few pieces of data confirming that. First by examining the harmonic amplitude graphs, the metal mouthpiece showed that the fundamental, although lower than the fundamentals of the other mouthpieces, gave greater difference in ratio when compared to the other harmonics. This proved my hypothesis that the metal mouthpiece could give greater energy in harmonics that gave a trumpet its distinct characteristics. Most of the mouthpieces harmonic amplitudes followed the same trend, except however in the 2 nd harmonic of the plastic mouthpiece, which was higher than the 3 rd harmonic unlike the other mouthpieces. This difference is negligible though, probably unnoticed by even the most trained of musical ears, because the 2 nd harmonic was always close in energy to the 3 rd, and in this case it just shot up a bit more. This all showed me that the harmonics and energies or individual harmonics stay generally the same no matter what material or density the mouthpiece is, as long as it is the same model. From the relative phase analysis, I noticed that the plastic and metal mouthpieces have VERY similar data points with respect to degrees of phase in harmonics. The wood mouthpiece however showed a much skewed graph of relative phases, such that the phase shifting is different compared to the other mouthpieces. This matched my hypothesis slightly, because I first believed that the rigidity of the mouthpiece would be the determining factor in phase analysis. The changes should be detectable, but further analysis was required. When I normalized the amplitudes and showed phase in degrees of a polar graph, it seems that the trend of the harmonics seemed was this: as the density decreased (metal-plasticwood), the 3 rd, 4 th and 5 th (strong) harmonics became less and less out of phase, as they moved

11 closer towards the fundamental. However, the 2 nd harmonic, the second to (and only slightly less than) the strongest for metal and wood but strongest for plastic, moved more and more out of phase as the density lowered. It started at about 240 degrees for the metal then went to 225 for the plastic and 220 for the wood. This might be detectable by a trained human ear if some one was looking for it, but by listening back to the recordings, I did not hear much difference for myself in this area. My hypothesis was wrong in this respect though, because as I originally thought, the less rigid the surface (and the less dense the material), the more out of phase this would cause the sound waves to be. However as you can see by the analysis of the graphs, the wood (least rigid) mouthpiece had more of the strong harmonics centered towards the fundamental, excluding the 2 nd harmonic. I once again could not hear these differences by listening to the sound files, although a more trained ear might be able to detect this change. Last but certainly not least, the biggest altering factor in the difference between mouthpiece materials seems to be the physical differences noted early on in the experiment. The metal was smooth and easy to slot notes and change pitches, while the plastic was very projectable in higher notes, but harder on the lips. The wood was very soft and sticky to the lips, so changing notes and playing consistently were hard. Maybe if the wood mouthpiece was made of a harder wood and polished to a smooth and rigid surface, it might be easier to play on and even produce a different tone. As far as my analysis goes though, the difference between these mouthpieces to a musical listener is minute, but to the player is great.

12 References: [1] "Brass." Wikipedia.org. 13 Dec Wikimedia Foundation, Inc. 13 Dec < [2] Walker, R. Mass, Weight, Density or Specific Gravity of Bulk Materials. 9 Oct SI Metric.co.uk. 13 Dec < si_materials.htm>.