Qualitative Analysis of the Trombone
By: Gregory Caceres-Munsell
Professor Errede
Physics 193
The Trombone is one of the most iconic instruments of our time, and historically one of
the most underestimated and surprising in its lasting influence. That known, I longed to look
more into why it is what it is: a sort of under the hood look at its appeal and ability, the causality
of a people’s love for it. Along with this I also sought to understand what differences can be
noted in a muted color - as mutes for brass instruments do not serve primarily to quiet it but to
change the effect of its sound for the listener’s sake - as well as briefly analyze differences
between varied recording equipment with consistent use of the trombone. My trombone is a
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Conn 88HO with F-Attachment (specific specs: .547" [13.89mm] bore, .562" [14.27mm] bore
through F attachment, 8-1/2" [216mm] rose brass bell, rose brass outer slide, 5G mouthpiece);
for the sake of research accuracy and understanding, I put forth that instruments, even of the
same type/maker/material can differ in consistency and sound quality, so that the results found
here may not represent all facets of the trombone’s sound and output.
Initial analysis consisted of recording in house with higher end equipment (The Marantz
PMD-671, 24-Bit Pulse Code Modulated with *.wav format data; digitizing frequency at 44.1
KHz, though it is competent for up to 96 KHz; recorded using a PMD-671 digital recorder with
flat frequency response from 20 Hz - 20 KHz) to view qualitatively and quantitatively what
occurred across multiple octaves, with alternate positions, and at neighboring notes along the
middle range; then additionally repeating all these steps and MATLab breakdowns with the
mentioned mute - a Stonelined straight mute on the Conn 88H, a noticeably darker sound
trombone of itself; later performing similar analysis with the alternate recording equipment: a
simple ear bud jack hooked up to audio interface - including amplitudinal display and an
Ethernet connection, feeding information to MATLab.
The initial analysis with The Marantz PMD-671 covered the above array, specifically in
the form of long-tones which contain the most consistent data in a three to six second time period
in the middle of the recording frame. This accounts for only about a fourth of the recording time,
but initial attack and ending decay as well as time taken stabilizing the pitch and volume are all
included in the recording. From there, clipping the time frame with the least amplitudinal
discrepancies is all that needed to be done on in house. Since the middle range notes showed
comparable results across frequencies, F3 is the example note here used in portraying analyses,
though Bb3, D3 and C4 were all recorded and observed.
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Most notable in the analyses performed by MATLab: the side-by-sides of Phase,
Frequency, and Amplitude VS Time graphs, and the Amplitude VS Frequency). For The Phase,
Frequency, and Amplitude VS Time, I found the differences formed by alternate positions and
altered tone color of particular interest, as they reflect the actual difference in sound that each of
us can clearly recognize upon hearing (with trained ears or not). Not to be used as the whole or
indicative of the full quality of a note, but as a comparison between the varied states of each item
listed above, the graphs below show just the fundamental and second harmonic. They are
presented in the following descending order: Trombone first-position F3 (normally around 175
Hz), Muted first-position F3, Sixth-position F3, and Muted sixth-position F3.
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The first thing to note in these graphs is most significantly the Frequency VS Time for
F3; although the natural occurrence for F3 lies at approximately 174.61 Hz, the fundamental F3
in the in house recording yielded somewhere between 175 Hz and 176.25 Hz. Although it
reflects a very small discrepancy in pitch, it can still be fairly noticeable; most clearly at T = 2
seconds, the discrepancy can be about as high as 16 cents off (based on a Log scale reflecting an
approximate difference of 1.00 to 1.50 Hz, where 5-6 cents is generally considered the “just
noticeable difference”). To a trained ear even a discrepancy of those few 5-6 cents can be clearly
discerned and interference inducing, so all the data that follows from knowledge of this
discrepancy should be taken with grain of salt. From there the portions most worth observing are
the comparisons across the alternate positions and altered color, since upon very brief
observation it’s clearly seen that the fundamentals and 2nd harmonics (within a determined
trombone position and progression of time) are mirrored almost to a T, save their difference in
value of course.
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[This representative difference in value can be seen graphically on page 7].
Unfortunately, definitive data did not result from the muted sound, since first position F3 withmute was sharp relative to the initial F3 while the sixth-position muted went down in pitch.
Although the general tendency for a straight mute is to sharpen the pitch, simply tossing the
sixth-position data would be inconsistent with the interests of this analysis, especially since the
first-position with-mute is at this point significantly higher in pitch than an F3 ideally would be
(nearly a quarter-tone so, in fact). That known it seems more fitting to simply discard all mute
data, although there wasn’t so much of a discrepancy for other pitches, I’ve dedicated this overall
analysis to F3, so as to remain consistent and without major flaw that’s what we will rely on to
draw conclusions on the general quality of the trombone’s sound. One thing we will take from
the muted sound is knowledge that the frequency change over time was noticeably amplified
which naturally results in the warmer color performers desire so fervently when making use of
straight mutes. From there all that are left are the comparisons for initial and final values for
Phase and Amplitude with respect to first and sixth-position F3 and the absolute mins and maxes
for each; the frequencies appear to be in comparable range so they will be treated as though with
equal standing, although it should be noted that alternate positions can often result in distorted
pitch. Luckily no such distortion occurred here, which is ideal, however it does not reflect a
general trend - especially for the less experienced in making adjustments for this. Back to the
Phase and Amplitude then, we notice that primarily there’s near no difference in value for initial
Phase. Afterwards the similarities end. Though they are within comparable range, the absolute
min for first position F3 is much lower than sixth (in fact the sixth position Phase never drops
below its initial) while the max for sixth position Phase is significantly higher than that of first
position (interestingly enough the sixth position fundamental max was even greater than that of
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the first position 2nd harmonic). For the Amplitude, again, not much similarity; in fact, they
scarcely even occur in the same range. The most notable observations are that sixth position
amplitude has much more of an even spread, without much variation, while first position sustains
greater resonance over time.
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Although there was little to do with the ear bud amplification, it still seems significant
enough to observe, if only briefly, the differences between in house recording and the clearly
unrefined recording device. Of greatest importance in understanding this comparison is the fact
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that (although recording conditions for in house were not completely ideal) the ear bud recording
could be even more hampered than this by the presence of heavy background noise and poor
room acoustics in which we collected data. This comes into even greater effect when we take
note that impedance for these ear buds was by nature extremely low, and they act very poorly to
keep out exactly this kind of background noise and even harmonic frequency spacing.
[Directly below: In House recording, then Ear Bud recording, respectively]
Of significant consequence was the bit of extra noise tagged onto the ear bud reading right before
the fundamental occurs, as well as an upwardly cascading harmonic spread.
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In all, there were many factors that could have created inconsistencies in data, which
surely influenced data outcomes. If these analyses were to be completed again it would definitely
be ideal to perform them in more isolated conditions, from traffic noise due to the time of day to
the heavy disturbance from ventilation and poor room acoustics (in house recording included),
results may well be consistent with each other, but not nearly as reliable as is best for a
qualitative analysis for the instrument as a whole. Additionally, I would have made attempt at
reading various models of the trombone, understanding large bore vs small bore sounds, and
experimenting across a larger range. Another significant issue would be the use of equipment in
acoustically resonant environments, as well as the time allowed for equipment to get a good
reading; for the sake of absolute certainty on amplitudinal behaviors I would have better made
sure that the time period over which I took data were longer, with great care to also establish a
closer-to-true fundamental for each note. If that were to be accomplished it would then be of
great interest to attempt varying degrees of sharp and flat pitches and compare results, behavior
consistency across harmonics, and possibly even recorded layering of off pitch notes with their
respective true fundamental to see the exam quantitative results of the sound wave interference
we know so well as “bad tuning.” This would open many doors into specific research for ideal
situations considering ‘true pitch’ versus relative pitch ideals depending on song, setting, and
style that we so often see ourselves adjusting for. These questions of quality in sound based on
frequency and slight amplitudinal interference can be of great interest, and I hope that this data
does, in fact, provide opportunities for deeper insight into these subjects.