I recently saw a reference to Frank Campos’ book, Trumpet Technique. In it, Campos tells of a story by Reynold Schilke.
. . . Arnold Jacobs and a tubist from Japan were trying out a new tuba in front of an electronic tuner. After Jacobs played, the tubist from Japan found he had to pull the tuning slide considerably farther out than Jacobs to play in tune. Schilke was curious about why the same length instrument would not play in tune for both men. After some investigation, he determined that Jacob’s oral cavity was much larger than that of the Japanese tubist, and that the vibrating air column created by each player originated within the oral cavity at the back of the throat, rather than at the mouthpiece. In this case, the air column was longer for Jacobs due to his larger oral cavity and shorter for the Japanese tubist, and this required a change in the length of the instrument to match the tuner.
– Campos, page 85
I located an article here, supposedly handed out by Schilke at brass clinics. In it he writes,
At the last point of rarefaction, which occurs in front of the bell of the instrument, a standing node is formed which gives a rescinding node going back through the instrument and culminates itself in the larynx of the performer. This is the reason why performers with different sized oral cavities will play the over-all pitch of the same instrument differently.
This is described a little differently in this article here, from the University of New South Wales Music Acoustics department. The authors state,
The instrument is open at the far end or bell. But it is (almost) closed at the other end. For a sound wave, the tiny aperture between the lips – which is on average a much smaller cross section than the bore of the instrument – is enough to cause a reflection rather like that from a completely closed end.
Later in that article they go on to state that there are actually two resonators involved with a brass instrument, not just the single one that Schilke hypothesizes.
Finally, we should mention here that the player’s lips actually interact with two resonators: those of the bore of the instrument, and those of the vocal tract. The instrument’s resonances are usually much ‘stronger’ than those of the tract, but the latter are still important.
My (admittedly non-expert) understanding of the physics involved is that the USW source is more correct. I don’t see how the size of the vocal tract actually changes the pitch by lengthening the vibrating air column since it happens between the lips and bell and not the bell and larynx.
I don’t necessarily agree with all of the conclusions drawn from the USW researchers either, though. In 2003 they published a paper in which they detailed the results from modeling both didgeridoo and trombone lip reeds in order to measure the acoustical impedances. For a didgeridoo, the influence of the vocal tract is quite prominent.
However, to make clear formants, the peaks and troughs in the impedance have to be really strong – the vocal tract has to have very strong resonances. If you have your vocal folds wide open, in the position normally used for breathing, you don’t get strong resonances because the lungs absorb energy at these frequencies. Instead, you must learn to keep the vocal folds almost closed. They are almost closed in speech, which is why speech has strong formants.
Where the authors go wrong, I believe, is here.
The glottis is modelled by a plate separating the trachea from the vocal tract. The plate has a round hole with smoothed edges. Its diameter is 5 mm, chosen because proficient wind players are reported to keep the vocal folds almost closed while playing.
Proficient wind players keep the vocal folds almost closed while playing? From what I can tell, this is exactly opposite of what most brass players actually try to do. In fact, traditional brass pedagogy emphasizes playing with as open a throat as possible, which greatly lowers the resonance of the oral cavity as much more of the sound gets absorbed by the porous lungs. Still, they did check this out with live trombonists too.
The shift in pitch, over the range studied, is typically 20 cents: a musically important effect for intonation. Preliminary measurements on experienced brass players showed a comparable shift in pitch when they were asked to lower the tongue, keeping all else constant.
So there does appear to be an effect on intonation happening in the oral cavity. What’s not addressed in the paper, unfortunately, is what the effect of blowing the air through a smaller opening has on the speed and pressure the air is striking the lips. As per Bernoulli’s Principle, forcing a fluid (like air, in this case) through a smaller opening is going to increase the speed that the air is traveling as it strikes the lips. Raising the tongue while playing makes the air strike the lips at a faster speed, while lowering it slows down the air speed before it strikes the lips. There’s a nice interactive flash demonstration at that link where you can see how this works.
This stuff goes over my head fairly quickly and I probably don’t have as good an understanding of all the physics as I’d like to think. I’m left with three hypotheses, perhaps which none of are completely accurate.
- The vibrating air column that produces the pitch on a brass instrument is between the bell and the larynx, as suggested by Schilke.
- There are two resonances that interact with each other, the primary one being the vibrating air column inside the instrument between the bell and the lips. The resonances from the glottis to the lips also effects the resonances inside the instrument, as suggested by the USW researchers.
- The effect on the pitch when lowering the tongue is related to the air pressure at the lips, not a resonance frequency inside the oral cavity.
Schilke’s explanation I think is just wrong. The USW conclusion seems to be drawing conclusions about brass technique based on didgeridoo playing, which has a distinctly different method of playing compared with orchestral brass instruments. My explanation is that of of non-expert and, as it turns out, is somewhat incomplete too.
For help with this, I turned to Vincent Freour, a PhD candidate in acoustics at McGill University in Candada. He was kind enough to respond to an email and sent me a link to his article describing a recent presentation he gave, Vocal-Track Influence in Trombone Performance.
I have to admit, the math of his article is a little hard for me to wrap my brain around, not having an academic background in physics. I was aware that as the brass musician plays higher, the reflections of the standing wave at the bell move closer to the mouth of the bell, resulting in less energy reflecting back to the lips. After a certain point, the bell begins to behave more like a megaphone, in part making it more difficult to play in the upper register.
Vincent explained to me that at the role of the tongue in the low and middle register is probably to shape the air stream and that the air pressure is regulated more by controlling the respiratory muscles and the lips. When the player ascends to the point where the standing wave reflection no longer provides a strong support to the lips that the tongue helps to tune the vocal track so that it helps contribute the the lip vibrating.
While I’m still left with questions, one thing that seems quite clear is that the tongue arch is an important part of brass playing and shouldn’t remain static in the mouth. The physics involved also help explain why some players will have different methods of positioning the tongue, adjusting to the variety of vocal tract size and shape that we find with different players.
Update: It turns out that I’ve got some more studying to do, as I’m a little off in my description of the physics here. As soon as I’ve got a better handle on this topic I will post a correction.