I was talking with Jim Antaki, one of the paper's authors, during the Howard Levy "Harp Summit" week in North Carolina November 1998, about his research and findings about the physical behavior of the harmonica. There are some surprising results.
One of the interesting points is that it appears that turbulences like those that cause a power line to vibrate in the wind are required for reed activation and sustained vibration. Here's a quote from the paper:
"In order to cause self-sustaining oscillations, air must flow past the reed in a manner which reinforces this vibration. St. Hilaire et al. have shown that such pressure instabilities could result when air flow is sufficient to cause boundary layer separation at the edge of the reed surface. When this occurs, the aerodynamic drag force on the reed increases as the gap decreases, and the reed moves against the air flow. Conversely, the drag force decreases when the gap increases, and the reed moves with the flow."
The reed moves against the air flow. This is a striking counter-intuitive finding.
"When playing a low blow note...the nominal, or 'average,' position of the blow reed moved away from the comb." This seems intuitive because during a blow the pressure in the chamber increases. BUT... "The draw reed, although nearly idle during blowing, appeared to displace slightly upward, into its respective reed slot and into the comb." So the increased pressure provided by the blow does not push the draw reed farther away from the comb. Aerodynamic effects draw it inward.
And further: "[on] low draw notes...the blow reed appeared to vibrate, albeit slightly... away from the comb." So, also, during a draw the blow reed moves against the airflow, and moves outward. It continues:
"Intuition would likewise dictate that the relative phase between the two reeds would result in their contrary motion: outward with blowing and positive pressure in the hole and inward with drawing and negative pressure in the hole. However, this was observed to be the case only for the high blow notes." What's this?! The notes don't act the same! Continuing "When any of the ten holes was drawn, the reeds were observed to oscillate in parallel with one another."
The reeds oscillate in parallel!? They open together and close together during draws. Very strange.
"Parallel motion of reeds can be interpreted as both reeds acting simultaneously to close, or open, their respective reed slots."
Another interesting finding is that the wave form of a blow note differs significantly from that of a draw note! "In most cases, the blow reed appeared to follow a sinusoidal trajectory, whereas the draw reed displayed a notable amount of superimposed third harmonic..." The diagrams show a little pause of the draw reed right as it crosses its slot. This is not evident for the blow reed.
Also, looking at the wave forms for both draw and blow reeds during a draw bend: ..."the bent note results in an almost composite of the two. The wave shapes and relative position of both the blow and draw reed displacements were observed to resemble those occurring for their respective straight notes. (This is worthy of recognition since the blow reed is no longer operating as a closing reed, but operates as an opening reed.)"
Here's more: "However, for both draw bends and blow bends, counterintuitive parallel motion of the reeds was demonstrated. Most intriguingly, this did not occur in holes 9 and 10."
And more strange with overblows: "The relative phase of the reeds for the overblows studied (holes 3 to 6) was observed to depend upon the location of the displacement transducer [the reed position measurement device used]. When placed near the roots of the two reeds of hole 5 and 6, the phase relation evidenced parallel motion; whereas, when placed at the tips, the motion was is opposition." The reeds are flapping in the breeze.... [my characterization].
"The common rule that bent notes are limited to within a semitone of the opposite note of the hole was substantiated in these studies."
On a lighter note "...a simple experiment was conducted in which a player [Howard Levy], lying supine, played specific fashioned notes and then held the configuration of the vocal tract while the oral cavity was filled with water and the required volume was recorded... It is probable that actual playing volumes were larger than measured, since when water was instilled, constriction of the glossopharynx and larynx occurred in order to suppress the swallow reflex and prevent aspiration."
Or, in Howard's words, "they were trying to drown me!"