"Flat Foot" Explained
More sophisticated flutes are longer at the foot, reaching down to C. If keys are absent, the last two holes are called vent holes, speaker holes or dummy holes. Even if extra fingers are required, C sounds out of the end of the flute, C# sounds out of the lowest hole and D sounds out of the second hole from the end. Here is the beginning of the problem: in the long flute, D sounds thru a side hole, not out the end as in the short flute.
Another observation is that the diatonic flute has generally small holes (say 40 to 50% of the bore, not 64 to 82% like the main holes of a modern flute). If we expect the long diatonic flute to honk on low D, then we want D to have a big hole, no? The trouble here is that enlarging the hole stretches the octave (and that hurts the tone, too). Worse, when the diatonic flute goes from 6 keys to 8 keys (to gain the faculty of playing low C# and C), we cut pad seats around the bottom two holes. These cuts make the wall thinner, stretching the octave even more. Logically, the vent-hole design (without pad seats) has the advantage here.
Perhaps some of the trouble comes from another location? Let’s go to the other end of the flute, up to the C# hole (it’s often the tonehole closest to the blowhole). This position is a pressure node for D1. Even when a finger seals this hole, there’s a cavity underneath that adds volume to the bore (a perturbation) at this critical point, and that cavity sends D1 down in pitch. Theobald Boehm made the tonehole chimneys (wall thickness) very small, gaining some advantages (while losing others).
So, D1 is flatted with a stretched octave. Well, if the flute designer has a stretched octave to deal with, he must choose to make a flute on which D2 is sharp, or one on which D1 is flat. If he, in the first case, makes D2 sharp, this note will be wrong in relation to its adja¬cent notes: the player will constantly be tripping over a bad note near the middle of the compass. Also remem¬ber that 8-key flutes of the early 19c were expected to play into the 3rd octave; a sharp D2 would cause trouble here. In the second case, the maker can move the hole down the bore, making D2 give correct pitch while D1 sounds flat. If he flats the notes in that neighborhood for consistency, and if he relies on lipping for these notes at the low end of the compass, then the flute-playing public will forgive him, but not in the first case.
In summary, "Flat Foot" is a design problem that results from a conflict between expectations (to reach low C, also play D with power) and construction limits (a stretched octave due to large holes and thin walls at pad seats). Flat Foot is a compromise that results naturally from those inherited constraints.
To maintain octave registration with resonance and power on low D, the "SIGNATURE" model flute employs traditional design details in an original combination: in the foot, the toneholes are not sunken but raised in order to make a taller chimney; the chimney walls are profiled in a gentle curve with a bias up-the-bore; the tailbore is increased; and the size of these toneholes is limited. Please remember that Albert Cooper departed from Boehm's original design by decreasing some hole sizes. In doing so, he improved tune and tone, thus setting a new standard. Of course, these details are part of a system to ensure resonance, response and playability for all notes on the "SIGNATURE" model flute.