The authors make a convincing case that the hard D is an example of what’s known as double Helmholtz motion, also observed in violins when the bow pressure is inadequate. The reed actually closes twice in each cycle of the note. “The soft D corresponds clearly to a Helmholtz regime with a short closing episode and a longer opening episode. For the hard D two closing episodes separated by a short opening episode can be observed during one period.”
“The overall difficulty of playing and settling the many reeds to play in tune makes it a story of lore with sometimes a feeling of hell (when out of tune !), not far away from heaven (the hard D when everything is in tune and stable), with such an instrument.”
Seems to my ear like the Hard Bottom D is similar to the Kaba on the Bulgarian Kaval, more or less Bottom D and Middle D sounding simultaneously. The reed vibrating at twice the speed of Bottom D would make sense, no?
With practice you can do that on flute, play notes that are half the lower octave and half the middle octave blended together. You can increase or decrease the relative presence of either octave.
Yes and no. A dose of middle D would put the second closing mid-way between two closings for bottom D. For hard D, the second closing isn’t in the middle; you get two closings near each other, and a longer open time before the cycle repeats. This kind of asymmetrical cycle would take a lot more high harmonics.
Thanks to Philip Westwell, via BigDavy, we have a slow motion video of hard D in action, that clearly demonstrates the asymmetrical double closure on hard D.
Since you can get a jump on a high A by starting a bottom D with excessive pressure (or dry air, as it is here now), it may be the extra note in the mix is a touch of a flat high A. That would produce the asymmetrical motion seen in the video
Lovely paper and worth sharing - for pipers and fluters at least.
Yet some “critique” (apart from the “notorious” woolen pipe nonsense):
A good few chanter-reed-combinations do indeed produce a Hard D (or more generally speaking a Hard-Bottom-Tone) simply by increasing the pressure slightly (Tuut - Mööp ) - no A-gracing necessary (preferably flat chanters but by no means solely).
) - no A-gracing necessary (preferably flat chanters but by no means solely).