Does There Exist a Trade Off In Bore Geometry for [Concert] Flutes?

As a reply to a post on Flute Forum that segued from how a flute played easier in the altissimo range compared to the regular, with the poster musing about conical versus cylindrical bores, and asking if there is generally a trade-off between ease of play in low and high register:

Short answer: yes.

Less short answer: it's not "just" about cylindrical bores versus conical bores -- the bore's inner diameter, the stopper position, tone hole positions, the size of tone holes, and the relative outer dimension at the tone hole (or tone hole height for the Boehm flute) matter as well. Acoustic models often simplify the flute to an open pipe ideal, with a column of massless air molecules that instantaneously form stationary [longitudinal] waves when a suitable energy source is provided.

But the reality is that real flutes have real air molecules with real mass/inertia, and we don't excite the end of the "open" pipe directly (we do it transversely), relying on the stopper to "bounce" our real energy source through with losses from all the air molecules' inertia, whether they are moving longitudinally down the pipe or venting through a tone hole. This means that the kinetic energy received from the air molecules farther from the embouchure hole is significantly less than the air molecules closer to the embouchure hole where the driving force (our air stream) is. Not to mention that sometimes, if the energy imparted is high enough (like playing high register notes), the air molecules farther away may still have enough energy to continue on beyond where they are "supposed" to "stop".

Long story short, without suitable engineering compensation, your flute will be horribly out of tune when you don't take into account all these real losses that the models simplify away when they are trying to explain things. "Cylindrical" bores and "conical" bores are just simplifications of the two broad compromises in flute design -- "cylindrical" bores have slight tapers nearer the head joint while the majority of the flute (i.e. the body + foot) are true cylinders; while "conical" bores have their tapers towards the foot of the flute body, with the head joint retaining a more or less cylindrical shape.

The ease of playing in low and high registers with respect to these two design choices is subjective. Humans are highly adaptable, so the real question is which of these two designs results in a flute that is more in tune with itself. A flute that is more in-tune with itself (i.e. when you overblow the pipe to select the appropriate standing wave mode, they form integer multiples of the fundamental frequency) will be easier to play across the registers. As to whether you can REACH the high notes, it depends on how easy it is to force anti-nodes at places where you WANT the wave length to be shorter (i.e. where you open your tone holes, and their sizes).

That said, I'm not the most knowledgeable about this. 😅

To add on a little for things that I didn't have the chance to write more about because it is, after all, still a Facebook post despite the length, real-world instrument making has many musical/artistic expression considerations that need to be taken into account even before the specific engineering trade-offs are chosen. The concert flute, for instance, had its shaped drastically adjusted and its first register flattened just so that its ambitus can be raised from the traditional 2 octaves and a fifth to a full 3 octaves, while overtone flutes like the fujara has the ratio of its inner diameter to bore length reduced greatly to facilitate the production of overtones instead.

I would go as far as to say that in many cases, any differences in musical/artistic expression considerations end up with that particularly designed/made flute being designated differently---you can see this even in the Wikipedia list of flutes.

But for my internal learning reasons, I tend to group them differently to facilitate cross-system training, keeping close mind to how to express the actual music with the particular flute, while also observing the subtle differences in choices for the positions of the tone holes. That latter bit usually does not affect the lowest register of the flute in question (it's usually a diatonic major scale, or rarely, some minor scale like the shakuhachi's pentatonic minor scale), but it does affect what kind of middle/high register pitches we can attain.

In the end though, as what sifu said before: we adapt to the instrument; the instrument does not adapt to us---that is the very fundamental fact. It is after our experience from adapting to the instrument that we eventually learn of its limitations, and then decide if those limitations are truly stumbling blocks for our expression (in which case it is time for a ``better'' version of the instrument), or if they were deliberate artistic choices.