"Perhaps flutists are more puzzled by the "parabolic head-joint" than by any other feature of the modern flute. The contraction in the bore is undoubtedly determined by experiment, and not by any mathematical calculation based upon the properties of the parabola. The translator has measured and plotted the curves of perhaps a hundred flutes, among which are specimens of nearly every celebrated make. Most of these curves do not in any way resemble a parabola; such resemblance as is possessed by the few may be described by saying that the curve which at first departs but little from the straight line, bends more and more rapidly as it progresses. But sometimes the portion with the greatest curvature is next to the cork and sometimes next to the tuning slide!"
Dayton C. Miller
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