Yes, though this only works for open cylindrical bores, i.e. flute-like objects. A cylindrical bore in a reed instrument would enclose one quarter wavelength of the fundamental, instead of one-half wavelength, and thus the length of the cylindrical pipe would be one half that of the conical pipe. This also means the stopped cylindrical bore overblows the interval of a twelfth rather than an octave, and accounts in large part for the big difference in tonal character between cylindrical and conical bagpipe chanters.
It is true however that the theoretical lengths of a closed-conical (i.e. uilleann/union pipe chanter) and open-cylindrical (i.e. flute/whistle) instruments are approximately the same, for any given pitch. This is pointed out in Benadeâs Fundamentals of Musical Acoustics and also Nederveenâs Acoustical Aspects of Woodwind Instruments (p. 9).
Drone lengths are somewhat different, since they are neither simple cylinders nor cones (they are, rather, âsteppedâ cylindrical bores). Things get a little more complicated there, and the pitch of a drone may depend somewhat on the ratio between the diameters of the inner âstandingâ joint and the outer âslideâ joint⌠(I havenât worked out all the math for that yet)
Lastly, as you no doubt are figuring out, âextrapolating to the apexâ of a conical bore is not so simple, there are many variables involved. A straight-line fit from bell to throat is not reliable, nor is even a âfitâ to the closest straight cone. Even measuring from bell to the end of a well-fitting reed is unreliable, as the âeffective apexâ lies beyond the end of the reed, and the âeffective lengthâ of the foot is a little longer than the physical length (it depends on the size and shape of the bell opening)..
Best regards,
Bill
