I have been trying to understand why two woodwind bore shapes behave so differently. My understanding is that one end of a woodwind is an antinode (driven by the reed of the instrument) and the other end is a node (where the tube is open to the atmosphere). a - - - - - - - - - - n In the case of the cylindar (e.g., clarinet) I understand how the length of the bore is 1/4 the total length of the wave that would be heard. I can see also that the next possible mode would be 3 x's shorter in period. There has to be an intervening node and antinode. A good visual equivalent is someone spinning a jump rope that is tied to a post at one end. We can get a half loop, or a loop and a half, or two loops and a half: there's always a half loop for the spinning arm/antinode. The result, for a clarinet is that the second mode for a given fingering is an octave and fifth above the fundamental. a - - - n - - - a - - - n This is also a well known part of the defining timbre for the clarinet: that the odd overtones predominate the low end of the frequency spectrum for a given note. I'm having trouble understanding why this doesn't also hold for conical bores. With saxophone and oboe and bassoon, all instruments with conical bores, the second mode is a pure octave above, and all the overtones are present in the lower part of the frequency spectrum. This seems to suggest that either the bell end has become an antinode or the reed has become a node, in order to fit a wave with half the period of the fundamental. NOT POSSIBLE: a - - - - - n - - - - - a n - - - - - a - - - - - n Neither of the above make physical sense, given one end is a reed and the other open to air. Can anyone point me to a good explanation of what is going on with conical bores? I got a glimmer of an idea looking at a discussion of pitch with a flaring brass instrument bell. It seems like different frequencies experience the "node" as being at a different location in the context of the flare (according to a diagram from a book by Arthur Benade). And a conical bore could maybe be considered analogous to a really long, stretched-out flaring. Is there some math that can illustrate or model what is going on, e.g., how the location of a node might be a function of the diameter of the bore of the tube?