I apologize for the erroneous length figures in my previous post. Not having a sax at hand, I used the lengths given by Olson in his textbook, which, when I consulted with actual sax players, were obviously wrong. Shame on him (and shame on me for not checking further).
Sill, the sax vs clarinet question is easy to answer, and though I was a little off on the lengths, the principles are the same as described previoiusly. The soprano sax is about 700 mm long compared to the clarinet's 670 mm (now I am using the figures from the website
www.phys.unsw.edu.au/~jw/saxacoustics.html).
The sax is basically a closed conical pipe having its fundamental wavelength at twice the length of the pipe and the clarinet is basically a closed cylindrical pipe having its fundamental wavelength at four times the length of the pipe. Thus the fundamental frequency of a conical pipe should be about an octave above that of a cylindrical pipe of the same length. The fact that the Sax (lowest note Ab3) is not quite a octave above the clarinet (lowest note D3) is because of several minor factors. It has a slightly longer length, and the end effects of the bells and mouthpieces are slightly different.
A little research is a wonderful thing!
