jus a few intrest questions: what level of conicity, (if that is a word) is needed to make it more like a sax. let`s say the tube is 1.5 mm thick and you make it conical by machining and leaving the top rim 1.5mm and the bottom rim 0.5mm. I think (imagine) this will allready lead to a more sax like sound. But does this mean you have to alter the fingering placement?I have been working on making something similar since Oct 2010. The Maui Xaphoon (and its plastic brother) are direct descendants of the HFP, same holing, same fingering. Mine, the Hot Water Pipe, is slightly different (see img).
The reason it sounds so low with such a short tube is that it partakes of Clarinet acoustics, not sax acoustics. Saxes are conical bore instruments (along with oboes, english horns, and bassoons) and the wave length of the lowest note is equal to (about) 2X the length of the tube. The clarinet is a closed-end cylindrical bore, and the wavelength of its lowest note is about 4X the length of the tube. You get a lot of bass per inch with the cylindrical bore. You also get only half the overtones (you get the odd ones).
The other big difference between them is that the Conical bores overblow at the octave, which keeps everything nice and consistent for the second register, fingering-wise; whereas the Cylindrical bores overblow at the 12th, which means that your second register begins at the fifth note of the octave, giving the little horn quite a range. I can produce reasonably musical notes over a 2-octave range, and a few more notes (completing the second register) that are neither reliable nor particularly musical.