Thank you for your encouragement Richard. Success, a full octave! Sometimes I wonder if what I want to do is as interesting as I think!
I followed the drift of what you said, suggesting that the longer the barrel the more chance of achieving an octave. I used a piece of Turkey oak (from a tree felled in our garden) a bit longer than the length of my longest bit, an 8mm auger bit, this let me create a hole to enlarge and as a guide at the end for the piston rod. I enlarged it, a little at a time, with several different sizes, ending up using a 12mm masonry bit the only one I have long enough, unfortunately this left the bore rather rough which need sanding with a bit of abrasive fitted to the end of a dowel. I then turned a piston to fit on an 8mm dowel, after a lot of easing it slid up and down. I then cut the notch for the reed and made the plug with a flat. At first I couldn’t get a note but after increasing the width of the flat on the plug I got one. The piston didn’t reliably change the note so I fixed a bit of leather to the end to create a better seal and managed a scale. After a bit more fiddling with the plug and filing the notch so it was very smooth I got a reliable scale. Turned the knob and glued it to the end of the piston rod. Because of the roughness of the inside of the barrel the slide action is a bit jerky. If I make any more I will need to get a better very long 12mm bit.
Length of barrel 190mm.
Bottom note Distance from “reed” to furthest position of the piston 133mm i.e. maximum extension.
Other end of a scale from “reed” 55mm .
Range from one end of the scale to the other 78mm. I have no idea what key this scale is in!
Overall length 215mm.