I have hand-wrapped a couple of air core tube coils/solenoids with 50 gauge wire (0.001 inch diameter). My goal is to obtain a resonant frequency of ~10 khz without the use of a capacitor and to keep the coil length (not the length of wire used) to ~3 inches. The first coil I wrapped is far too fast at a resonant frequency of ~148 khz. I then wrapped another coil but this time completed two layers. For the double layer coil I made sure to maintain the wrapping orientation using the right hand rule for both layers (i.e. the first layer was wrapped over-to-under and the second layer continued this over-to-under pattern). The second layer was started at the end of the first layer and was wrapped back towards the first layers starting point. Both layers are the same continuous piece of wire.
Channel 1 (yellow) is just the gate signal for a transistor and is left in the image as it is the trigger for the scope, Channel 2 (purple) is what I'm after. Besides the coil change there is no other change to the circuit or the microcontroller program controlling it. There is a layer of regular scotch tape between the two wrappings. Another interesting point is that after (tearfully) dismantling the first two-layer attempt I had the idea to remove only the outer layer and hook up the inner layer to the o-scope. This "rang" as expected and looked very much like the first image posted here.
On a more human note I'd like to point out that hand winding each coil with such small wire is a process that takes many hours and leads to strained eyes and hand cramps :) Since the length of the wrapped coil is ~3 inches and each wrap only accounts for ~.001 inch of that 3 inches, this process took around 6000 wraps... and this not counting screw ups! If it took less time and effort I would just try the other obvious configurations before coming to StackExchange with blistered, trembling fingers and crossed eyes. But it does take so long and so here I am.
Where did I go wrong?