I needed a quick alarm tone generator for a piezo speaker, and with no 555 at hand, this turned out to work quite well, and it’s just as small. It operates with just a few mA current. It is a 1950’s Baxendall circuit from this paper.
A toroid from Amidon (FT-37-43) was used and 40swg enemelled (about 36AWG). Anything thicker won’t allow the turns to fit. There are 100 turns on the collector coil (ends painted green in the photo below).
18 turns of feedback coil (connected to transistor base) was wound on top, spaced out. The circuit consumed about 6.5mA for me (change R2 for a louder sound if needed, but it was loud enough). R1 is not a critical adjustment, it could be replaced with a couple of resistors if needed. It can run from a lower voltage with no modifications. At 1.5V, it was still emitting sound (lower volume), with 0.7mA current consumption.
C1 is to some extent dependent on the piezo capacitance, but you’re virtually guaranteed to hear a tone at some frequency in the correct ballpark, with the capacitor mentioned and the same toroid and windings.
The coil was partially wound, then the winding was held in place with some impact adhesive, then the rest of the coil was wound and secured with adhesive again. The ends were marked for this coil (just used some acrylic modelers paint). The 18-turn feedback coil was just wound on top, and was left unmarked. The values of 100 turns and 18 turns were just guesses – to have enough inductance on the collector winding (it will be around 3.5mH with this coil incidentally), and to have enough coupling and feedback with the second winding. With the inductance set, C1 was then picked for oscillations at a few kHz. The trace across the piezo is shown here.