It's funny, I was just thinking this morning about an old article in (I think) Television magazine that I read in the 80s when I was getting into electronics. The author was talking about some service notes he'd received for a particular model of Philips radio, which had just come out, and it was when shops tended to have their own service department that would repair things right there in the shop - and also, apply any "factory fixes".
One such fix was described as "Fix VIUPS", and involved changing a couple of resistors and adding a couple of capacitors. Not really any difference, but the author did think it seemed to make the amp a bit more stable and less inclined to make squealy ploppy noises at high volume when the battery was low. But, curiosity got the better of him, so he rang the Philips rep - what's this "VIUPS"?
No idea. But I'll get hold of someone at head office you can ring. Okay, what's this "VIUPS" thing? No idea, said the head office guy, but I can put you in touch with one of the factory engineers in Eindhoven.
So, a call came in, an international call! Quite a big deal in the 80s. "What's this VIUPS Fix thing in the service notes?" he asked the guy.
"Aha yes", he said in a heavy Dutch accent, "the VIUPS is the noise the set makes when the fault is present."
VIUPS VIUPS VIUPS. Yup.
The most easy way to annoy a neighbor using AM radios, it's using a regenerative AM receptor with too high gain. Could oscillate and begin to emit noise at the same freq that are you tuning. Adding a simple carbon microphone to it, and setting the gain to the max, was a very easy way of building a AM radio emitter.
I made a program that generate random topology and uses spice simulation to find if it oscillate. The goal was to find some novel LC oscillators. It worked, it found many different oscillators. I let it ran for a while and soon I found out that the simplest possible LC oscillator has 1 inductor, 2 capacitors, 1 resistor and 1 transistor. I found many different variations of it, I called this class of oscillators "LCCRT oscillator" and it also always had 2 internal nodes so that's not very large search space (40000 combinations) so I generated all possible combinations and I found out there are exactly 12 distinct LCCRT topologies.
Basically any time cap connects to a rail it can be placed to other rail as well, and any time one rail connects via resistor, the resistor can also be moved to other rail. This creates 12 possible combinations. I tested them in real life and they are stable, even used one in metal detector.
Of course it found many different topologies. Some times they were unique, other times they could be simplified into already found oscillator. It can also use multiple transistors not just one. You can find entire project on github, it is a ngspicejs script: https://github.com/dvhx/lc-oscillator-finder
One of my favorite books is Tremaine's Passive Audio Network Design, seems appropriate right now. Passive circuit design is great fun and a lost art.
Never lose this
You want a frequency generator that oscillates with a constant period/frequency. Even an unbalanced oscillator can just be divided by two to provide uniformity. However, it turns out that building something that is not sensitive to any outside inputs (temperature, strain, voltage, time, etc) is really hard to do over a very wide frequency range (from ~DC to many MHz), but from that you can build a stable clock.
Look up Allan Variance, if you're looking for bit of a rabbit hole on clocks and oscillators and other sensors.
The first being the "Two Transistor Metronome" that I can't even remember where I saw first - possibly Electronics Today International or Hobby Electronics, although Practical Electronics was a contender - we didn't get that one much though. I remember my dad and I building this when I was probably about seven or eight, and I've built loads since.
It's a relaxation oscillator where the two transistors form more-or-less an SCR, which fires when its (negative-going) gate voltage exceeds its anode voltage. Kind of.
A similar circuit using three transistors and a diode is used in the oscillators in the Roland TB303 and Korg MS10/20/50 series, with a current source used to set the capacitor charging time so you get a nice linear sawtooth. Conveniently the expo converter turns an incoming control voltage into an exponentially-rising current, which is just what you need!
I guess hobbyists nowadays are just using SI5351 and calling it a day.
Well... Using a NOT (really a NAND) gate was a very classic way of generate clocks for discrete logic.
Why the first two circuits fail is also pretty obvious without derper circuit analysis: to get reliable oscillation you don't only need amplification, you also need some time setting element, usually in the form of a capacitor (or involuntary capacitance).