OK - this one is far less critical than the type you need in SSB receivers.
There are 2 oscillators. They work at a much higher frequency than you could ever hear, into several hundred kHz probably. One or both may have their coil inductance modified by being brought near metal.I am guessing that one, called the "reference frequency" is probably intended to keep a relatively constant frequency, and not be involved in being brought near the metal, but it need not be so.
When two different frequency signals F1 and F2 are put into a linear amplifier, they may have gain, but they do not distort or affect each other. If instead the device is non-linear, like a diode - or in this case, a transistor biased into non-linearity, near cut-off, or clipping, then you get some multiplied products of the originals as well.
There will be the original F1 and F2 in there, but also there will be some at frequency (F1+F2), the sum, and also (F1-F2), the difference. In this circuit, it is the difference that is used.
Known as the "beat frequency", it is the same principle as you would hear if you tweak a string on a guitar, while the same note is played on another instrument close by, and one is tuned a little. As the notes get closer to being the same, you hear a throbbing, or beat which gets slower and slower as the notes match. The beat frequency is the difference, and it gets very slow until it disappears, and the notes are the same..
The oscillators are a high frequency version of the same phenomenon, and the whole idea is great sensitivity. If both oscillators A and B are going at hundreds of kHz, then it only takes a tiny relative change in one to produce a very noticeable (audio) difference frequency.
Q1 and Q2 are the oscillators. Q3 with Q4 are the non-linear mixer-audio combination. It looks as if Q3 is the mixer, then the capacitors filter out the sum component, leaving only the difference. Q4, Q5 and Q6 amplify the difference audio frequency enough to drive the speaker. There will be some part of the procedure where the oscillator is "set zero beat" at the start condition, and from then on, any metal nearby that would affect the inductance, and pull the frequency, which should result in a very audible note, getting higher in pitch as you get closer. You might also hear variants, such as the note dropping to zero beat, then rising in pitch again.
In all of this, it is no big deal to just wind the coil to a physical size that suits you. Provided both have the same inductance to get to zero beat, thats OK. Even if one coil is different dimensions, it can have turns added or removed to get the oscillation frequency to match. Here is where I think the nut being moved on the pipe .. is the way the initial oscillation frequency is set.