A radio transmitter that is tuned to transmit at one frequency will also naturally emit signals at multiples of that frequency. This is because the basic transmitter circuit is an oscillator and oscillators naturally oscillate at multiples of the frequency they're tuned to oscillate at. This base frequency is called the fundamental and the multiples thereof are called harmonics (although the fundamental frequency is also called the first harmonic, so if the fundamental is 100 kHz then 200 kHz is the second harmonic, not the first). This phenomenum is similar to resonance in musical instruments, except that it's happening with radio waves, not sound.
In a radio transmitter these harmonics are undesirable. If your station is authorized to operate on 1000 kHz, you don't want it also transmitting on 2000 kHz, 3000 kHz, etc., frequencies that you're not authorized to use. So radio transmitters include circuitry to suppress the harmonics, to prevent them from being radiated.
Sometimes, however, these measures fail and then you can start to hear harmonics on the air, sometimes at a considerable distance from the station. That's where the subject becomes interesting for DXers, some of whom find harmonics to be an interesting target to seek.
While I was checking out the mediumwave band from my hotel room here in St. Anthony, NL, I came across a fairly strong station carrying CBC Radio One (English) on 1200 kHz. There are no CBC stations on 1200 kHz anywhere in eastern Canada. I immediately checked 600 kHz, where local CBNA is located, and found that it was the same programming. So this must be CBNA's second harmonic. I was only a couple of kilometres from their transmitter site so I wasn't surprised to pick up the second harmonic - even a properly tuned station can still emit very weak harmonics that are audible close to the transmitter site. But this one was very strong.
Next I decided to see if CBNA was audible on any other of its harmonics. The results were surprising: I heard the station on almost every one of its harmonic frequencies up to 10200 kHz - the 17th harmonic. Specifically it was audible with a fairly strong signal (clear on some frequencies, distorted on others) on 1200, 1800, 2400, 3000, 3600, 4200, 4800, 5400, and 6600. Only on 6000 was it missing, and that's probably because Radio Havana was dominating that frequency. It was also audible with a much weaker, fragmentary signal on 7200, 8400, 9000, and 10200 kHz. Time: 0202-0220 UTC.
I have no idea how far away these harmonics can be heard. But since even weak signals can propagate long distances on shortwave, this might give DXers a chance to hear Newfoundland on shortwave.
[Next day: I heard the second harmonic on 1200 kHz with a good solid signal on the car's radio as I was driving out of town. I was already on the highway a bit outside of St. Anthony, However, it wasn't audible when I was a few dozen km from St. Anthony.]