Harmonics of SW and MW Broadcast stations are frequently seen at long distances. A couple of weeks ago Radio Verdad (Guatemala) on 4055 kHz was noted on its 2nd, 3rd, 4th, 5th , 6th, and 7th harmonics (8110, 12165, 16220, 20275, 24330, and 28385 kHz) in North America. It was first detected on the 7th harmonic in the 10 M band and once it was realized what it was the others were hunted down. I personally only heard the 12165, 16220, and 28385 signals with identifiable audio, and a couple of other freqs with weak carriers. That was pretty interesting since Radio Verdad runs only about 1 kW of power. If you look in the latest A12 Combined schedule you will see the 7th harmonic listed, but I don’t think any of the others were added to the schedule.
The math on the 2nd harmonic (27260 kHz) of Radio Australia on 13630 kHz is actually pretty easy to understand. That transmitter is rated at 100 kW, or +80 dBm. If the 2nd harmonic is 40 dB down, or one ten-thousandth the power, that still leaves +40 dBm, or 10 Watts, of power on 27260 kHz. The antenna will have gain and directionality on 13630 kHz which means it will likely be fairly efficient at the 2nd harmonic. 10 W into a 0 dB gain antenna can indeed work the World on 10/11 M when the band is running well.
Many transmitters are spec’ed at 50 or 60 dB down on the 2nd harmonic, but a failed component can push the harmonic power up pretty easy. I have seen 100 and 250 kW transmitters that are slightly out of adjustment sometimes run the 2nd harmonic as high as 10 or 15 dB down, meaning as much as 10000 Watts of power in the harmonic. In exceptional cases the harmonic can have the same or more power than the target frequency, but that typically does not last long
T!