Wonder of harmonics in amateur radio!
Major amateur radio bands have been allotted as harmonics of each other. It is not by chance, but by design. We will have a look into what are the pros and cons of harmonics in amateur radio. The usual lowest band in amateur radio is 160m, though recently still lower bands have also been allocated in some regions. 160m is 1.8 MHz. The next band is 80m or roughly 3.6 MHz, the second harmonic of 160m band. The popular 40m or 7 MHz band can be considered as the second harmonic of the lower end of 80m band, that is 3.5 MHz. 14 MHz, the popular band for long distance or DX contacts is the second harmonic of 7 MHz band. Then comes 21 MHz, which is the third harmonic of 7 MHz. 28 MHz or 10m band is the fourth harmonic of 7 MHz or second harmonic of 14 MHz. Now what about the VHF and UHF frequencies? 2m band is roughly the third harmonic of 6m band. 70cm UHF band is roughly the third harmonic of 2m band.
That is about the harmonic relationships of major amateur radio bands. Even the WARC bands have some harmonic relation. The 30m band is just below the third harmonic of 80m band. The advantage of harmonic relationship of the amateur radio bands in the early homebrewing era was that it was easy to use harmonics of the fundamental frequency for the higher bands. Suppose you have an oscillator for 3.5 MHz, its second harmonic can be filtered and amplified to work on 7 MHz. Fourth harmonic could be used on 14 MHz. Downside was that if the bandpass filters were not good, a 3.5 MHz transmitter would also radiate on 7MHz and 14 MHz, causing interference to other stations working on those frequencies. This problem is quite unlikely with modern radios having good harmonic suppression and band pass filters.
Another advantage of harmonic relationship of amateur radio bands is in the use of lesser number of antennas. An end fed half wave dipole antenna (EFHW) resonates on all its harmonics. So a 40m long EFHW for 80m band will also work on 40m, 20m, 15m, 10m and even 6m with fair SWR. This reduces the need for multiple antennas to work other bands. That is why EFHWs are popular for portable operations where the scope for multiple antennas are limited. Same applies to most apartments these days where access to the terrace and option for multiple feedline cables is limited.
In case of center fed half wave dipole antennas, the situation is slightly different. They have good SWR on odd harmonics of the fundamental frequency. For example, 7 MHz antenna can be conveniently used for 21 MHz, but not for 14 MHz. On even harmonics, the antenna presents a very high impedance. Hence 7 MHz antenna cannot be used for 14 MHz or 28 MHz. But a 40m antenna can present fair SWR on 6m which is roughly the seventh harmonic. That is why my fan dipole with 40m elements also resonates on 6m with fair SWR. Of course, best results will be for a dedicated 6m antenna.
An extreme example of odd harmonic resonance is between VHF and UHF antennas. I used to work Amateur Radio on International Space Station with uplink on VHF and downlink on UHF, with a single CP22E VHF antenna. Still more extreme example was that I could occasionally work Space Station with my 40/10m combination dipole. That could be 5th harmonic of 28 MHz (10m) on VHF and 15th harmonic of 28 MHz on UHF! If I calculate the harmonics of 40m elements, that will be 21st harmonic for VHF and 63rd harmonic for UHF. I do not know exactly which harmonics worked for me. But I know that I have been able to have a contact using the VHF/UHF transponder of Space Station with the HF antenna. My friends have been able to check in to local VHF repeaters with 40m antenna quite well.