Note: This article discusses the merits of a 3/4 (three quarter wave) vertical -vs- a 1/4 (quarter wave) antenna.
You can build a 40m vertical quarter wave antenna and ground mount it with 16 x 4m radials and operate it at the third harmonic; 21MHz.
Actually, all my experimentation has shown that if you multiply the quarter wave resonance by 3.03, you’ll have the next available usable band. In this case, if you tune a 40m vertical to 7.00Mhz, you’ll have the whole of the 15m band to play with with a centre-point of 21.300Mhz. Oh, and you’ll still have the whole of 40m band under 1.3:1.
Now here’s the controversy:
Most people who read antenna publications or the ARRL handbook believe that if you actually make this antenna, you’re creating a cloud-burner on 15m.
Technically correct (sort of) – but for DX, wrong.
On the surface, the 10m long 40m vertical that’s used on 21.225MHz does indeed look like a cloud burner. Here it is. 15m band in green -vs- a pure quarter-wave in red).
(click to expand quarter-wave in red, three-quarter wavelength in green)