Why always just three antenna wave lengths ever discussed?

Hello,
I'm trying to re-enter the ham radio hobby again after some time away. My question is about antenna wave lengths. Why are antenna wave lengths always commonly discussed as being 1/4-wave, 1/2-wave or 5/8-wave? Why aren't other wave fractions ever discussed or considered? It always seems like it's just these three: quarter, half or five-eights- that's it! no others, period. You either have one of these three antenna wave length's or you have none at all.
Thanks

They are simple to construct, don't require a lot of exotic matching devices, are time proven effective.

For a vertical antenna a 1/4, 1/2 or 5/8 wavelength and a few others put much of their signal at the horizon where you need it. A 3/4 wave or full wavelength and some others will have a null at the horizon and put signals up in the air and down at the ground where it doesn't do much good.

For a horizontal wire at HF its a different story because you can orient the antenna to make use of lobes and nulls, so you will find 3/4, full wavelength and others used horizontal at HF.
prcguy

In addition each wavelength will have a different feed point impedance requiring some kind of matching network to match the feed line to the antenna.
BB

Actually there is often discussion of the "random long wire" amongst hams and in these forums. Not much use at VHF but can work on the HF bands fairly well. A "random" long generally wire is deliberately cut NOT to resonate on any of the bands it will be used to transmit on, but to be useable with a Transmatch ("antenna tuner").

Also there's lots of discussion of large loops which are one wavelength long on the lowest frequency band and two or more wavelengths as you tune higher. Also magnetic loops which are far smaller than a quarter wave.

So I think the premise of your question is wrong.