Snip...
We're using different definitions of "resonant". The definition I use
says that an antenna can only resonate on a frequency. (Pretty much,
the frequency a dip meter will indicate when coupled to the antenna.)
It can have a bandwidth over which it can be used, but the resonant
point is (usually) one single frequency. Discones look like dipoles
with the 2 legs being different lengths, so the best one could say -
using my definition - is that they "resonate" on the frequency at
which the disc is 1/2 wavelength in diameter and the frequency at
which the cone element length is 1/4 wavelength.

But they probably are the best tradeoff for multi-band scanning.

Let's use an accepted engineering definition- resonance is defined when the
input Z has zero reactance- a properly designed discone (disc and cone- not
a skeletal version) is virtually reactance free over a very wide band.
Discones may look like dipoles- although you really have to be imaginitive,
is a derivative of the bicone antenna (replace the disk with another cone).
With proper included cone angle and proper machining of the junction (this
limits hi end performance) it is a wonderfully broadbanded antenna.

Dale W4OP