Ian White, G3SEK wrote:

A few more thoughts, in case they're useful to Dan or anyone else:

* It's sometimes possible to make an automatic two-band network. For
example, the same 33ft end-fed vertical can be matched as both a
half-wave on 20m *and* a quarter-wave on 40m, with one network and no
switching. The same goes for a 66-footer (vertical or inverted L) on
40/20, or a 130-footer on 160/80.
. . .

Wes Hayward, W7ZOI, published either a QST article or a Technical
Correspondence piece about doing this, many (10? 15?) years ago. A
search of the QST CDs should turn it up. If I recall correctly, he
concluded that either a two-band solution could always be found, or that
he wasn't able to find a combination that he couldn't find a two-band
solution for.

Just by observing this newsgroup, though, it seems like very few hams
are any longer interested in matching an antenna to a feedline,
preferring to buy ladder line and a tuner instead.

Roy Lewallen, W7EL