In setting up a multi-band vertical, I know that as a general rule, you should choose a length that is non-resonant on all the bands you want to use and specifically avoid anything that would be a multiple of 1/2 wavelength...
Actually I prefer
to use 1/2 wavelength verticals when I can. They work well, and
I've never had problems matching them.
The limitation is in the automatic antenna tuners that use relay-switched coils and capacitors,
because the half wave antennas have a high feedpoint impedance, hence high voltages that
can arc the relay contacts.
In fact, there is a simple matching network that uses two capacitors and an inductor that
will match such an antenna simultaneously on two bands, such as a 80m quarter wave on
40m, or a 20m quarter wave on 10m. I've used this on both 80/40m and 40/20m over the
years. Narrows the SWR bandwidth somewhat on the lower band, but otherwise works fine.
Put a capacitor and coil in series between the coax inner conductor and the antenna, such
that the combination is series resonant on the low band, and on the high band it provides
the proper inductance to match the high impedance in conjunction with a small capacitor from
the antenna to ground. Requires a bit of setting up, but then the antenna is matched on
both bands without an additional tuner, and probably on 12/15/17m with a tuner.
My question is how far away from a 1/2 wavelength do you have to be to still be able to tune it up?
That depends on the specifications of your tuner, the radiator diameter, ground system losses, etc.
But as an example, S9 sells 29' verticals for use on 40m and 20m, so 14 1/2' should work for 20/10m.
Also, I read somewhere that even though the recommendation is to set the length for 1/4 wavelength on the lowest band of operation, you can get by at 80% of that length.
There are a lot of things you can "get by" with, often at the expense of efficiency. Depending
on the feed and loading methods, you can go down to half size or smaller, though somewhere
around 2/3 is probably a better lower limit. But making the whip 80% of a quarter wave on the
lowest band will certainly work - a friend has the 29' S9 vertical I mentioned previously and
does quite well on 40m (though he has added a bit of base loading to it so he doesn't need
a tuner in the shack.)
The other thing to consider is making the antenna LONGER than 1/4 wave on the lowest band,
as that improves the efficiency somewhat. Conventional wisdom is that the antenna shouldn't
be longer than 5/8 wave on the highest band, though performance really doesn't degrade much
until you get over 3/4 wave in the practical world. Certainly if you want to work 30m or 40m,
this would be preferred. Basically it would be the equivalent of the common 43' vertical cut in
half, though 20' should work if that is a convenient radiator length. (The issue would be to
avoid 1/2 wave on 15m or adjacent bands.) I remember an article in QST many years ago
using a 24' vertical on all bands 10m through 80m with a manually-switched matching network
in a box at the base. (Manual switching avoids the problems with relays in autotuners.)