The following is a simple guide to go by, It is not something you would find in a book, Its just my opinion. Peter Pride
The tuned frequency of the antenna is the most important aspect of an antenna, If say, your transceiver is transmitting on 477MHz then you must use an antenna tuned to 477MHz. The transmit bandwidth of an antenna depends on many aspects of an antenna, It's type, thickness, length, gain to mention a few, You will need to see the individual antenna specs, to get the bandwidth information of a particular antenna you wish to transmit with.
However, where the receiving efficiency of an antenna is concerned the guide I go by is this, within 10% of the antennas transmit tuned frequency you will get the best possible receiving strength, the receive strength will gradually reduce in performance outside that range.
For example, for 477MHz the antenna is tuned to 477MHz the radio will receive excellently using that antenna on 477MHz + or - 47.7MHz ie: 429MHz to 525MHz. Another example, an antenna tuned to 124MHz will receive excellently on 124MHz + or - 12MHz = 112 to 136 MHz (Entire Airband).
This guide does not apply to ground independent antennas below 200MHz (they are extremely narrow banded).
It's just a guide, not a rule, as many antennas can have a larger or smaller bandwith depending on their type.