Sometimes the wrong answer to a question is the most useful in real life sound engineering. Well not often, but this time it is so.
If you fix the thought in your mind that all mics pick up background noise equally, then you will be aware that background noise is problem and take steps to do something about it.
Searching for a 'magic microphone' that rejects background noise won't do you any good.
But if you look a little deeper, there are some ways choice of microphone can affect background noise, but in most cases not by very much.
The biggest difference in background noise pick up would be between an omnidirectional microphone and a hypercardioid microphone.
An omnidirectional microphone is equally sensitive all round, so clearly it picks up background noise from all round.
A hypercardioid microphone is much more focused, therefore will pick up the sound source you want more strongly than the background noise. So if background noise is an issue, this is the type of mic you should use.
Also, some mics take more kindly to very close sound sources. The closer the sound source, the louder it will be in comparison to the background noise.
Another point is that any directional microphone will display the proximity effect by which a source that is close to the mic will have its low frequency content boosted.
Sometimes this is so pronounced that it extends into the mid range band, and therefore the level as a whole rises. This too will have the effect of reducing background noise, since background noise by definition will be more distant and not be affected in the same way.
The Coles 4104 noise-canceling microphone is such a mic. However, its sound quality is tuned to speech rather than music.
The best/most practical ways not to suffer from background noise are these (in order)...
It is worth going to considerable trouble to make sure that your recordings are background noise free.
By the way, background noise is nearly always much higher in level than the self noise of the microphone. So worry about the background noise first.
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