Limiting would be to make it "louder" (after normalizing) if that's what you want.
If you don't want to change
anything you might want to skip the limiting and simply adjust the volume(s). Slight limiting may not be audible, but at some point it does begin to affect the sound.
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and finally compare to other songs in terms of loudness
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You can get a loudness meter/scanner to check the UBU R128 loudness of your tracks and your reference track. I can't make a personal recommendation, but
dpMeter3 is one that I've played with.
You probably can't match the loudness of a modern professionally mastered popular music track without excessive "damage". And, you might not want to do that because you'll kill the dynamic contrast.
If you're making an album. Normalize all of the tracks (for peaks at or near* 0dB). Then if they don't sound equally-loud, choose the quietest sounding track as your reference and bring the louder tracks down to match (assuming you want them all equally-loud). Normalizing is simply an overall volume adjustment. It doesn't affect the quality/character of the sound.
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test it on several audio systems
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I
think that's more-commonly done at the mixing stage. But at some point it's a good thing to do, especially if you don't have good monitors in a good room and/or lots of experience.
Here's my collection of mastering links. (The Moulton Labs articles are rather old, but there's still lots of good information.)
Moulton Labs - What's This Mastering Business Anyway?
Moulton Labs - Tips n' Tricks For Mastering
Izotope - Ozone Mastering Guide (This is written for Ozone but most of it can apply no matter what tools you are using.)
REAPER Forum - Discussion of a particular mastering job (The mastering discussion starts at post #8).
Mastered For iTunes
* Some people like to normalize to -1dB or so for a couple of reasons -
To allow for inter-sample-overs. I don't worry about that. I trust the DAC to do the right thing on the analog-side. Plus, I've never of anyone who could hear clipping from an inter-sample over in a proper-scientific-blind listening test.
Or if you are making MP3s, MP3 compression tends to boost some peaks and reduce other peaks, so if you normalize the original to 0dB the highest-peaks on the MP3 often go over 0dB. That's not a problem for the MP3 format since it can go over 0dB without clipping. But if you play the MP3 at "full digital volume", you'll clip your DAC. Again, it's not something I worry about. I've never heard of this slight-clipping being audible. If you're hearing a compression artifact you're probably hearing something else. And if you are making an MP3, you already know it's a lossy format so you've already accepted the fact that it's imperfect.