"Breathing" of the air

"BTW - added "air" from manipulation of the recording by the playback system or harmonic resonance or reverb etc. can be pleasant too. So more "air" can also be used to describe equipment that adds its own signature to the recording."

Agree. I think you can easily be able to discern if this is indeed a manipulation or truer to recording sound, by listening to other cues- lIke fast and quick transients do have air but won't linger on too long vs slower and gentle notes meant to to vibrate will and in case of manipulated sound will not sound entirely in phase and coherent- something will be off.

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The first time I ever heard "air" in my system was an amazing thing to me. Went out and told a couple of non-audiophile friends about it...when they evntually came over to visit, I excitedly put on a couple of cd's do demonstrate what I was talking about. After a couple of minutes of listening, they looked at each other and then they looked at me like I was crazy....they couldn't understand what all the fuss was all about. To me, it was sonic bliss.

Man, this is a lonely hobby....kind of like being on earth alone and I can only communicate to other beings on other planets via radio (internet).
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"..which is so evident in live music and rather difficult to reproduce properly at home, even with the "right" recordings."

Absolutely agree with Detlof on this. This is one of the many key reasons Stereo systems will never sound like the real thing: recordings can't 'thoroughly' record air and systems can't 'thoroughly' reproduce 'air'. But if done right can come awfully close in creating believable illusion.

Steve Hoffman, the well-known recording engineer calls it the "Breath of Life". I might as well let him explain it. Browse this page of his website. It's fun and you'll learn a lot:
http://www.stevehoffman.tv/dhinterviews/

Agree with Atmasphere about the confusion in the "air".

As far as "breathing", in vocals and particularly reed instruments, like sax, my experience leads me towards 2 and 3 inch soft dome mids first and planar ribbon mids second. It's a quality I demand but I'm not saying either is more accurate.