Why does the "A in C major" tone play whenever a strange event occurs in The World? Mai Minase first notices this in .hack//Liminality when she and Tomonari Kasumi are attacked by the First Phase, Skeith.

The "A in C major" tone (ハ長調ラ音) seems to recur whenever some strange event happened "The World" and it's subsequent iterations, like in "The World R:2," like when Azure Kite appeared, the appearance of one of the Phases, or activation of an Avatar. 

Why does this tone play during these events in both the anime series and the games?

http://www.youtube.com/watch?v=BN987vxtiuQ
There are a few things that point to why the A in C minor tone was chosen for this purpose.
The Bell
The first is in a subset of the lyrics from In the Land of Twilight Under the Moon. This part of the lyrics seems to reference A in C minor in that this tone, which is unique enough to be commonly used for tuning instruments (via tuning fork), is sometimes known for its similar sound to a bell (as in the video you linked).

High and loud, the sound of your bell of the
Twilight... ringing...
All alone, it rings and echoes in twilight
  — SIGN Original Soundtrack 2, .hack Wiki

Liminality
The second is somewhat more convincing; the sound may be considered a manifestation of Liminality. The game can, of course, make contact with the human mind, and the tone itself is subliminal. This means it was probably programmed in by Harald, being key to this mental contact, much like hypnosis (which uses specific types of lights for maximum effect).
In reality, there is nothing special about the properties of A in C minor (with the exception of its ability to be easily differentiated from other notes); it is heard at approximately 440Hz, though its range extends as low as 435Hz. However, in the .hack//Liminality OVA, it is (incorrectly) stated that the tone is the highest note a human can hear. In the .hack universe, most people are unable to hear this tone, but Mai can.
Overall
It seems that the note itself was chosen for its uniqueness (especially in that it is easy for the human ear to hear), as well as its faux property of being the highest note humans can hear. The A in C minor tone itself is not exceptionally notable outside of the .hack universe.
The note itself is also the first letter in the musical scale and its use is somewhat akin to déjà vu in The Matrix, though these are not as likely to be related.