HyperCard: Microsoft Mail Conflict & Fix

I am experiencing problems using System Software 6.0.4, Microsoft Mail 2.0, and HyperCard 1.2.5.

While using HyperCard, I receive a Microsoft Mail message. At that point, my machine produces a high-pitch tone. (This tone cannot be stopped unless I quit HyperCard or initiate a beep tone from my Macintosh within HyperCard.

What's going on here? Is there a fix?
HyperCard also has a similar conflict with some versions of InBox.

As of April, 1990, the only workaround is to turn off the notifying chime until the problem is resolved.
Published Date: Feb 18, 2012