Unfortunately you missed the Calgary Folk Festival, and the Calgary Stampede (yes, it's big, but it's possible to find interesting bits, including Cowboy Poetry).
My daughter is getting married August 6, and I'm leaving for Ontario August 7, so there's no point in giving you my phone number. Also, things tend to slow down on the folk scene in the summer. Get a Thursday copy of the Calgary Herald, and check the Hit List (but your visit will be almost over by then).
If you like Celtic sessions, try the James Joyce Saturday afternoons, Henry the Eighth or Tullamore Wednesday evenings.
If you can manage an hour's drive west of town, the Canmore Heritage Days Folk Festival (one of my favourites) is on that weekend, August 5 to 7. You might run into my daughter and her husband on their honeymoon, too.
Check out this website too: http://www.acs.ucalgary.ca/~bmccombs/calfolk/default.htm. Barry McCombs maintains an events listing.
Hope you find something to your liking.