Actually, the date for the cross-quarter depends on what system you use. Most Neopagans use the fixed date, which yes, is August 1st. However, the true cross-quarter - the actual astronomical midpoint between Summer Solstice and Autumn Equinox - does not happen until August 7th. That's when I celebrate. In part because when I started making my own calendars, it irritated me that the tides weren't the same length. So I switched to the true cross-quarter so they are the same length, plus or minus a day.