On first of September (2015) a week ago, Google updated their logo, to a new one. They also updated the Favicon, but on the way looks like they have ruined the Google Calendar Updating Favicon.
Before the update, the Google Calendar Favicon was updating and showing today date (day of the month) - Very cool. Now it's just another tab with the same Google favicon logo as any other tab or window.
Now - Bad:
Before - Good: