The idea is the following:
All day events and special days are colour coded; the colour is selectable to tell different types of days apart.
Appointments are shown in a radial grid that runs either from 6am to 6pm (day view) or 6pm to 6 am the next day (night view). Day view and night view are selected using the sun/moon buttons on the month bar. The radial grid thus represents a traditional clock, split at the bottom at 6 o'clock.
The example shows only appointments that last an hour and start at the full hour. Of course, the grid can be made more fine grained. To avoid very tiny segments, appointment lengths and start times should probably rounded off at quarters of an hour.
Events from multiple calendars could also be shown in distinguishing colours, although the resulting calendar could be quite painful to the eyes ;-).