[technothrasher]

Traditional Japanese timekeeping kind of did both. The "am" and "pm" time periods started at midnight and noon, but the clocks themselves started at dawn. The hours counted down from hour 9 to hour 4 (they did not use 3-1). Each of the hours was approximately two modern hours, but their individual lengths changed every two weeks to keep the periods aligned with the sun. The twelve hours on the linear clock dials ran: 6,5,4,9,8,7,6,5,4,9,8,7 (and then a final 6 to match the first six, since it was a linear instead of circular dial).