BelMarduk notes the different periods in a day. For better than 1500 years, Europeans observed some form of the canonical hours, the system used in monasteries, which had 3-hour periods, with the monks gathering in the chapel to chant the appropriate office for each. These were:
Matins: at midnight
Lauds: 3 a.m.
Prime: daybreak or 6 a.m.
Tierce: 3 hours after Prime, or 9 a.m.
Sext: noon
Nones: 3 hours after Sext, or 3 p.m.
Vespers: sunset, or 6 p.m.
Compline: 3 hours after Vespers, or 9 p.m.
The names for the daytime hours show that they are the first, third, sixth and ninth hours of the day. (Which is how you know what the King James Version of the Bible is talking about when it mentions "the sixth hour" or "the ninth hour".)
Towards the end of the Middle Ages, in many monasteries, some of these were combined, like Matins and Lauds, sung at midnight, and Vespers and Compline sometime between sunset and the hour for retiring. Also Tierce might be conjoined right after Prime, and Nones right after Sext. So that by the time of the Reformation many communities had Matins/Lauds at midnight, Prime/Tierce at daybreak or 6 a.m., Sext/Nones at noon, Vespers/Compline around sunset or somewhere between 6 and 8 pm.
Fractions of these periods were called in the German fashion (where halb sechs is 5:30 or halfway to six), such as half nones = 1:30 p.m. or thereabouts, or halfway from sext to nones.
