How were/are days subdivided in non-Gregorian calendars?

In the Gregorian calendar, a day is subdivided into 24 hours, which each contain 60 minutes, which each contain 60 seconds. Internationally, a derived version of this calendar called UTC is used nowadays which still basically* follows this rule.

In the Calendrical Calculations paper by Nachum Dershowitz and Edward M. Reingold it is mentioned that in the Hebrew calendar, a day is subdivided into 24 hours, each containing 1080 'parts'.

While subdivisions of 24 and 60 are mathematically 'smart' (you're able to divide 60 in equal halves, thirds, quarters, fifths, sixths and tens) I wonder what kind of day subdivisions were used in other parts of the world, such as ancient China and ancient Persia. I also wonder about civilizations such as the Mayans: They ought to have had their own way of day-subdividing, right?

It seems that nowadays these have been mostly replaced by the Gregorian hours/minutes/seconds and it is very hard to find information about the timekeeping units that have been used in the past.

What other day subdivisions have been used besides hour/minute/day subdivisions by other calendars and why?

• I was under the impression a "calendar" generally refers to how the year is divided up into days, and makes no statement whatsoever about how the user might be dividing up their days. – T.E.D. Jan 8 '17 at 1:20
• I agree with @T.E.D. "Calendars" is one thing, "division of the day" another. Perhaps you could reformulate your question. – fdb Jan 8 '17 at 18:43
• @fdb I happily would, if someone can tell me how "division of the day" is colloquially named. – Qqwy Jan 8 '17 at 20:40
• I'm fairly certain that you usually translate most major subdivisions into "hours", like you use "month" even for other similar-sized divisions of days. Much finer division than hours should be rather rare, as you need precision timekeeping for it to make sense. – andejons Jan 9 '17 at 23:10