If the time was 15:34, how could I refer to the 60-minute period between 14:00 and 15:00? If I were to say the last hour it would likely mean the period from 14:34 to 15:34.
So how do I express time period from x-1 o'clock till x o'clock, irrespective of how many minutes have passed x o'clock.
It's like the difference between 'every hour' and 'on the hour'.
There seems to be some consensus that any 60-minute period one refers to should be called an hour, but I don't agree...
If I want to refer to the period between 14:00 and 15:00, I call that between 2 and 3, whether I mean the whole period or some incident that occurred within that time frame:
I was sleeping between 2 and 3.
How many customers did we have between 2 and 3?
The nice thing is that you can use the same expression for time periods other than 60 minutes as well.
I think the clearest way to indicate this is simply to explicitly state the start time: "(the hour) from 14:00 to 15:00" or "the hour starting at 14:00". This might seem like a non-answer, but I'm not sure how often you'd ever need to express this meaning without knowing the specific time.
A useful answer will depend on the context in which you want to use it, how technically precise it should be (need you worry whether now might be considered exactly x:00), etc.
Quite informally but plainly, you might use
The hour that began 60 minutes before the beginning of the current hour.
You might also use the term top of a/the hour:
From the top of the hour prior to the current hour to the top of the current hour.
Idiom definition:
at the top of the hour
Fig. at the exact beginning of an hour. (Alludes to the big hand on a clock pointing to the 12. Often heard on television or the radio. See also at the bottom of the hour.)
Every class in my school starts at the top of the hour. Our next newscast will be at the top of the hour.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. S.v. "at the top of the hour." Retrieved April 20 2015 from http://idioms.thefreedictionary.com/at+the+top+of+the+hour
If the time was 15:34, how could I refer to the 60-minute period between 14:00 and 15:00?
The full hour block starting and ending on the hour. Quite a mouthful!
I agree with @Jim Reynolds that the best choice will depend on some more context than you're giving in the question, but I can think of two ways to specify it relatively clearly and concisely:
1) "the hour before the current hour" seems to describe it relatively cleanly and unambiguously, though it will depend on whether "the current hour" is an acceptable phrase to describe the "anchor time" of your period
2) "the previous whole hour" would likely work in many situations if you are speaking to a precise or literal audience (e.g. software engineers) who would recognize the phrasing as an attempt to describe a time period (a "whole hour" that presumably starts with minute zero and ends with minute 59) with a position relative to "now"
In essence, you're asking if there is an hour-based equivalent to the calendar month. Native speakers certainly would understand the difference between
She rented the car five times in the last month.
and
She rented the car five times in the previous calendar month.
There is no direct equivalent for hours in English (there is no common phrase such as the "clock hour" for instance), but I think in many cases using one of the two suggestions above would probably work.
'This last full hour past' perhaps, though that is a bit archaic/high fantasy in construction.
