Learn English – How to name a 15-minute period

The Wikipedia article 12 Hour Clock is worth quoting at length:

Confusion at noon and midnight

It is not always clear what times "12:00 a.m." and "12:00 p.m." denote. From the Latin words meridies (midday), ante (before) and post (after), the term ante meridiem (a.m.) means before midday and post meridiem (p.m.) means after midday. Since strictly speaking "noon" (midday) is neither before or after itself, the terms a.m. and p.m. do not apply. However, since 12:01 p.m. is after noon, it is common to extend this usage for 12:00 p.m. to denote noon. That leaves 12:00 a.m. to be used for midnight at the beginning of the day, continuing to 12.01 a.m. that same day.

However, because practical confusion is still possible, some style guides recommend replacing "12:00 p.m." with "12:00 noon" and "12:00 a.m." with "12:00 midnight".

The American Heritage Dictionary of the English Language (Fourth Edition, 2000) has a usage note on this topic: "Strictly speaking, 12 a.m. denotes midnight, and 12 p.m. denotes noon, but there is sufficient confusion over these uses to make it advisable to use 12 noon and 12 midnight where clarity is required."

Many U.S. style guides, and NIST's "Frequently asked questions (FAQ)" web page, recommend that it is clearest if one refers to "noon" or "12:00 noon" and "midnight" or "12:00 midnight" (rather than to "12:00 p.m." and "12:00 a.m."). Some other style guides suggest "12:00 n" for noon and "12:00 m" for midnight.

The Canadian Press Stylebook (11th Edition, 1999, page 288) says, "write noon or midnight, not 12 noon or 12 midnight." Phrases such as "12 a.m." and "12 p.m." are not mentioned at all.

The use of "12:00 midnight" or "midnight" is still problematic because it does not distinguish between the midnight at the start of a particular day and the midnight at its end. To avoid confusion and error, some U.S. style guides recommend either clarifying "midnight" with other context clues, or not referring to midnight at all. For an example of the latter method, "midnight" is replaced with "11:59 p.m." for the end of a day or "12:01 a.m." for the start of the next day. That has become common in the United States in legal contracts and for airplane, bus, or train schedules, though some schedules use other conventions.

My advice is to use "12:00 noon" instead of "12:00 p.m." and "12:00 midnight" instead of "12:00 a.m." Realize that readers may be confused which day 12:00 midnight belongs to, so make sure context makes it clear.

No-one says “thirty past”, perhaps because it is equidistant with “thirty to”, something else no-one ever says. It is always half past. You can of course say 6:30, though, which is pronounced “six thirty”.

It doesn’t matter if it “seems more straightforward” to you to use numbers greater than thirty for minutes, because in fact one never does that when saying something like “twenty of six”. If you said 5:40, that’s of course different. It can’t be “forty after five o’clock”; it can only be “twenty to six” or “five forty”.

People wouldn’t normally say “twenty-three to seven”, because that’s too precise for most clock-reading on a normal dial, or for most people’s purposes. One would just say “it’s about/almost twenty to seven”.