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I want to say that "symmetrical ramps are used at the [changeover from one quarter hour to the next quarter hour]".

I have found the idiom "turn of the hour" but have not found "turn of the quarter hour".

If there is no such term, is it acceptable to say "changeover from one quarter hour to the next"?

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    You can say "on the quarter hour", or perhaps, "on each quarter hour". It's not in common usage these days but any horologist will know exactly what you mean. – Mick Oct 14 '16 at 9:36
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    Have you considered saying "ramps are used every 15 minutes*? – FatMan Oct 14 '16 at 10:34
  • maybe transition? – John Feltz Oct 14 '16 at 12:09
  • @Mick: "On the quarter-hour" is sometimes used that way, but it more often means roughly "every hour, at fifteen past the hour". So I'd hesitate to suggest that without being sure that the context will clarify the intended meaning. – ruakh Oct 14 '16 at 22:51
  • What are ramps?? – Lambie Feb 4 '17 at 16:22
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Yes, the word is "(each and) every"

Don't use "at the" because "at the" refers to 1 thing.

This is good:

Symmetrical ramps are used at every quarter hour.

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First of all it's not really clear whether you are speaking about "a continuous action with a pause" or "an action that only occurs at a fixed interval". In any case there are several possibilities:

  • "The symmetrical ramps are used every 15 minutes (quarter of an hour)".
  • "The symmetrical ramps are used once per quarter of an hour".
  • "There's an interval of 15 minutes before the symmetrical ramps are used again".
  • "The delay (wait, rest) time before the symmetrical ramps are used again is 15 minutes".

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