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xkcd #2846: Daylight Saving Choice
(imgs.xkcd.com)
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The Julian calendar is the one that has no special rule for leap years. It is currently October the 12th in the Julian calendar.
The calendar that is used all around the world is the Gregorian calendar.
What you mean is called the ordinal date (at least by Wikipedia: https://en.wikipedia.org/wiki/Julian_calendar, see the disambiguation note at the top)