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When it is necessary to allocate a week to a single month, the rule for first week of the year might be applied, although ISO 8601-1 does not consider this case explicitly. The resulting pattern would be irregular. There would be 4 months of 5 weeks per normal, 52-week year, or 5 such months in a long, 53-week year.
The 4–4–5 calendar is a method of managing accounting periods, and is a common calendar structure for some industries such as retail and manufacturing. It divides a year into four quarters of 13 weeks, each grouped into two 4-week "months" and one 5-week "month". The longer "month" may be set as the first (5–4–4), second (4–5–4), or ...
A leap week calendar can take advantage of the 400-year cycle of the Gregorian calendar, as it has exactly 20,871 weeks: with 329 common years of 52 weeks plus 71 leap years of 53 weeks, a leap week calendar would synchronize with the Gregorian every 400 years since (329 × 52 + 71 × 53 = 20,871).
The week number can be described by counting the Thursdays: week 12 contains the 12th Thursday of the year. The ISO week-numbering year starts at the first day (Monday) of week 01 and ends at the Sunday before the new ISO year (hence without overlap or gap). It consists of 52 or 53 full weeks. The first ISO week of a year may have up to three ...
ISO 8601 includes a specification for a 52/53-week year. Any year that has 53 Thursdays has 53 weeks; this extra week may be regarded as intercalary. The xiuhpōhualli (year count) system of the Aztec calendar had five intercalary days after the eighteenth and final month, the nēmontēmi, in which the people fasted and reflected on the past year.
Broadcast calendar years can have either 52 or 53 weeks. A broadcast calendar will have 53 weeks in a leap year where January 1 falls on a Saturday or Sunday, or in a common year where January 1 falls on a Sunday. In the 21st century, 53-week broadcast calendar years are 2006, 2012, 2017, 2023, 2028, 2034, 2040, 2045, 2051, 2056, 2062, 2068 ...
If 1 January falls on a Friday, then it is part of Week 53 of the previous year (W53-5). If 1 January falls on a Saturday, then it is part of Week 53 of the previous year if that is a leap year (W53-6), and part of Week 52 otherwise (W52-6), i.e. if the previous year is a common year.
They have years of either 364 days (52 weeks) or 371 days (53 weeks), thus preserving the 7-day week. Proposals mainly differ in their selection of a leap rule, placing of the leap item (usually middle or end of the year), in the start day of the week and year, in the number (12 or 13) and size of months and in connected naming; some are ...