logo To Foot
© J R Stockton, ≥ 2012-03-04

Date Miscellany II.

No-Frame * Framed Index * Frame This
Links within this site :-

The Day, the Month, and the Year

The Second is the fundamental unit of time, now defined to considerable accuracy in the International System of Units (SI) by reference to an atomic resonance frequency. It defines the Minute and the Hour (unambiguously, apart from Leap Seconds).

The "infinitely" distant Fixed Stars represent the Universe as a whole.

In this page, the Calendar is Gregorian, the location is England, and the time is the present day, unless otherwise indicated. The English Calendar has been standard Gregorian since 1752.

Metrologically

For metrologist-grade definitions of time scales, seek within Date and Time Index and Links.

Astronomically

I've been told that the International Astronomical Union (IAU) still considers the day - but which day? to be the base unit of time.

The Day

The common definition of the Day is that of the daylight/night cycle, which is governed by the longitudinal position of the Sun with respect to the local meridian. This, averaged (hence "Mean Time"), gives the ordinary length of the Civil Day, nominally 86400 SI seconds; recently the Mean Solar Day has been of the order of 0.02 ppm longer on average, which difference is the reason for using Leap Seconds.

It is convenient for the same local time to be used over a large region. So we have Time Zones; within a Zone the Standard (Winter) Time is independent of location, having a constant offset (normally an exact number of hours; sometimes of half- or quarter- hours) from the Mean Time of the Greenwich Meridian. Time Zones are not affected by Summer Time.

The Civil Day

The Civil Day is commonly considered to be of 24 hours. But in many places in the more-or-less Temperate Zones, the Day is annually once of 23 hours (at the start of Summer Time) and once of 25 hours (finish of Summer Time)*. Forgetting this can have unfortunate consequences. The start and finish date and time vary from place to place; and the rules are also mutable. Remember too that the seasons depend on the hemisphere, Northern or Southern.

Those who change their longitude rapidly enough can also be afflicted with days of lengths down to (at present) about 90 minutes and up to ... ?

* : In one place, 23½ & 24½ hours.

The Equation of Time

There is an annual near-periodic solar-day-length variation (of range about 50 seconds), due both to the ellipticity of Earth's orbit and to the angle (23.5°) between orbital and rotational axes. These effects lead to the "Equation of Time" (Wikipedia), which relates sundial time to local solar mean time; the difference at a given location can be up to 16.5 minutes, corresponding to 4° of longitude. The shape of the curve has a slow drift due to perihelion shift; its position is affected by Leap Years.

To obtain local clock time from a sundial, one must allow for the Equation of Time, for the offset in longitude from the nominal longitude of the time zone, and for possible Summer Time.

The Sidereal Day

The Sidereal Day nominally represents the rotation of the Earth with respect to the Fixed Stars. It is about 23 hours 56 minutes 04 seconds long; the difference necessarily amounts to one day per year, minor effects apart. The time for one rotation of the Earth varies, seasonally and otherwise, on a millisecond scale.

Sidereal time equals mean solar time near the September Equinox.

The Global Day

Sometimes, one must remember that a given date lasts for much more than 24 hours. Ideally, it should start in Time Zone 24 and broaden across the world, finally reaching Time Zone 1, 23 hours later. For an hour that date should be everywhere; then the following day should sweep across for the next 23 hours, making the date in question last for 47 hours.

Additionally, one must allow for Summer Time, which perhaps makes a 48-hour global day.

But it may actually start in Time Zone 26, (Christmas Island, and in Summer also Tonga) (Kiribati?) and finish in American Samoa and other places without Summer Time in Zone 1; that gives 49 hours in all. Apparently, some places changed time for the Millennium, to get the so-called First Sunrise. Or perhaps for other reasons. They may have changed back.

Other Days

The Civil Day has begun at various times of the solar day, and, for example, dates in the Hebrew and Islamic Calendars begin variously at 6 p.m. and at sunset.

Until the mid-1800s, the solar time of the locality was used.

The British Civil Day has been midnight to midnight for at least several centuries. In 1880, by Act of Parliament, the legal time for Great Britain was made Greenwich Mean Time; see Time Miscellany.

The Royal Naval Day

Centuries ago, the Nautical Day began at the previous local noon. For sailors, p.m. of a given date therefore preceded a.m. The Royal Navy abandoned that system from late 1805. Trafalgar (1805-10-21) logs used the old system. British merchant shipping changed later; some foreign shipping had not changed by 1884.

Before about 1750-1800, ships' dates were not adjusted on crossing the Anti-Greenwich Meridian or thereabouts.

The Astronomical Day

Until 1925.0 civil time, the Astronomers' Day began at noon of the corresponding civil Greenwich day (standard or winter time), and was by them called GMT; it can better be called Greenwich Mean Astronomical Time (GMAT) to distinguish it from legal GMT (UT).

The Shortest and Longest Days

1924-12-31 GMAT must have been 12 hours long.

Some RN Nautical Day in 1805-6 must have had 36 hours (not necessarily on the same date for all ships).

By Roman law, the intercalated day of a Leap Year was not differentiated from the previous day (hence bissextilis); therefore in Leap Years VI Kal. Mart. was 48 hours long ( LexScripta). Likewise in a Statute of Henry III.

References
This Site

Since this site is for general use, I tend to use UTC to mean the present UTC (with leap seconds), and GMT for time which has exactly 60×60×24 = 86400 seconds every day and agrees with London Winter Time. I understand that UT (Universal Time) is, for experts, a better term for the latter; but it seems to me that it is too likely not to be understood, or to be taken as a typo.

The Night

For Twilight, see Time Miscellany.

The Month

The Calendar Month has been distinct from the Lunar Month for millennia, in the general European Calendar. For the variation of February, see Leap Years.

The Lunar Month represents the orbiting of the Moon around the Earth with respect to the Sun. For Moon phases, and eclipses, see Astronomy / Astronautics 2).

There are almost exactly 235 Lunar Months in 19 Solar Years - the Metonic Cycle - and the period can be divided into 12 12-month years and 7 13-month years.

New Moon is close to the start of the Hebrew and Islamic Months.

See also The Calendar Month below.

Moons in a Month

There must be a Full Moon (and any other given phase) in every Calendar Month, except for February; there can be two in any Month, except February - those can easily be shown taking the Lunar Month as constant and near 29½ days, and I doubt whether corrections to that are enough to make a difference. Two in a month must occur about 7 times in every 19 years, as the 19-year Metonic Cycle of 19×12 = 228 calendar months contains almost exactly 235 lunations.

It is possible to have two Full Moons in both January and March of a year. Duncan Steel, in his book Eclipses, gives 1961, not 1980, 1999, 2018, & 2037 as being such years, related to the Metonic Cycle. These occurrences depend on the Time Offset(s) used.

See [sci.astro] Time (Astronomy Frequently Asked Questions) (3/9) C.08. which says that a Blue Moon is the second Full Moon in a calendar month.

SkyPub once explained that a Blue Moon is the third Full Moon in a season which contains four (7 times in 19 years; see The Hebrew Calendar), and so on 20-23 Feb/May/Aug/Nov.

The Year

The underlying common definition of the length of the Year is that given by the seasons, governed by the latitudinal position of the Sun with respect to the Equatorial Plane. This, on average, is the Tropical Year, nominally of 365.2425 days; it is the difference between this and 365 days which is the reason for Leap Years. The true value is currently about 365.2421875 days or 365d 5h 48m 45s.

For astronomical definitions, see in such as Kaye & Laby.

The Civil Year is either 365 or 366 days long; this is usually remembered, even if some people have odd ideas about the Leap Year rules. But it may be slightly longer (or shorter) than expected; see Leap Seconds.

The interval between successive instances of the same Spring/Autumn Day-of-Year (-DDD) or Date-of-Year (-MM-DD) can also vary by an hour, because of Summer Time.

On the Gregorian Calendar, the Year averages exactly 365.2425 days = 31,556,952 seconds = 365d 5h 49m 12s (Julian : 365.25 d = 31,557,600 s = 365 d 6 h).

The civil Year is now always taken as starting on January 1st; in earlier times (England, before 1752; Scotland, before 1600), it was for some purposes taken as starting on a different day - often, and in those cases, the New Year (and its number) began on March 25th.

There are only 14 types of year (but 15 for ISO 8601 Week Numbering); a year may be Leap or ordinary, and it can start with any day of the week. A table showing the years of each type is in my year-set.txt; the type of each year is evident in my greg-1mo.txt.

A common year, being of 365=52×7+1 days, ends with the same day of the week as that with which it started.

The Sidereal Year nominally represents the orbiting of the Earth around the Sun with respect to the Fixed Stars. Other Years have different astronomical definitions.

There have been years of other lengths, even on calendars related to the Gregorian. 46 BC had 445 days (Calendar FAQ) in Rome. 1582 AD had 355 days in Rome; 1751 AD had 282 days in Britain; 1752 AD had 355 days in Britain; and elsewhere, calendar-change years were short by 10-13 days. Roman Catholic ecclesiastical 1910 seems to have had 372 days.

Astronomers' Years

Astronomers like to be different, traditionally starting their dates 12 hours after legal GMT. Also, they sometimes start years on January 0th.

Their Julian Years are of 365.25 days (Caesar's average) but do not match those of the Julian Calendar. Instead, their year scale starts at 1900 January 0.5, which is December 31st noon by legal GMT - though different starting years may be used.

The UK Financial Year

The UK Financial Year starts on April 6th.

I have read that this is because, up to 1752, it started on Lady Day (March 25th); and, when the calendar changed, no-one wanted to pay full tax for a short year (so GB FY 1752-3 had 365 days); and, I believe, there was a further shift to allow for the "missing" 1800-02-29 (GB FY 1799-00 had 366 days, but no Feb 29th).

But on 2004-11-01, the Daily Telegraph reported that, in 1972, as a result of a question asked in 1965, the Inland Revenue said that Lady Day, March 25th, had been the end of an accounting quarter; in 1752, this became April 5th. The Annual Balance had been at Michaelmas (September 29th), then from 1752 at Christmas, but in 1832 it was moved to the Quarter Day in Spring to be near Budget Day.

See also Income Tax Months (below) and Income Tax Weeks.

UK FY 2000-1 was NOT a leap year; it had only 365 days.

Other countries have different arrangements.

The Four Seasons

See a respectable Almanac. See also NRC, Canada - When do the seasons start?", which has UTC equinox and solstice times for 2000-2020.

At an Equinox, the centre of the Sun lies in the plane of the Earth's equator. At a Solstice, the Earth's orbital and rotational axes are co-planar. Those are not the formal definitions.

Astronomically, each Season starts at the corresponding Equinox or Solstice; for current dates of these, use Solar Data at heavens-above, or see NRC above. Because the Earth's orbit is elliptical, the breaks are not uniformly spaced; Spring and Summer are longer, in the Northern Hemisphere, than Autumn and Winter, by about four days each.

NMM, UK describe Equinoxes and solstices, with dates and times for 2000-2010. USNO has Earth's Seasons / Equinoxes, Solstices, Perihelion, and Aphelion, 2000-2020. +

In the Southern Hemisphere the seasons are half a year different. Within the Tropics, the four Temperate Seasons must scarcely be applicable, and wind & rain seasons are more important.

According to Whitaker's Almanac, in Britain (popularly) Spring is Feb Mar Apr, Summer is May Jun Jul Aug, Autumn is Sep Oct, Winter is Nov Dec Jan. I disagree.

Philip Eden, of The Daily Telegraph, wrote that, meteorologically, the Seasons are Mar Apr May, Jun Jul Aug, Sep Oct Nov, Dec Jan Feb; but that the Americans start Spring at the Equinox.

It seems sometimes convenient to use a fixed day-of-month, the 21st, to start a Season.

For determining the Date of Easter Sunday, March 21st is used as the First Day of Spring - Council of Nicæa AD 325 and later authorities - the nominal Vernal Equinox.

If the Seasons always change on the 21st of the month :-

Index := ((Month - Ord(Day<21)) div 3) mod 4 ;

determines the Season; and using xor 2 will flip the hemisphere. JavaScript : JavaScript Date and Time 0 : Date Object Information.

See, for Earth orbit geometry, The Seasons and the Earth's Orbit - Milankovitch Cycles" (USNO).

I have read that "Astronomical Algorithms" (2nd ed) by Jean Meeus, Willmann-Bell Publishers, ISBN 0-943396-61-1, is a good reference.

Moons in a Season

For a seasonal Blue Moon, see above. There are normally three Full Moons in a season, occasionally four; two seems just possible, on the astronomical definition of a season and not necessarily at the present epoch. Two in Winter 1961/2 has been suggested, between solstice and equinox; and three other cases in the first two millennia.

Midsummer

Midsummer may be celebrated on the weekend after a given, but uncertain, date in June.

Midsummer Time is a term which can be used for Double Summer Time.

Quarter Days

In England, Wales, and Northern Ireland, the Quarter Days are Lady Day (Mar 25), Midsummer Day (Jun 24), Michaelmas Day (Sep 29) and Christmas (Dec 25). Before 1752, the English Civil Year started on Lady Day.

In Scotland, the Term Days were Candlemas (Feb 2), Whitsunday (May 15), Lammas (Aug 1) and Martinmas (Nov 11), until (CDWF) an Act of 1990 changed those dates to Feb/May/Aug/Nov 28th; it seems that in Scotland "Whitsunday" != "Whit Sunday". The Removal Terms are May & Nov 28th.

Various Systems of Dating

Catholic / Anglican, Anglo-Saxon / European / American, British / Commonwealth peoples in general now use the one Gregorian scheme, with historical variations.

Others do their own thing, but most recognise the Gregorian system as more or less essential for international and/or business purposes.

For other calendars, see via Liste des calendriers.

There is a little more at Non-Gregorian Calendars.

The Calendar Century and Decade

The secular Gregorian Calendar repeats every 400 years, as decreed in the Papal Bull at the end of Section 9 and in Section II of the Calendar (New Style) Act (1750 c. 23). See below for more on calendar repeats.

Century

A Century, like a Millennium, properly begins with a year bearing a number which ends with 01. The 20th Century, 1901-2000, is one year later than the Nineteen-Hundreds. The Nth Century is often referred to as cN or c.N so we are now in c21.

A common Gregorian century, being of ((365=52×7+1)×4+1)×25-1 = 36524 = 5217×7+5 days, ends with the day of the week two before that with which its predecessor ended.

And after 400 years Gregorian, (((365=52×7+1)×4+1)×25-1)×4+1 = 146097 = 20871×7+0 days, the day of the week of the start of the year repeats; (4×-2)+1=-7.

For any given date within a Gregorian century (any given ##-##-##) there can only be four possible days of the week. For the start of a century - 2001-01-01 Mon, 2101-01-01 Sat, 2201-01-01 Thu, 2301-01-01 Tue - showing the stated differences - before and after which the pattern repeats.

And, as the last ten months of a year have in total 306=43×7+5 days, the day after a Gregorian-only Leap Day must be a Wednesday.

As the Gregorian Calendar repeats every 2000 years, a Millennium can only start on two possible days of the week, for example 2001-01-01 Mon and 3001-01-01 Thu.

I sometimes use the term "centade" for the years X00-X99.

Decade

The 200th Decade would properly be 1991-2000, but decades are called after the year which introduces all but the last digit.

A Decade with three Leap Years is preceded and followed by the same day of the week; the others, with two Leap Years, are a day shorter.

The Calendar Month

The Month situation is far too complex for me, except in the Julian and Gregorian Calendars. From near the beginning of the First Century, the Julian / Gregorian months have had their current sequence and lengths (the year number was incremented annually, but not always between Dec 31st & Jan 1st). Revolutionaries have differed.

February is 28 or 29 days long - Leap Years.

Number of Days in a Month
 From    Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
 BC 45    31  29/30   31    30    31    30    31    30    31    30    31    30
 BC  7    31  28/29   31    30    31    30    31    31    30    31    30    31

For the UK, the EU, and much of NA, October is the longest month of the year - because of the extra hour in the last Sunday, when Summer Time ends.

Summing the letter-values, a=1 to z=26, of the three-letter abbreviations of the English names of the months gives 12 different results : Jan 25, Feb 13, Mar 32, Apr 35, May 39, Jun 45, Jul 43, Aug 29, Sep 40, Oct 38, Nov 51, Dec 12; this could be used in an algorithm.

In any year, 4/4, 6/6, 8/8, 10/10, 12/12 are all on the same day of the week.

In any year, there are always two months, January being one, with identical calendars – starting on the same day of the week and having the same length, or finishing on the same date and day of the week. In leap years, the second month is July, otherwise it is October. January starts on the same day as the previous May, February as the previous June. Also, May 1st, September 25th, and Christmas Day are always on the same day of the week.

Day-in-Year to Month, Day

I have found (using dateprox.pas), that, when starting the year with March 1 = day 1, the binary daycount shifted right by five places (divided by thirty-two) gives the cardinal number (0..11) of the Month for over 90% of days, so the correct number can then readily be obtained by a single comparison with a pre-tabulated month-end daynumber and incrementing if necessary, without concern for variation in the length of February.

An algorithm for the reverse operation, from Meeus, is in JavaScript Date and Time 0 : Date Object Information.

Length of the Month

In some systems, including Java and ECMA JavaScript, the length of the month M in the year Y can be determined by setting a date of Y M+1 0 and then reading back the day. Beware of Netscape JavaScript; at least one version differs.

The lengths of the months can be calculated :-
excluding February, as 30 + (5546 shr M) and 1
  or as 30 + Ord(Odd($15AA shr M)) ;
excluding Leap Day, as 28 + ($3BBEECC shr 2*M) and 3 ;
in 1901-2099, as
  28 + ($3BBEECC shr 2*M) and 3 + Ord((m=2) and (Y mod 4 = 0)) .

Zeller's Congruence

Zeller presented a relationship between the date and the day of the week; it implies a formula for the month-lengths, except for February. See in Zeller's Formulae.

Thirty-Day Months

ISO 8601:2004 Section 2.2.12 refers, slightly, to 30-day months; it does not clearly define their implementation.

From an Excel (97 SR-1) help file on the DAYS360 function (Excel 2003 agrees) :-

... Use this function to help compute payments if your accounting system is based on twelve 30-day months.

... U.S. (NASD) method. If the starting date is the 31st of a month, it becomes equal to the 30th of the same month. If the ending date is the 31st of a month and the starting date is earlier than the 30th of a month, the ending date becomes equal to the 1st of the next month; otherwise the ending date becomes equal to the 30th of the same month.

... European method. Starting dates and ending dates that occur on the 31st of a month become equal to the 30th of the same month.

According to that, in Europe the 31st of a month is considered as part of the 30th, and February has one or two invisible days.

I seek references to authoritative definitions.

JavaScript code using the above is at JavaScript Date and Time 3 : Input and Lengths.

I've seen a suggestion of other "local rules"; in Germany, the last day of February may be promoted to be the 30th, and in the USA something similar may occur. One must check applicable authority.

HM Revenue and Customs Tax Months

Similar to UK Tax Weeks; the HM Revenue and Customs definition is :-

Income tax months (tax months)

Income tax months are periods following on from each other in an income tax year. They start on the 6th of one month and finish on the 5th of the following month. The first income tax month is 6 April - 5 May inclusive, the second income tax month is 6 May - 5 June inclusive, and so on.

Info supplied by Bill Lyons.

US Internal Revenue Service Months

The US IRS evidently clusters weeks into monthly 4/5-week Report Cycles, numbering the weeks as YYYYWW from Jan 1 or near that; details unknown.

Australian Rent Months

I've read that in Australia, when paying rent monthly, it's 13/3 times the weekly amount, paid in advance. That gives a discount of about 1.25 parts in 365.25 for paying less often.

Calendar Repeats

See also Date Miscellany I and Leap Years; this section disregards Easter and linked dates.

Over any range without a missing ##00-02-29, the properties of the Julian and Gregorian calendars match. Those periods are [1501]-1699, 1701-1799, 1801-1899, 1901-2099, repeating every 400 years thereafter.

Gregorian Calendar

"According to ISO 8601 (for a summary of this international standard, check Markus Kuhn, via my Date and Time Formats) there is no change of the rules after 2000 and the rules are periodic every 400 years."

Consider the number of days in 400 years of the Gregorian Calendar :-

        400 × 365       Taking all years as ordinary,
            + 100       but every fourth is leap,
            -   4       apart from the centuries,
            +   1       except for one.
        =========
           146097 = 7 × 20871.0 → integer weeks in 400 years.

Alternatively, 400 years is 97×366+303×365 days; take mod 7 of each to get 6×2+2×1 = 12+2 = 14; 14 mod 7 = 0; so 400 years is a multiple of 7 days.

Thus the present secular calendar therefore repeats, including day-of-week, every 400 years. 400 years is 146097 days (in Octal, 435261 days - note a pattern; Hex 23AB1) or 20871 (Octal, 050607; Hex, 5187) weeks.

In 400 years there are 4800 months each containing one 13th. Some 13ths are Sunday, some ..., ... Saturday; but 4800/7 is not an integer, so the 13ths (and the other days) cannot be evenly distributed among the days of the week. (However, in between 1900 and 2100, the calendar can be considered as Julian; so see below.)

Averaged over 400 years Gregorian, the thirteenth day of the month is most commonly a Friday; 43/300 (688 out of 4800) are so; program mjd_date can now enumerate this. For results, see freq-tbl.txt.

To reason this out, it is necessary to do a little real work; there are only 14 types of year (Leap or not, starting Mon to Sun - as in my year-set.txt), and the number of each type in 400 years can be counted; and each type contributes a certain number of 13ths. It might be easier to consider the year as starting on March 1st; there are now only 7 types of year for 13th-counting.

February 29th, when in a "century" year, is always a Tuesday; but Sunday, Tuesday, and Thursday are overall least common for February 29th (13/97), with Monday and Wednesday the most common (15/97).

In any span of time which does not include a "missing" February 29th, such as 1901-2099 and 2101-2199, the Gregorian Calendar matches the Julian with a constant offset; and therefore repeats every 28 years as below.

Julian Calendar

Consider the number of days in 28 years of the Julian Calendar :-

         28 × 365       Taking all years as ordinary,
            +   7       but every fourth is leap.
        =========
            10227 = 7 × 1461.0 → integer weeks in 28 years.

Thus the Julian Calendar, and the present secular calendar in between non-Leap "00" years, therefore repeat, including day-of-week, every 28 years. 28 years is 10227 days (in Octal, 23763 days; Hex 27F3) or 1461 (Octal, 2665; Hex 5B5) weeks.

In 28 years there are 336 months each containing one 13th. Some 13ths are Sunday, some ..., ... Saturday; and 336/7 is an integer, so the 13ths can be and are, as are all other days of the month, evenly distributed.

A Leap Year Calendar repeats after 28 years; those for non-leap years repeat after 11, 11, 6 years, totalling 28.

Combined Calendars

The average Julian Year is 365.25 days; 4 years are 1461 days. The average Gregorian Year is 365.2425 days; 400 years are 146097 days. The highest common factor is 3, the lowest common multiple is 71149239 days, which is 194800 Gregorian years and 194796 Julian years, which are four times 48700 and 48699 years. The calendars have a relative drift of one year in 48700 Gregorian years.

In 194800 years, the Gregorian calendar completes exactly 487 cycles of 400 years; in 194796 years, the Julian calendar completes exactly 6957 cycles of 28 years; in each case, exactly 10164177 weeks or 71149239 days. After 194800 years, a set of combined Gregorian/Julian diaries can be re-used, in the same order. There will be duplication within the diaries; there seem to be 7×(365+366)×2 = 10234 different patterns.

Other Possible Calendars

Revised Leap Years

It would be more accurate to have a Leap Year every 4 years, except for every 128th year - Leap Years.

Consider the number of days in 128 years of this Revised Calendar :-

        128 × 365       Taking all years as ordinary,
            +  32       but every fourth is leap,
            -   1       except for one.
        =========
            46751 = 7 × 6678 + 5 → non-integer weeks in 128 years.

Thus this Revised Calendar would therefore only repeat, including day-of-week, every 7×128 = 896 years. 896 years is 327257 days (in Octal, 1177131 days; Hex 4FE59) or 46751 (Octal, 133237; Hex, B69F) weeks.

In 896 of these Revised years there would be 10752 (Octal, 25000; Hex, 2A00) months each containing one 13th. Some 13ths are Sunday, some ..., ... Saturday; and 10752/7 is an integer (1536), so the 13ths (and the other days) could be evenly distributed among the days of the week. I have not worked out whether they would be so, but it seems likely.

The change should be made between 1920 and 2048, since it makes no difference within that range.

A similar proposal was made by J H von Mädler in 1864, to start nominally in 1801, and so with a first difference from Gregorian in 2028.

Revised Months

The twelve Months of the Year should be given lengths of 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 30/31 days, which would simplify date calculations.

Revised Year Subdivision

How about having 10 equal munths each of 4 equal wheks, each whek being of 9 days and consisting either of 6 workdays and a three-day whekend (in that order) or of 3+1+3+2, which gives a day off "mid-whek" and two at the "whekend" ? With 3+1+3+2, by convention Day 4 could be preferred for thoughtful private activities, Day 8 for enjoyment, and Day 9 for recuperation.

There would at the end of the year be either five or six days, termed a whik, with Christmas being celebrated on the third day (ShoppingDay, GoAwayDay, FestivalDay, BoringDay, GoBackDay, and sometimes LeapDay).

There could be four seasons of 2.5 munths each, perhaps superseded by five seazons each of two munths. The whik would as necessary be appended to the previous period.

Leap Weeks

In ISO 8601 standard week numbering, most year numbers have 52 weeks but some have 53 weeks.

ISO 8601 does not use the term "Leap Week".

With the Calendar changed from 365/366 days in the year to 52/53 weeks in the yeer (present months would be replaced by 4-week munths), there would, setting aside "religious" holidays, be the same calendar each yeer - with the last week occasional.

Dating could be YYYY-WW-D or YYYY-MM-DD with Week 53, the Leap Week, being numbered in munth 14. Events would be on the same day and day-of-week in each yeer.

Christmas could be in Week 52 always, or in the last week of the yeer, or delayed until Week 1.

Easter presently spans 35 dates MM-DD, possibly 36 Day-Numbers DDD; with Leap Weeks it would span 5 or 6 Sundays. It could be fixed onto one of those by a minor modification of the Easter Act 1928.

Summer Time rules would be slightly modified, too.

A Fixed Calendar

The following JavaScript shows, crudely, a calendar based on ISO week numbering.
* ISO : All yeers are 52 or 53 weeks, Mon to Sun
* ISO : Turn-of yeer is always in -3 to +3 days from Gregorian
* All yeers are the same, apart from an occasional final 7-day leap week/munth/quorter, as in 2004
* Munth lengths are 30 or 31 or sometimes 7 days
* Munths are 0 to 11 or 12, to avoid 13
* Four quorters are the same, and symmetrical 30 31 30
* Remove 2 & 61 from the lines that set M & D to get a different distribution, 31 30 30
* Uses ISO YWD code; if combined, parts may simplify.

Year :  

As the above is based on the Gregorian Implemention, the yeer-lengths are not as regular as they might be. It would be better to base it on YearNo := Trunc(WeekCount*400/20871) , eventually, or on such other ratio as astronomy currently suggests.

Who?

A few personal names are over-used, and it is well to know who is associated with what.

Which Julius?

The term "Julian" is over-used in this field; the following should clarify.

Caius/Gaius Julius Caesar

Of Rome (BC, ~100 to ides martii 44). Calendar Reformer; Pontifex; Invader; Commentator; Dictator; Assassinee.

After him : the Julian Calendar; the month July; the Shakespeare play.

Julian Epochs, beloved of Astronomers and having years of 365.25 days, are named after the Julian Calendar Year; and the Julian Century has 36525 days.

Julius Caesar Scaliger

Joseph Justus Scaliger (1540-1609) drew attention to the Julian Period (7980 years). It is often said that he named it in honour of his father JCS; but Scaliger wrote that the reference is to the Julian Year. See in Date Miscellany I, and JJ Scaliger, la période julienne et les jours juliens

Who Knows?

The "IBM" or "business" Julian Date : YYYY-DDD and derived forms; annual daycount from January 1st = 001. It is properly (ISO 8601) termed Ordinal Date.

Etc.

Which Gregory?

See Chambers' Dictionary, Brewer, and other sources.

Pope Gregory I

Sixth Century : the Gregorian Chant.

Pope Gregory VII

Eleventh Century : the Gregorian Reform.

Pope Gregory XIII

Sixteenth Century : the Gregorian Calendar; the Gregorian University.

Pope Gregory XVI

Nineteenth Century : the (Vatican) Gregorian Museums.

Others

James Gregory (1638-75) : the Gregorian Telescope.

Etc.

Which Dionysius?

Dionysius

Greek god of wine; Bacchus; son of Zeus.

Dionysius the Elder

BC 430 to 367 : Tyrant of Syracuse.

Dionysius the Younger

Next Tyrant of Syracuse.

Dionysius of Halicarnassus

First Century BC : Greek rhetorician.

Dionysius the Areopagite

First Century AD : Athenian, convert of St Paul (Acts xvii 34).

Saint Dionysius

Third Century : St Denis, bishop of Paris, martyr, patron saint of France.

Dionysius Exiguus

Denis the Little (c. 500-560;) : a Scythian monk ; the numberer of years.

Etc.

Annual Holiday Dates (including Easter),
The Date of Easter Sunday,
The Hebrew Calendar.

See also Date Miscellany I, which precedes this; Zeller's Formulae; Calendar Weeks, Date and Time Scales, and Time Miscellany.

Home Page
Mail: no HTML
© Dr J R Stockton, near London, UK.
All Rights Reserved.
These pages are tested mainly with Firefox and W3's Tidy.
This site, http://www.merlyn.demon.co.uk/, is maintained by me.
Head.