Complete Definitions of 3 Month-Start-Uniform Seasonal Calendars

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Complete Definitions of 3 Month-Start-Uniform Seasonal Calendars

Michael Ossipoff

(Apologies!  I realize that this is a long message, and that a long message shouldn't be re-sent to a mailing-list. But my previous sending of it didn't have a subject line. A message without a subject-line doesn't show up as the message that it is. Hence the necessity to re-send it. Again, apologies--I really do know better than to do this under ordinary circumstances, but this is an exceptional circumstance.)


I’ve defined two 6-season month-systems for 6-season astronomical-terrestrial seasonal-calendars.  They both start the year near the South-Solstice (as determined by a specified version of the general Nearest-Monday class of year-start rules). 

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One of my proposed astronomical-terrestrial seasonal calendars starts its Nominal-South season at its year-start date (…in the tradition of French-Republican and Asimov’s World-Seasonal, which both start their Nominal-South season near or at the South-Solstice). Such an arrangement sacrifices some seasonal-accuracy for simplicity and neatness.

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The other starts its Nominal-South season 3-weeks before its year-start date (I call that a -3 wk “offset” of the South-Season start with respect to the year-start). I don’t know of a precedent for that. It achieves intentional tailoring of the season-start dates, to better match experience and consensus, at the expense of simplicity, structural-symmetry and neatness.

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Nor have I heard of precedent for an astronomical-terrestrial seasonal-calendar that recognizes 6 seasons.

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Unavoidably, the -3 wk offset splits the South season between two calendar-years, and likewise splits the South1 month.  …a neatness-sacrifice for the purpose of an intentional choosing of when to start the South season.

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I’ve now changed both month-systems and my names for them. So, the 0 offset and -3 wk offset 6-season astronomical-terrestrial seasonal calendars that I define here aren’t the same ones that I’ve previously been proposing.

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I additionally propose a no-months WeekDate calendar that is identical to ISO WeekDate, except that it’s Nearest-Monday rule (the same as that of my two above-mentioned proposals) is based on the South-Solstice.

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As I said in my subject line for this message, I’ll completely define those three calendars in this message…the 0 offset calendar, and the -3 wk offset calendar, and the simple, minimal South-Solstice WeekDate calendar.

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In both of my calendars that have months, every month of every year starts on the same day of the week, a Monday. 

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In my WeekDate calendar, of course every year, and every numbered week, starts on a Monday.

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A calendar can be defined by its year-division system and its year-start rule.

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Topics in this post:

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1. First I’ll completely define, in the section directly below, the specific Nearest-Monday year-start rule for my three calendar-proposals. (They all use the same one.)

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2. Then I’ll define the year-division systems for my three proposals.

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The 1st  one is a WeekDate system that doesn’t use months. The 2nd and 3rd ones are astronomical-terrestrial seasonal month-systems, based on 6 seasons.

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My three calendar-proposals have the following names:

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South-Solstice WeekDate

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6-Seasons  0 Offset

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6-Seasons  -3 wk Offset

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3. Lastly, I’ll return to the subject of year-start rules, for a (optional, not necessary) more general explanation and definition of the general class of Nearest-Monday year-start rules.

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Here is the year-start rule for my three calendar-proposals:

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1. All three of my calendar-proposals use the closeness-measure that says:

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The year starts with the Monday that starts at the midnight that’s closest to the “intended-time”(specified directly below).

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2. For my calendar-proposals, every 365.2422 days, the end of that 365.2422 day period is the intended-time, for the purpose of starting a calendar-year with the Monday that starts at the midnight that’s closest to that intended-time.

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…where the first 365.2422 day period, of that sequence of end-to-end 365.2422 day periods, started at the South-Solstice (Winter-Solstice in the Northern-Hemisphere) of Gregorian year 2017.

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(365.2422 was chosen because roughly every 365.2422 days the Sun returns to the same ecliptic-longitude, and our year returns to the same seasonal time-of-year. This is an arithmetical rule that approximates the South-Solstices of years subsequent to 2017.)

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That’s a brief statement of the Nearest-Monday version for all three of my calendar-proposals.

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I should add that each year is numbered the same as the Gregorian year that starts on the Gregorian January 1st that next occurs after the start of my calendars’ year-start.  (But of course, after the 1st year of a new calendar, each next year just has the next consecutive whole number.)

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Three Year-division systems that, with the above-defined year-start rule, define three seasonal calendars:

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First, all 3 of these calendars start on the day determined by the above-described Nearest-Monday rule as the Monday that starts nearest to the South-Solstice.South-Solstice WeekDate:

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Identical to ISO WeekDate, except based on the South-Solstice instead of Gregorian January 1st.

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Starting with the week beginning on the Monday on which the year starts, each week is consecutively numbered, and the date is expressed by the week-number and a day-of-the-week-number.  For example, today (Roman-Gregorian December 22nd) is:

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2018-W52-6

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…i.e. the 6th day (Saturday) of the 52nd week of the year.

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South-Solstice WeekDate qualifies as a seasonal calendar—an astronomical seasonal calendar—because it starts its year on the Monday that starts nearest to the South-Solstice.

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It’s the minimal seasonal calendar.

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6-Seasons 0 Offset:

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The 6 seasons are: Winter, Pre-Spring, Spring, Summer, Pre-Autumn, Autumn.

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…or, internationally named, for solar-declination:

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South, Pre-Northward, Northward, North, Pre-Southward, Southward.

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The nominal South season is defined as starting on the first day of the year.

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Here are the seasons’ month lengths, in weeks. For each season, each numeral tells the number of weeks in one of its months:

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South 443

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Pre-Northward 4

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Northward 443

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(Of course North, Pre-Southward, and Southward follow the same pattern)

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Writing that half-year’s season’s weeks in each of their months in a single row:

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443  4  443

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In some years, Nearest-Monday will give the year an extra week—53 weeks instead of 52. The 53rd week is just called “Leapweek”, and isn’t part of a month. But it’s part of the South season.

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Today (Roman-Gregorian December 22nd) is Southward3  Week 3  Saturday.

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6-Season  -3 wk Offset:

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This calendar differs from the previous one in that its nominal South season is defined as starting 3 weeks before the end of the 52nd week of the year.

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The seasons are named the same as those of 6-Season 0 Offset.

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Here are the first half-year’s (half of a seasonal-year’s, not half of a single calendar-year’s) seasons’ month-lengths, in weeks:

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South 544

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Pre-Northward 5

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Northward 44

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Here are that half-year’s (half of a seasonal-year’s, not half of a single calendar-year’s) seasons’ months’ lengths in weeks, all in one row:

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544  5  44

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Because the Month of South1 is split in two by the beginning of a calendar year, and, in order to reset all of the numbers to 1 for the new year, the part (3 weeks) of South1 that’s in the old year is designated the month of Early-South.  The part (2 weeks) of South1 that’s in the new year is called South 1 (because it’s the new year’s 1st month in the South season).  The additional, 5th,  and last remaining, month of South is of course called South2.

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Of course, as months, Early-South and South1 are separately week-numbered.

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Leapweek is dealt with the same as in 6-Seasons 0 Offset.

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Today (Roman-Gregorian December 22nd ) is Early-South  Week3  Saturday.

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For anyone who wishes it, what follows below is a wordier and more general explanation and a broader and more general Nearest-Monday definition that covers other possible versions of Nearest-Monday.

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Disregard and skip the next section, which concludes this post, unless you’re interested in that wordier and more general explanation, discussion and definition.

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Here’s the Nearest-Monday rule used by ISO WeekDate and Hanke-Henry:

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The year starts on the Monday that’s closest to our Gregorian January 1st for the Gregorian year with the same year-number.

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But Nearest-Monday can be generalized to choose, as the year-start, the Monday that’s closest to any desired “intended-time”, such as, for example, the South-Solstice (Winter-Solstice, for locations north of the equator).

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That “intended-time” could be any solstice or equinox, or it could be an arithmetical approximation to one of them (such as my proposals use, as described earlier above.

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Two definitions of “closeness” to the intended-time:

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1. The year starts with the Monday closest to the day that contains the intended-time.

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or

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2. The year starts with the Monday that starts at the midnight closest to the intended-time.

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#1 is briefer, but #2 is more accurate.  I prefer #2, but #1’s brevity could make it preferable.

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For the time-being at least, my proposals use closeness-measure  #2.

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Choices for the intended-time:

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1. As mentioned above, any actual solstice or equinox could be the intended time.

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That could be called an “astronomically-defined intended-time”.

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2. Or it could be an arithmetical approximation to a solstice or equinox  (…such as used by my proposals, as described earlier, above).

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(My proposals use an arithmetical approximation to the South-Solstice)

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Here’s how such a rule goes:

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Roughly every 365.2422 mean-solar days, the Sun returns to the same “ecliptic-longitude” , and the year returns to the same seasonal time-of-year.

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So then, say that every 365.2422 days, a year starts on the Monday that’s closest (by one of the above two closeness-measures) to the end of that 3656.2422 day period.

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…where the first 365.2422 day period in that sequence of 364.2422 day periods starts at some specified instance of a particular solstice or equinox.  For instance, my proposals start the sequence at the South-Solstice in Gregorian 2017.

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365.2422 mean solar days is the value that I find on the Internet, for the average time it takes for the Sun to return to the same ecliptic-longitude.  (…averaged over the various ecliptic-longitudes at which one could measure that return-duration).

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That average duration, 365.2422 mean days, is called the “mean-tropical-year”.

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That’s the tropical-year that my proposal uses, and nothing more need be said here about tropical-years.

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So disregard the following section, between the rows of asterisks (“****”), unless you’re curious about generalizing this rule to other tropical-years.

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Let me briefly say what that means:

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In general, a “tropical-year”  is the duration between two successive passages of the Sun by some specified point on the ecliptic. The length of a tropical year is the time that it takes for the Sun to return to that same particular place on the ecliptic.

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Because of perturbations of the Earth’s orbit by other celestial bodies, the tropical-year durations measured with respect to different places on the ecliptic are different.

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The mean-topical-year is the average of the tropical years measured with respect to the various points of the ecliptic. As I said, that’s the tropical-year that my proposals use, and its duration that I found on the Internet, is 365.2422 days.

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But, if desired, of course a different tropical year could be used. For example, the South Solstice tropical year (the duration between successive South-Solstices) could be used. Likewise, the similarly-defined North-Solstice tropical-year, Northward Equinox tropical-year, or Southward-Equinox tropical year could be used.

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To refer to whatever tropical year is being used for Nearest-Monday, I’ll call it the “reference-tropical-year” (RTY), and, in general, when the tropical year isn’t specified, I’ll denote its duration by the letter “Y”.

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So—bottom line for this section—One could, if desired, for complete generality, substitute, in the above rule-definition, “Y” for 365.2422    …to allow for a choice to use a different tropical year other than the mean-tropical-year as the RTY (reference-tropical-year).

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But I just use the mean-tropical-year, 365.2422 says, for the arithmetic approximation to the South-Solstice, for Nearest-Monday.

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Repeating the Nearest-Monday rule version that my proposals use:

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All three of my calendar-proposals use the closeness-measure that says:

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The year starts with the Monday that starts at the midnight that’s closest to the “intended-time”.

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For my proposals, every 365.2522 days, the end of that 365.2422 day period is the intended-time for the purpose of starting a year. …where the first 365.2422 day period of that sequence started at the South-Solstice (Winter-Solstice in the Northern-Hemisphere) of Gregorian year 2017.

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That’s a brief statement of the Nearest-Monday version for all three of my calendar-proposals.

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Early-South  Week 3  Saturday  (6-Seasons  -3 wk Offset)

Southward3  Week 3  Saturday  (6-Seasons  0 Offset)

2018-W51-6  (ISO WeekDate)

2018-W52-6  (South-Solstice WeekDate)

December 22nd  (Roman-Gregorian)

December 23rd  (Hanke-Henry)

1 Nivȏse (Snow-Month) CCXXVII  (French Republican Calendar of 1792) Peat

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Michael Ossipoff