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Michael Ossipoff

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). 

.

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.

.

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.

.

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

.

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.

.

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.

.

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.

.

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.

.

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

.

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

-----------------------------

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

.

Topics in this post:

.

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.)

.

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

.

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.

.

My three calendar-proposals have the following names:

.

South-Solstice WeekDate

.

6-Seasons  0 Offset

.

6-Seasons  -3 wk Offset

.

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.

------------------------------

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

.

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

.

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

.

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.

.

…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.

.

(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.)

.

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

.

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.)

---------------------------------------------------------

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

.

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:

.

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

.

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:

.

2018-W52-6

.

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

.

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.

.

It’s the minimal seasonal calendar.

.

6-Seasons 0 Offset:

.

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

.

…or, internationally named, for solar-declination:

.

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

.

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

.

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

.

South 443

.

Pre-Northward 4

.

Northward 443

.

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

.

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

.

443  4  443

.

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.

.

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

.

6-Season  -3 wk Offset:

.

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.

.

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

.

Here are the first half-year’s seasons’ month-lengths, in weeks:

.

South 544

.

Pre-Northward 5

.

Northward 44

.

Here are that half-year’s seasons’ months’ lengths in weeks, all in one row:

.

544  5  44

.

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.

.

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

.

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

.

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

-----------------------------------------------------------

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.

.

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

.

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

.

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

.

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).

.

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.

.

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

.

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

.

or

.

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

.

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

.

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

.

Choices for the intended-time:

.

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

.

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

.

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

.

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

.

Here’s how such a rule goes:

.

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.

.

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.

.

…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.

.

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).

.

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

.

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

.

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

****************************************************

Let me briefly say what that means:

.

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.

.

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.

.

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.

.

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.

.

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”.

.

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).

.

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

*******************************************************

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

.

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

.

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

.

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.

.

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

--------------------

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

.

Michael Ossipoff

 

 

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Re: Six-Season Calendar

k.palmen@btinternet.com
Dear Michael and Calendar People

An important consideration is when in the year is the leap week inserted.


Season's Greetings

Karl


Saturday Gamma December 2018
----Original message----
From : [hidden email]
Date : 22/12/2018 - 09:03 (GMT)
To : [hidden email]
Subject :


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). 

.

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.

.

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.

.

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

.

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.

.

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.

.

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.

.

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.

.

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

.

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

-----------------------------

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

.

Topics in this post:

.

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.)

.

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

.

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.

.

My three calendar-proposals have the following names:

.

South-Solstice WeekDate

.

6-Seasons  0 Offset

.

6-Seasons  -3 wk Offset

.

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.

------------------------------

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

.

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

.

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

.

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.

.

…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.

.

(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.)

.

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

.

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.)

---------------------------------------------------------

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

.

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:

.

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

.

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:

.

2018-W52-6

.

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

.

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.

.

It’s the minimal seasonal calendar.

.

6-Seasons 0 Offset:

.

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

.

…or, internationally named, for solar-declination:

.

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

.

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

.

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

.

South 443

.

Pre-Northward 4

.

Northward 443

.

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

.

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

.

443  4  443

.

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.

.

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

.

6-Season  -3 wk Offset:

.

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.

.

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

.

Here are the first half-year’s seasons’ month-lengths, in weeks:

.

South 544

.

Pre-Northward 5

.

Northward 44

.

Here are that half-year’s seasons’ months’ lengths in weeks, all in one row:

.

544  5  44

.

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.

.

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

.

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

.

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

-----------------------------------------------------------

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.

.

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

.

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

.

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

.

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).

.

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.

.

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

.

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

.

or

.

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

.

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

.

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

.

Choices for the intended-time:

.

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

.

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

.

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

.

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

.

Here’s how such a rule goes:

.

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.

.

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.

.

…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.

.

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).

.

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

.

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

.

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

****************************************************

Let me briefly say what that means:

.

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.

.

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.

.

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.

.

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.

.

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”.

.

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).

.

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

*******************************************************

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

.

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

.

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

.

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.

.

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

--------------------

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

.

Michael Ossipoff

 

 



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Re: Six-Season Calendar

Michael Ossipoff
Karl--

The leapweek, named as "Leapweek" is inserted at the end of the year, after the last month.  Leapweek is counted as part of the South season, but not part of any month.

Michael Ossipoff
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Re: Six-Season Calendar

Michael Ossipoff
In reply to this post by k.palmen@btinternet.com
Yes, Sesaon's Greetings.    ...long a celebratory time in our Northern temperate latitudes, when the seasonal-year has begun to return in our direction,

Early-South  Week 3  Sunday  (6-Season  -3 wk Offset)
2018-W52-7
2 Nivose  CCXXVII  Bitumen

Michael Ossipoff



Michael Ossipoff



On Sat, Dec 22, 2018 at 5:16 AM K PALMEN <[hidden email]> wrote:
Dear Michael and Calendar People

An important consideration is when in the year is the leap week inserted.


Season's Greetings

Karl


Saturday Gamma December 2018
----Original message----
From : [hidden email]
Date : 22/12/2018 - 09:03 (GMT)
To : [hidden email]
Subject :


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). 

.

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.

.

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 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 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 mean solar days, 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

 

 



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Re: Six-Season Calendar

k.palmen@btinternet.com
In reply to this post by Michael Ossipoff
Dear Michael and Calendar People

Thank you for letting me know. This has an effect on when the equinoxes and solstices occur in the calendar year.

Karl

Friday Delta December 2018
----Original message----
From : [hidden email]
Date : 22/12/2018 - 21:19 (GMT)
To : [hidden email]
Subject : Re: Six-Season Calendar

Karl--

The leapweek, named as "Leapweek" is inserted at the end of the year, after the last month.  Leapweek is counted as part of the South season, but not part of any month.

Michael Ossipoff