Skip to content

Latest commit

 

History

History
395 lines (334 loc) · 25.1 KB

Rivendell_Drift.md

File metadata and controls

395 lines (334 loc) · 25.1 KB
Raw

The Drifting of the Calendar of Imladris through Time

Contents

How the Calendar of Imladris drifts apart from the Gregorian calendar

If the Calendar of Imladris (a.k.a. the Rivendell Reckoning calendar) starts reckoning on a proleptic Gregorian year 1, March 22nd, and because the Gregorian calendar has a leap-year every 4 years but the Calendar of Imladris only has a leap-year every 12, then in years 1 - 12 Rivendell New Year's Day (Yestarë) will fall on March 22, 22, 22, 21, 21, 21, 21, 20, 20, 20, 20, and 19. This is because the Gregorian calendar adds a leap-day in years 4, 8, and 12, and the February 29 leap-day is added before Yestarë in those years, causing it to fall a day earlier in the Gregorian calendar than in the previous non-leap year. When the Calendar of Imladris has its first leap-year in year 12, it adds 3 extra Middle-days (Enderi) in the autumn of that year, which allows Yestarë to fall on March 22 once again in year 13. This pattern of Yestarë falling on March 22 - 19 repeats for years 13 - 24, and every 12 years until year 100.

The Calendar of Imladris will have had a leap-year in year 96, so Yestarë would fall on March 22 again in year 97. Since the proleptic Gregorian calendar omits its leap-day in year 100, its next leap-year is not until year 104, and since the Calendar of Imladris' next leap-year would be in year 108, then in years 97 - 108 Yestarë would fall on March 22, 22, 22, 22, 22, 22, 22, 21, 21, 21, 21, and 20. Then in years 109 - 120 Yestarë would fall on March 23, 23, 23, 22, 22, 22, 22, 21, 21, 21, 21, and 20. This means the 12-year pattern of Yestarë dates in March has shifted so that Yestarë now falls between March 23 - 20 in years 109 - 192.

Since the proleptic Gregorian calendar omits another leap-day in year 200, then in years 193 - 204 Yestarë would fall on March 23, 23, 23, 22, 22, 22, 22, 22, 22, 22, 22, and 21. The cycle shifts again in 205 so that Yestarë falls between March 24 - 21 in years 205 - 299. Once again, the Gregorian calendar omits its leap-day in year 300. Since that year is a leap-year in the Calendar of Imladris, Yestarë falls on March 22 in year 300, then March 25 in year 301, and the cycle shifts again so that Yestarë falls between March 25 - 22 in years 301 - 432.

Note that the Gregorian calendar does not omit its leap-day in years divisible by 400, which is why this pattern continues past year 400, but recall that the Calendar of Imladris omits its 3 extra Enderi every 432 years. So Yestarë does not "leap" from March 22 in the year 432 to March 25 in year 433, so in years 428 - 444 Yestarë would fall on March 23, 23, 23, 23, 22, 22, 22, 22, 21, 21, 21, 21, 20, 20, 20, 20, and 19. This means that the Calendar of Imladris 432-year cycle has put it back in sync with this proleptic Gregorian calendar's 400-year cycle, so that Yestarë falls on March 22 - 19 once again in years 433 - 500 (the same pattern as years 1 - 100).

Now note that this 32 year difference between these calendars' cycles will add up, so that after the year 1700, the Gregorian calendar's shorter 400-year cycle will have omitted 1 more leap-day than the Calendar of Imladris 432-year cycle will have omitted by the end of year 1728. This causes the Calendar of Imladris 432-year cycle to permanently shift a day later in the Gregorian calendar's 400-year cycle, so that the pattern of Yestarë dates in March becomes the following:

  • Yestarë falls on March 23 - 20 in years 1729 - 1788.
  • Yestarë falls on March 23 - 21 in years 1789 - 1800.
  • Yestarë falls on March 24 - 21 in years 1801 - 1896.
  • Yestarë falls on March 24 - 22 in years 1897 - 1908.
  • Yestarë falls on March 25 - 22 in years 1909 - 2088.
  • Yestarë falls on March 25 - 23 in years 2089 - 2100.
  • Yestarë falls on March 26 - 23 in years 2101 - 2160.

Then in 2160 the Calendar of Imladris omits its 3 extra Enderi and the pattern of Yestarë dates in March becomes the following:

  • Yestarë falls on March 23 - 20 in years 2161 - 2196.
  • Yestarë falls on March 23 - 21 in years 2197 - 2208.
  • Yestarë falls on March 24 - 21 in years 2209 - 2292.
  • Yestarë falls on March 24 - 22 in years 2293 - 2304.
  • Yestarë falls on March 25 - 22 in years 2305 - 2496.
  • Yestarë falls on March 25 - 23 in years 2497 - 2508.
  • Yestarë falls on March 26 - 23 in years 2509 - 2592.

Then in 2592 the Calendar of Imladris omits its 3 extra Enderi and the pattern of Yestarë dates in March becomes the following:

  • Yestarë falls on March 23 - 21 in years 2593 - 2604.
  • Yestarë falls on March 24 - 21 in years 2605 - 2688.
  • Yestarë falls on March 24 - 22 in years 2689 - 2700.
  • Yestarë falls on March 25 - 22 in years 2701 - 2892.
  • Yestarë falls on March 25 - 23 in years 2893 - 2904.
  • Yestarë falls on March 26 - 23 in years 2905 - 2988.
  • Yestarë falls on March 26 - 24 in years 2989 - 3000.
  • Yestarë falls on March 27 - 24 in years 3001 - 3024.

Gradually, over the millennia, the Calendar of Imladris 432-year cycle will continue to drift away from the Gregorian calendar's 400-year cycle, so that Yestarë will fall on later and later dates in the Gregorian calendar.

The examples include tables that demonstrate these cycles generated using this project's calendars!

How the Calendar of Imladris drifts apart from the Shire Calendar

The leap-year cycles of the Calendar of Imladris drift in a similar way when compared to the Shire Calendar, though in a slightly different way due to the slightly different leap-year rules of the Shire Calendar, which omits a leap-day every century, including every 4th century (year 400, 800, etc.), but the Shire Calendar could have also had Millennial Leap-years, which have 2 leap-days every 1000 years.

If the Calendar of Imladris started reckoning a new 432-year cycle from Shire-reckoning year 1 on 'April' 6 (Astron 6), which means their leap-year cycles would be in sync (for example, if Rivendell Reckoning year 1 corresponded with Shire-reckoning year 1), then because the Shire Calendar has a leap-year every 4 years but the Calendar of Imladris only has a leap-year every 12, then in years 1 - 12 Rivendell New Year's Day (Yestarë) would fall on Shire April 6, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, and 4.

Notice this is a slightly different pattern compared to the drift in the Gregorian calendar, since the modern Gregorian calendar adds its February 29 leap-day in year 4 before the Rivendell Reckoning Yestarë in that year, but the Shire Calendar does not add its Overlithe leap-day in its year 4 until midsummer, which is after the Rivendell Reckoning Yestarë in that year. So the Rivendell Reckoning Yestarë would not drift back in the Shire Calendar until year 5 in this example, but it would drift back in the Gregorian calendar's year 4 in the example above. This is also why the Rivendell Reckoning Yestarë would drift back 3 times in this 12-year cycle in the Gregorian calendar, but only 2 times in 12 years in the Shire Calendar of this example.

When the Calendar of Imladris has a leap-year in year 12, it adds 3 extra Middle-days (Enderi) in the autumn of that year, which would allow Yestarë to fall on Shire April 6 once again in year 13. This pattern of Yestarë falling on Shire April 6 - 4 would repeat for years 13 - 24, and every 12 years until year 100.

The Calendar of Imladris would have a leap-year in year 96, so Yestarë would fall on Shire April 6 again in year 97. Since the Shire Calendar omits its leap-day in year 100, its next leap-year is not until year 104, and since the next leap-year in the Calendar of Imladris would be in year 108, then in years 97 - 108 Yestarë would fall on Shire April 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, and 5. Then in years 109 - 120 Yestarë would fall on Shire April 7, 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, and 5. This means the 12-year pattern of Yestarë dates in the Shire Calendar has shifted so that Yestarë would now fall between Shire April 7 - 5 in years 108 - 192.

Since the Shire Calendar omits another leap-day in year 200, then in years 193 - 204 Yestarë would fall on Shire April 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, and 6, and the cycle shifts again in 205 so that Yestarë would fall between Shire April 8 - 6 in years 205 - 300.

Once again, the Shire Calendar omits its leap-day in year 300. Since that year is a leap-year in the Calendar of Imladris, Yestarë would then fall on Shire April 9 in year 301, and the cycle shifts again so that Yestarë would fall between Shire April 9 - 7 in years 301 - 396.

The Shire Calendar omits another leap-day in year 400, so in years 397 - 408 Yestarë would fall on Shire April 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, and 8. The cycle has now shifted so that Yestarë would fall between Shire April 10 - 8 in years 409 - 432.

Recall that the Calendar of Imladris omits its 3 extra Enderi every 432 years. So Yestarë would not "leap" from Shire April 8 in the year 432 to Shire April 10 in year 433, and instead Yestarë would fall back to Shire April 7 in year 433. Now the cycle has shifted so that Yestarë would fall between Shire April 7 - 5 in years 433 - 492.

The pattern for years 1 - 432 repeats in a similar way for years 433 - 864:

  • Yestarë would fall on Shire April 7 - 5 in years 433 - 492.
  • Yestarë would fall on Shire April 7 - 6 in years 493 - 504.
  • Yestarë would fall on Shire April 8 - 6 in years 505 - 600.
  • Yestarë would fall on Shire April 9 - 7 in years 601 - 696.
  • Yestarë would fall on Shire April 9 - 8 in years 697 - 708.
  • Yestarë would fall on Shire April 10 - 8 in years 709 - 792.
  • Yestarë would fall on Shire April 10 - 9 in years 793 - 804.
  • Yestarë would fall on Shire April 11 - 9 in years 805 - 864.

Then in 864 the Calendar of Imladris would omit its 3 extra Enderi and the pattern of Yestarë dates in the Shire Calendar would become the following:

  • Yestarë would fall on Shire April 8 - 6 in years 865 - 900.
  • Yestarë would fall on Shire April 9 - 7 in years 901 - 996.

If the Shire Calendar incorporated the Millennial Leap-year rules of the Kings' Reckoning, then it would have 2 leap-days in year 1000. So in years 997 - 1008 Yestarë would fall on Shire April 9, 9, 9, 9, 7, 7, 7, 7, 6, 6, 6, and 6.

So the pattern for rest of this cycle has shifted:

  • Yestarë would fall on Shire April 8 - 6 in years 1009 - 1092.
  • Yestarë would fall on Shire April 8 - 7 in years 1093 - 1104.
  • Yestarë would fall on Shire April 9 - 7 in years 1105 - 1200.
  • Yestarë would fall on Shire April 10 - 8 in years 1201 - 1296.

Then in 1296 the Calendar of Imladris would omit its 3 extra Enderi and the pattern of Yestarë dates in the Shire Calendar would become the following:

  • Yestarë would fall on Shire April 7 - 6 in years 1297 - 1308.
  • Yestarë would fall on Shire April 8 - 6 in years 1309 - 1392.
  • Yestarë would fall on Shire April 8 - 7 in years 1393 - 1404.
  • Yestarë would fall on Shire April 9 - 7 in years 1405 - 1500.
  • Yestarë would fall on Shire April 10 - 8 in years 1501 - 1596.
  • Yestarë would fall on Shire April 10 - 9 in years 1597 - 1608.
  • Yestarë would fall on Shire April 11 - 9 in years 1609 - 1692.
  • Yestarë would fall on Shire April 11 - 10 in years 1693 - 1704.
  • Yestarë would fall on Shire April 12 - 10 in years 1705 - 1728.

Then in 1728 the Calendar of Imladris would omit its 3 extra Enderi and the pattern of Yestarë dates in the Shire Calendar would become the following:

  • Yestarë would fall on Shire April 9 - 7 in years 1729 - 1800.
  • Yestarë would fall on Shire April 10 - 8 in years 1801 - 1896.
  • Yestarë would fall on Shire April 10 - 9 in years 1897 - 1908.
  • Yestarë would fall on Shire April 11 - 9 in years 1909 - 1992.

Once again, if the Shire Calendar incorporated the Millennial Leap-year rules of the Kings' Reckoning, then it would have 2 leap-days in year 2000. So in years 1993 - 2004 Yestarë would fall on Shire April 11, 11, 11, 11, 10, 10, 10, 10, 8, 8, 8, and 8. Then Yestarë would fall on Shire April 10 - 8 in years 2005 - 2100, and a similar pattern continues as above, only with slightly later Shire dates.

Gradually, over the millennia, the Calendar of Imladris 432-year cycle would continue to drift away from the Shire Calendar (or Kings' Reckoning) 1000-year cycle, so that Yestarë will fall on later and later dates in the Shire Calendar.

Note that these patterns only apply if the Rivendell Reckoning and Shire Calendar leap-year cycles are in sync, but there is no reason to assume that they were in sync in Middle-earth, and the relationship of the Calendar of Imladris to the Shire Calendar can be slightly more complicated if their leap-years are not in sync.

For example, suppose the Calendar of Imladris has a leap-year in T.A. 3001 so that it adds its 3 leap-days in the autumn of that year, and suppose that causes Yestarë to fall on Shire April 7 in T.A. 3002 (as it happens in the alignment of the default settings of these Middle-earth calendar simulations). So in the years T.A. 3002 - T.A. 3013 Yestarë would fall on Shire April 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, and 4.

This is because the Shire Calendar has its leap-years in T.A. 3004, 3008, and 3012, but the next Rivendell Reckoning leap-year wouldn't be until T.A. 3013.

  • In the years T.A. 3002 - T.A. 3004 Yestarë would fall on Shire April 7.
  • The Shire leap-day in the summer of T.A. 3004 would then cause Yestarë to fall on Shire April 6 in the years T.A. 3005 - T.A. 3008.
  • The Shire leap-day in the summer of T.A. 3008 would then cause Yestarë to fall on Shire April 5 in the years T.A. 3009 - T.A. 3012.
  • The Shire leap-day in the summer of T.A. 3012 would then cause Yestarë to fall on Shire April 4 in T.A. 3013.
  • Finally the Calendar of Imladris would have a leap-year and add its 3 leap-days in the autumn of T.A. 3013, causing Yestarë to fall on Shire April 7 once again in T.A. 3014.

The year that the Calendar of Imladris starts its reckoning would determine how its leap-year cycles line up with the Shire Calendar leap-year cycles.

The examples include tables that demonstrate these cycles generated using this project's Middle-earth simulation calendars!

Aligning the Calendar of Imladris to the Shire Calendar

Tolkien never stated when the Calendar of Imladris was established or from what year it started reckoning. In Appendix D he stated that Rivendell's New Year's Day (Yestarë) "corresponded more or less with Shire April 6", and The Tale of Years (Appendix B) lists the "Meeting of Celeborn and Thranduil" on Shire April 6 in Third Age (T.A.) 3019, which is said to have taken place on the "New Year of the Elves". That should mean Rivendell's Yestarë was also on Shire April 6 in T.A. 3019. In fact, this is the only known Calendar of Imladris date given with a corresponding Shire or Gondor date.

The following table shows some possible alignments of the Rivendell Reckoning's Yestarë to Shire dates around the end of the Third Age. In this table I'm using IV for Fourth Age years, III for Third Age years, II for Second Age years, and Iys for Years of the Sun in the First Age.

The first row displays a potential first Yestarë for year 1 of the Rivendell Reckoning calendar, given as a proleptic Shire Reckoning or Kings' Reckoning date. The first column displays a year around the end of the Third Age, and the following columns display the Shire Reckoning month/day for Yestarë in that year.

Note that in every column, Yestarë falls on Shire April 6 in III 3019.

III-IV year Iys 1, 3/30 II 1, 3/27 II 1697, 4/4 III 1, 4/2 III 1601, 4/6
III 3009 4/5 4/5 4/8 4/5 4/5
III 3010 4/5 4/5 4/8 4/5 4/5
III 3011 4/5 4/5 4/8 4/5 4/5
III 3012 4/5 4/5 4/8 4/5 4/5
III 3013 4/4 4/4 4/7 4/7 4/4
III 3014 4/7 4/4 4/7 4/7 4/4
III 3015 4/7 4/4 4/7 4/7 4/4
III 3016 4/7 4/7 4/7 4/7 4/4
III 3017 4/6 4/6 4/6 4/6 4/6
III 3018 4/6 4/6 4/6 4/6 4/6
III 3019 4/6 4/6 4/6 4/6 4/6
III 3020 4/6 4/6 4/9 4/6 4/6
IV 1 4/5 4/5 4/8 4/5 4/5
IV 2 4/5 4/5 4/8 4/5 4/5
IV 3 4/5 4/5 4/8 4/5 4/5
IV 4 4/5 4/5 4/8 4/5 4/5
IV 5 4/4 4/4 4/7 4/4 4/4
IV 6 4/7 4/4 4/7 4/4 4/4
IV 7 4/7 4/4 4/7 4/4 4/4
IV 8 4/7 4/7 4/7 4/4 4/4
IV 9 4/6 4/6 4/6 4/3 4/6
IV 10 4/6 4/6 4/6 4/3 4/6
IV 11 4/6 4/6 4/6 4/3 4/6
IV 12 4/6 4/6 4/9 4/3 4/6

Note: The code used to generate this table is also included in the examples directory, with a live version in this project's hosted examples pages.

So in order for the Calendar of Imladris to start reckoning from Iys 1 and end up on Shire April 6 in III 3019, the first Yestarë would have to have been on a proleptic Kings' Reckoning Súlimë 30 in Iys 1, which would correspond with a proleptic Shire March 30. Or if the Calendar of Imladris started reckoning from II 1, the first Yestarë would have to have been on Kings' Reckoning Súlimë 27 in II 1 (proleptic Shire March 27). If it started reckoning from II 1697 (the year Rivendell was founded), the first Yestarë would have to have been on Kings' Reckoning Víressë 4 (proleptic Shire April 4) in that year. For III 1, the first Yestarë would have to have been on Kings' Reckoning Víressë 2 (proleptic Shire April 2). Finally, if for some reason the Calendar of Imladris started reckoning (or restarted a new 432-year leap cycle) from III 1601 (the year the Shire was founded), the first Yestarë would have to have been on Shire April 6 in that year.

That is all assuming the Kings' Reckoning and Shire Calendar are incorporating all "millennial additions" and Stewards' Reckoning adjustments. Without those, the first Yestarë would correspond to even earlier dates in one or both of those calendars in order to end up on Shire April 6 in III 3019.

Aaron Chong suggests that the Calendar of Imladris could have started its reckoning from the first Year of the Sun in the First Age in his blog post Tolkien's Legendarium versus Astronomical Reality. I also noticed this suggestion in the forum post Middle-earth chronology, by James "the Just" Strom, which is also linked in Aaron Chong's blog post, but the earliest reference I can find for this suggestion was made by Darrell A. Martin in the Mythlore 54 (Summer 1988) article "J.R.R. Tolkien's Calendars or The Saga of Hador The Incompetent".

Note that even if the Calendar of Imladris started reckoning from the 1st Year of the Sun, that doesn't mean it was necessarily invented and already in use in that year. It could have been invented anytime later, but reckoned its rules and leap-days retroactively starting with the 1st Year of the Sun. This would be similar to how the Kings' Reckoning began its reckoning from the 1st year of the Second Age even though Númenor was not founded until II 32.

Interestingly, since Rivendell's Yestarë must fall on Shire April 6 in S.R. 1419 (Shire-reckoning 1419 which is III 3019), reckoning the Calendar of Imladris from either the first Year of the Sun in the First Age or from the start of the Second Age allows its Yestarë to fall on Shire April 4, 5, 6, or 7 from about S.R. 1400 (III 3000) until about S.R. 1500 (IV 80). This can be demonstrated with these Middle-earth calendar simulations. So either of these seem to fit nicely with Tolkien's statement that Rivendell's Yestarë "corresponded more or less with Shire April 6".

Reckoning from the start of the Second Age is less likely, though, since Tolkien wrote in Appendix D about a note on the Calendars of the Red Book (a.k.a. The Reckoning of Years by Meriadoc Brandybuck) that states that the omission of the 3 extra Enderi at the end of a 432-year cycle 'has not happened in our time' (which would be the time of the writing of the Red Book of Westmarch).

The 1st Year of the Sun in the First Age was 590 years before the start of the Second Age, the Second Age ended with II 3441, and the count of Shire-reckoning years starts with Third Age 1601 (S.R. 1 = III 1601). If the Calendar of Imladris did start reckoning from the beginning of the Second Age, then it would have ended a 432-year cycle and omitted its leap-days just 20 years after the War of the Ring in S.R. 1439 (IV 19). Starting with the Years of the Sun in the First Age means this calendar completed a cycle in S.R. 1281 (III 2881; 9 years before the birth of Bilbo Baggins) and its next leap-day omission wasn't due until S.R. 1713 (IV 293; more than 100 years after the Red Book was copied in Gondor).

For this same reason, we can also exclude reckoning from the founding of Rivendell in II 1697 (otherwise a 432-year cycle would have ended in S.R. 1407 / III 3007), and from the start of the Third Age (otherwise a 432-year cycle would have ended in S.R. 1424 / IV 4).

We can probably also exclude the concept that a new cycle started with the colonization of the Shire in III 1601. Although this cycle is very close to the cycle aligned with Iys 1, it would have ended a 432-year cycle in S.R. 1296 / III 2896, which is 6 years after the birth of Bilbo Baggins, and arguably during "our time" according to the hobbits who wrote the Red Book. Besides, what year of significance (to the Elves) would be considered year 1 in the Calendar of Imladris in order for its leap-year cycle to align with III 1601?

Note that the names of the months (or "seasons") and the leap-year rules of the Calendar of Imladris indicate that it's a solar calendar, and according to the Elves' mythology, the Sun was created and first set sail across the sky starting with the Years of the Sun of the First Age. So the "years" were of different length before that time, which makes it very unlikely that the Elves would use something like the Calendar of Imladris to reckon time before then.