How did Tony Shearer calculate Harmonic Convergence?


Tony Shearer, in his 1971 book, Lord of the Dawn, says that when Quetzalcoatl departed, he left a prophecy of "13 Heavens and 9 Hells". Each Heaven and Hell cycle was 52 years ("years" being 365-day haabs*) in length, and he would return at the end of the 13 Heavens, then the 9 Hells would start. 

Cortez landed at the Yucatan on April 21st 1519, (according to several sources ), fought several battles, and rounded up support from enemies of The Aztec Emperor, Moctezuma, then marched on the capital city - Tenochtitlan (where Mexico City now stands), on August 16th 1519**. See this page on Cortez

The Aztecs welcomed Cortez as Quetzalcoatl (also bearded & white-skinned as Quetzalcoatl had been), since scouts reported he had arrived in ships bearing the sign of Quetzalcoatl - the Cross of 4 directions (he also arrived in the prophesied year of 1 Reed).

So, exactly 9 Calendar Rounds after the confrontation between Cortez & Moctezuma, (a Calendar Round is 52 haabs of 365 days each), the 9 Hells would end.

There are 18,980 days in a Calendar Round (52 x 365), and 9 Calendar Rounds amounts to 170,820 days. If we add 170,820 days to August 16th 1519, (Julian date) using the  free GEDCOM date calculator, then the end of the Hell cycle comes out as 21st April 1987 (Julian date = 4 May 1987 Gregorian date). However, Tony Shearer calculated it as 16th/17th August, 1987, which is over 100 days later, as John Major Jenkins points out . Jenkins says that in Shearer's book Beneath the Moon and Under  the  Sun (1975),

"on page 115 we read that 170,937 days after  April 21st, 1519, the Fifth World will end; on the next page  we  are given  the date August 16th, 1987 as the end date. This calculation  is off by over 100 days, meaning that Harmonic  Convergence should  have  happened in early spring! The mid-August date  was probably chosen because the astrology was fortuitous".

So, Shearer says he added 170,937 days to the date that Cortez landed. This is 117 days more than the required 170,820 days in 9 calendar rounds. The explanation is that there are exactly 117 days between the date Cortez landed and the date he confronted Moctezuma. Therefore, this is the same as saying "170,820 days after August 16th 1519, the fifth world will end".

As we have already seen, 170,820 days after August 16th 1519 (JD) is 21st April 1987 (JD), which is 4th May 1987 in the Gregorian calendar. Likewise, 170,937 days after April 21st 1519 (JD) is also 4th May 1987 (Greg). This calculated date for Harmonic Convergence is 104 days before August 16th 1987...when you take into account the extra 13 days between the Julian & (current) Gregorian dates (104 + 13 = 117),  it now seems blatantly obvious how the error was made...

If 170,937 days are added to 16th August 1519 (instead of April 21st), then you arrive at...August 16th 1987! (JD)  This happens to be exactly 9 x 52 (468) Julian Years, since there are 117 Julian leap days in 468 years - coincidentally, the same number of days as there were between the landing of Cortez and his meeting with Moctezuma.

From Jenkins' article, it seems possible that Shearer may have found confirmation for the miscalculation above  because, according to the count he was using (which was only 1 day away from the True Count), 16th August 1987  was the day 13 Ahau, which is considered by many to be the last day in the 260-day Tzolkin (although Jenkins has argued that this is just an arbitrary arrangement). Thus, it seemed that the end of the 9 Hells was coincident with the point between the days 13 Ahau and 1 Imix (by the 584284 correlation); 16th/17th August 1987. 

To my surprise, the Kalachakra prophecy, The Seneca Indian Prophecy, and  The Cherokee Calendar Wheel, (UPDATE 23/10/2002: and Steven McFadden's new essay on Mayan priest Carlos Barios), all seem to indicate that there is a 25-year "time of transition" before 2012, so it seems that 1987 was an important time, and that 25 haabs later, (after 4th May 1987), on 27th April 2012, the "Crossing" will start. Alternatively, if Shearer's dates were right for some reason, then 25 haabs after August 16/17 1987 will be August 9th/10th 2012. A third possibility is that 25 haabs before winter solstice 2012, was the key date - 28th December 1987.

Actual Known Calendar Rounds in 1987 & 2012 (from Tzolkin by John Major Jenkins, p.288)

In the Teotitlan Calendar Round, there was a Calendar Round beginning on JD 13th June 1519. 9 Calendar Rounds (Hell Cycles) later, brings us to 1st March 1987 (Greg); 25 haabs later = 23rd February 2012.

In the Tikal Calendar Round, there was a Calendar Round beginning on JD 15th July 1544. 9 Hell Cycles later brings us to 2nd April 2012 (Greg).



* I use the Mayan term here, rather than the Aztec, for consistency throughout this site.


**However, according to this web page , and this one, the encounter took place on ("8 Wind") November 8th 1519! (which would make the end of the 9 Hells 27th July 1987; 25 haabs later = 20th July 2012); this page and this one say it was ("9 Wind") August 22nd 1519 (which would make the end of the 9 Hells, 10th May 1987; 25 haabs later = 3rd May 2012). Unfortunately, in 1519, neither November 8th or August 22nd (nor Shearer's dates of April 21st or August 16th) was the day 8 Wind, or 9 Wind. However, November 9th 1519 (JD) was the day 8 Wind, in the Caso/ True count correlation.

The Timelines site says Cortez landed at Vera Cruz on March 13 1519, agrees on November 8th as the day of the Cortez/Moctezuma encounter and gives a few more significant conquest dates. None of these work out as 8 Wind or 9 Wind either. 

Since the recorded (8/9 Wind) date in 1519 was apparently the one that allowed a correlation between Aztec and Julian/Gregorian calendars, I thought it would be a simple matter to locate it, but all the dates quoted, whether in Julian or Gregorian, did not correlate to a Wind day. I was just about to give up on the problem when I discovered the Escritorio site that says Cortes landed at Vera Cruz on April 13 1519...which (if entered as a Gregorian date), was the day 9 Wind in the year 1 Reed, according to the calculator ***. This is equivalent to the Julian date 3 April 1519. 

This means that 9 Hells after this new date for Cortes' landing gives the date: 20th December 1986 (GD); 25 haabs later = 14th December 2011 (GD). However, the year 1 Reed started on JD 25th January 1519 and 9 hells after this gives 13th October 1986 (GD) 25 haabs later = 7th October 2011 (GD). Perhaps also significant is the "terminal day", after which the year 1 Reed is named; JD 19th January 1520; 9 Hells after this, is 7th October 1987 (GD); 25 haabs later = 30 September 2012 (GD).


EVENT                                    DATE  (corr# 584283)          9 Calendar Rounds (Hells) later          plus 25 haabs

Beginning of year 1 Reed       25 January 1519 (JD                 13 October 1986                      7 October 2011

Landing of Cortes (1)                13 March  1519 (JD)               29 November 1986              23 November 2011

Landing of Cortes (2)   (13 April Greg) 3 April 1519 (JD)         20 December 1986             14 December 2011 

Landing of Cortes (3)                      21 April 1519 (JD)                 7 January 1987                     1 January 2012

Easter calculator :Easter Friday 1519 = 22 April (JD) 1519 (= 2 May Greg) 8 January 1987            2 January 2012

Easter Calculator: Easter Friday = 22 April 1519 (JD)

Day 1 Reed in Year 1 Reed    Wednesday 4 May 1519 (JD)        20 January 1987                 14 January 2012

Teotitlan Calendar Round              13 June 1519 (JD)                   1 March 1987                   23 February 2012

Tikal Calendar Round                    15 July 1544  (JD)                    2 April 2012                    

Cortes meets Montezuma (1)       16 August 1519 (JD)                   4 May 1987                            27 April 2012

Cortes meets Montezuma (2)        22 August 1519 (JD)                  10 May 1987                             3 May 2012

Cortes meets Montezuma (3)      8 November 1519 (JD                 27 July 1987                            20 July 2012

Cortes meets Montezuma (4)  theoretical 9 November 1519 (JD)   28 July 1987                             21 July 2012

Cortes meets Montezuma (5)   theoretical (28 November 1519)   August 16/17 1987              August 9/10 2012

"Terminal day"of 1 Reed  (=2nd Day 1 Reed) 19th January 1520 (JD)  7 October 1987               30 September 2012

Beginning of year 1 Coatl                24 January 1521 (JD)              12 October 1988                    6 October 2013

Fall of Tenochtitlan                          13 August 1521 (JD)                 1 May 1989                           25 April 2014

Terminal Day of year 1 Coatl          18 January 1522 (JD)               6 October 1989               30 September 2014


*** Go to, - Preferences page, and set to advanced level, Alfonso Caso correlation (584283) and Terminal kind of year-bearer. 
"Mesoamerican calendars vary in their method for naming the year. Some calendars name the year after the first day of the year. Most calendars, as the Aztec calendar, name the year after the last day of the last month (meztli) of the year. This is the 360th day of the year, the one just before the 5 unlucky days. The day the gives its name to the year is called the year-bearer. Note that this date always occurs twice a year". The day on which Tenochtitlan fell to Cortes was 13th August 1521, which was recorded as the day 1 Coatl in the year 3 Calli. This is the basis of the Caso correlation and agrees with the True Count.


Harmonic Convergence: Tony Shearer first calculated Harmonic Convergence as being nine 52-year Hell cycles after the arrival of Cortez, (interpreted as the return of Quetzalcoatl by the Aztecs), which he took as 21st April 1519 (JD) (which was the day before Good Friday). He calculated that 9 x (365.25 x 52) days, (or 170,937 days) after Cortez’ arrival would be August 16th 1987. However, the answer should have been 21 April 1987 JD, which is 4 May 1987 in the Gregorian calendar. But this is just the first error, since Hell cycles are Calendar Rounds, which are each 52 haabs in length, and a haab is a 365-day year, not the 365.25-day Julian year. This means there was an error of +117 days, (there are 117 leap days in 52 x 9, or 468 years), and the end of the nine Hell cycles should have been 117 days earlier, which is 25 December 1986 (JD) or 7 January 1987 (GD). Shearer should have used 9 x 52 x 365 days, or 170,820 days. Instead of adjusting 117 days back, the date was adjusted 117 days forward from the 21 April 1987 (JD) date to 16 Aug 1987, but this was taken as a Gregorian date, rather than a Julian date. This seemed to be a meaningful date, because in the correlation Shearer was using (corr#584284, or one day away from the True Count), August 16th 1987 was the day 13 Ahau, which is the “last day” in the Tzolkin. The 17th August 1987 was thus (in the 584284 correlation) the day 1 Imix, or the “first day” of the Tzolkin. So, Harmonic Convergence should have been on 25th December 1986 (JD) or 7th January 1987 Gregorian. Total error = +221 days or (2 x 117) – 13 (where 13 is the accumulated difference between Julian and Gregorian dates).

Some people who have tried to understand how Harmonic Convergence was calculated have concluded that it must have been calculated from the day that Cortez met the Aztec emperor Moctezuma, since, coincidentally, this happened 117 days after 21st April (when he landed), on August 16th 1519 (JD). Exactly 468 Julian years later (9 x 52 Julian years or 170,937 days), would be August 16th 1987. This calculation incorporates both errors of 117 days and the Gregorian/Julian error.

Arguelles used Shearer’s calculation for Harmonic Convergence, but subsequently developed an Aztec/Maya based calendar system called Dreamspell, that used the same 54-day error Tzolkin count he used on The Mayan Factor p.131 (see below). This system ignores the leap-year day of February 29th every four years, and the result is that the 54-day error is reducing by one day every four years. In March 2004, the error will be down to 49 days. In the Dreamspell count, Harmonic Convergence 16/17 August 1987 happened on the days 3 Men and 4 Cib, which means that all the meaning involved in calculation of Harmonic Convergence as 13 Ahau and 1 Imix –as the start/end of the Tzolkin – is lost.

Date Calculation Errors in The Mayan Factor

The 54-day error cannot be explained away as an intentional correlation, since it is inconsistent with all the other dates in The Mayan Factor:

1: (p.45; p.110) The Mayan Factor says that the zero day of the Long Count was in 3113 BC instead of 3114 BC; using the alternative terminology of 3113 BCE or year –3113 would have been correct, but probably just as confusing to those not familiar with calendrics. This was most certainly the cause of the one-year error in Sergey Smelyakov’s The Auric Time Scale and The Mayan Factor, who did use the Arguelles book as his main source of information on Maya calendrics. Error = +368 days. 2: On p.29 The Mayan Factor says that Good Friday in 1519 was the day 1 Reed in the Aztec calendar (1 Ben in the Maya); this is an error of +12 days, since 1 Reed was on 4 May Julian (JD) or 14 May in the Gregorian calendar (GD), and Good Friday occurred on 22 April (JD) or 2 May (GD). Good Friday actually occurred on the day 2 Imix (Alligator) according to the True Count. 3: On p.131, The Mayan Factor says that the 20th June 1986 was the Tzolkin day 10 Ben, whereas it was actually the day 8 Kawak in the True Count. This is an error of +54 days. 4: On p.131 the Mayan Factor says that the 20th June 1986 was the Haab day 9 Kayeb, whereas it was actually 12 Zotz. This is an error of -108 days. 5: On p. 131, The Mayan Factor also says that 20th June 1986 was the Long Count date whereas it was actually This is an error of +690 days. 6: On p.131, The Mayan Factor says that 20th June 1986 was 1,862,599 days after zero-day, whereas it was actually 1,862,319 days after zero-day. This is an error of  +280 days. 7: On p.148, and p.169, The Mayan Factor says that the first day of Harmonic Convergence, 16th August 1987, was day number 1,863,022, after the zero-day, whereas it was actually day number 1,862,741 after zero-day. This is an error of +281 days. Anyone using the Long Count figures or the Day numbers above, to calculate forward to the end of the Long Count, would calculate the end-point (day or 1,872,000 days after zero day) to be 16 March 2012, 15 March 2012, or 31 January 2011. 8: On p. 196, The Mayan Factor says that 8th October 1986 was the Tzolkin day 1 Imix, whereas in the True Count, this was the Tzolkin day 12 Manik. This is an error of +52 days. 9. On p. 196, The Mayan Factor says that 8th October 1986 was the day 12 Zotz in the Haab calendar, whereas it was actually 0 Yax. This is an error of -110 days. 10. Final Katun: On p. 161, 179 and 200, The Mayan Factor says that the final (260th) Katun of the 13-baktun cycle will start in 1992. In Dreamspell, he later refines this to July 26th 1992. It actually started on April 5th 1993. A Katun is 7200 days – approximately 19.72 years, not 20 years! This is an error of -254 days.  


Update Feb 05:

More Detailed Error Analysis Shows Bigger Discrepancy

Peter Meyer compared one date in The Mayan Factor (Nos. 3 -6 above) to a date in Arguelles' earlier book, Earth Ascending (p.166 - the Tzolkin and Haab dates are given as 3 Cib, 2 Mac, and said to correspond to 25 March 1988). He found that the nearest correlation to the standard GMT correlations used by Maya scholars, that the Earth Ascending date could have occurred, would have been an unknown correlation that would put the end of the 13-baktun cycle on the 8th April 2009 (and the date itself therefore would have been 11th  July 1984). This is an error -1353 days. Peter Meyer found that if the date from The Mayan Factor (on p.131, mentioned at Nos. 3-6 above) is analyzed in its entirety, the combination would have been in error by at least -1354 days. This is also an unknown correlation, and differs from  the one in Earth Ascending, by one day.


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