Along with the Ho Tu, the 8 Trigrams, the I Ching, and the Lo Shu, the Stem-and-Branch Cycle of 60 pattern is a useful structure for preserving and transmitting cultural and scientific knowledge. The first 24 years of the Stem-and-Branch Cycle of 60 that began in 1984 (after the first 78 cycles of 60 = 4680 years) are: 4681 (1984) year of Wood and Rat 4682 (1985) year of Wood and Ox 4683 (1986) year of Fire and Tiger (Fire burns Wood) 4684 (1987) year of Fire and Rabbit 4685 (1988) year of Earth and Dragon (Fire's Ashes make Earth) 4686 (1989) year of Earth and Snake 4687 (1990) year of Metal and Horse (Metal comes from Earth) 4688 (1991) year of Metal and Sheep 4689 (1992) year of Water and Monkey (Water tempers Metal) 4690 (1993) year of Water and Chicken 4691 (1994) year of Wood and Dog (Wood grows from Water) 4692 (1995) year of Wood and Pig 4693 (1996) year of Fire and Rat 4694 (1997) year of Fire and Ox 4695 (1998) year of Earth and Tiger 4696 (1999) year of Earth and Rabbit 4697 (2000) year of Metal and Dragon 4698 (2001) year of Metal and Snake 4699 (2002) year of Water and Horse 4700 (2003) year of Water and Sheep 4701 (2004) year of Wood and Monkey 4702 (2005) year of Wood and Chicken 4703 (2006) year of Fire and Dog 4704 (2007) year of Fire and Pig The 12 animals of the cycle are shown
on stamps of the United States Postal Service issued in January 2005.
The Stem-and-Branch cycle was used by Ta Nao to set
up the Chinese Calendar that started about 4,700 years ago
when Huang Di became the third of the Five Rulers.
The Five Rulers, beginning with Fu Xi, were the first emperors
of China's current historical period, which began
after the turbulent period following the last Ice Age.
The longest period covered by a Chinese calendar system
is somewhat over 380,000,000 years,
which is similar to a date described on Maya Stela D at Quirigua.
It was calculated in the Daming Li (Great Brilliance Calendar)
around 1200 AD as the Taiji Shang Yuan (Supreme Pole Superior Epoch)
based on the time it takes for the Lunar synodic month
to be in phase with the Solar tropical year.
The relative periods must be known to make accurate
predictions of Solar and Lunar eclipses.
Since the periods are not commensurable in terms of Earth days,
the more accurately you measure the periods,
the longer the Epoch between times that the periods are in phase.
About 700 AD, with less precise Solar tropical year
and Lunar synodic month, the Dayan Li (Great Expansion Calendar)
calculated the Superior Epoch to be 96,961,740 years,
which is similar to a date described on Maya Stela F at Quirigua.
During the 6th century AD, the precession of the equinoxes
was estimated to be about 1 degree in 75 years,
for a period of 365.25 x 75 = 27,393.75 years,
a bit longer than the currently accepted value of about 26,000 years.
About 26 BC, the Santong Li (Three Sequences Calendar)
calculated the period of 23,639,040 years,
which is about the time that Dolphins with large brains appeared,
as the least common multiple of
138,240 years
derived as the period of conjunctions of all 5 major planets
and
4,617 years
derived from:
the period of 235 lunations, 19 years, called a Chang;
27 Chang, 513 years, called a Hui, for 47 Lunar eclipse periods;
3 Hui, 1,539 years, called a Thung, to get a round number of days;
and finally 3 Thung, 4,617 years, to get a concording period
of lunations, Solar tropical years, eclipse periods,
and 60-year Stem-and Branch cycles.
Going back prior to 26 BC,
we get to the Sifen Li (Quarter-Remainder Calendar)
of the Fifth Century BC, which was based on
a Solar tropical year of 365 1/4 days and
a Lunar synodic month of 29 499/940 days,
so that there are 19x12 + 7 = 235 lunations in 19 years.
For a lunation of 29 499/940 days, 81 lunations is
the smallest number of lunations that make a round number of days.
That period of 81 lunations is 2,392 = 184 x 13 days.
Since the lunar eclipse cycle is 135 months,
the shortest period of whole days in which the
eclipse cycle can be completed is
2,392 x 5 = 11,960 days or
135 x 29 499/940 x 3 = 11,960 days.
The period of is 46 Tzolkins,
where the Mayan Tzolkin of 20 x 13 = 260 days.
The Great Tzolkin of 46 Tzolkins reconciles
the eclipse cycle with the 260-day Tzolkin cycle.
Still earlier, the Chinese divided a Solar year of 365 1/4 days
into 24 parts, 12 Jie (sections) and 12 Zhongqi (mid-periods).
Perhaps as long ago as the Shang oracle bones, the Chinese knew
that the Solar tropical year of about 365 1/4 days
was incommensurable in terms of Earth days with the
Lunar synodic month of about 29 1/2 days,
and they may have known about the cycle
of 235 lunations in 19 Solar years.
The Chinese 13th century BC oracle bone value for
the Lunar synodic month was 29.53 days.
The Chinese Sifin Li 5th century BC
value was 29 499/940 = 29.53085 days.
The Chinese 237 AD value of Yang Wei was 29.530598 days.
The 1996 space satellite value was 29.530588 days.
The Torah-code Jewish calendar value is
29 + 12/24 + 793/(1080x24) = 29.530594 days.
A nice graphic on the web page of David B. Kelley
shows the Chinese Stem-and-Branch Cycle of 60.
You can also see it by clicking HERE.
This is the numerical structure of the Chinese Stem-and-Branch Cycle
of 12x10 = 4x3 x 5x2 = 120,
which reduces to reduced to 4x3 x 5 = 60:
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 1 2
1 2 3 4 5 6 7 8 9 10 11 12
3 4 5 6 7 8 9 10 1 2 3 4
1 2 3 4 5 6 7 8 9 10 11 12
5 6 7 8 9 10 1 2 3 4 5 6
1 2 3 4 5 6 7 8 9 10 11 12
7 8 9 10 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 9 10 11 12 1
9 10 1 2 3 4 5 6 7 8 9 10 1
The Mesoamerican Mayan Tzolkin Cycle is 20 x 13 = 260 days.
The Great Tzolkin of 46 Tzolkins = 46 x 260 = 11,960 days
reconciles the eclipse cycle with the 260-day Tzolkin cycle.
This is the numerical structure of
the Mesoamerican Tzolkin Cycle of 20x13 = 5x4 x 13 = 260,
which is irreducible:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1
7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1
The Mesoamerican cycles of 20x18 = 5x4 x 2x9 = 360,
which reduces to 5x4 x 9 = 180,
and
260x365 = 5x4x13 x 5x73 = 94,900,
which reduces to 4x13 x 5x73 = 52 x 365 = 18,980,
and
260x360 = 5x4x13 x 5x8x9 = 93,600,
which reduces to 13 x 5x8x9 = 13 x 360 = 20 x 234 = 4,680,
are similar in structure.
REFERENCES:
Joseph Needham, Science and Civilization in China, Cambridge University Press.
Needham's Science and Civilization in China is many large volumes. A somewhat updated introductory summary is Li, Qi, and Shu, by Ho Peng Yoke (University of Washington Press, 1987).
The Maya (4th ed), Michael D. Coe (Thames and Hudson, 1987).
The Ancient Maya, Sylvanus. G. Morley adn George W. Brainerd, revised by Robert J. Sharer (4th ed) (Stanford 1983).
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