Tun, Tzolkin, and XMS

The Maya are said to have used many calendars, several of which remain unknown to outsiders.  Three of their calendars are fairly-well known; these calendars are based on the standard 24-hour day, called kin.  

• Tun (literally, stone) is regarded as a prophetic calendar by the Maya people.  It comprises 360 kin partitioned into 18 uinal (or winal, month), each with 20 kin.
• Tzolkin is the sacred calendar of the Maya; it comprises 20 periods of thirteen kin, or 260 days.  Together these two form the basis of the Maya timekeeping system.
• Haab (365 kin) reflected the Mayan solar year, and was used as a civil calendar, strictly used for accounting, taxation, and perhaps agriculture.

Ian Lundgold's statements:

All Mayan calendar dates, including personal birthdays, dedications and most sacred ceremonial events were measured in 360-day periods called, tuns.  All dates "carved in stone" throughout the Mayan and Toltec world are tun dates...

This Tun, 360 day calendar is the only Maya calendar directly connected to the Tzolkin and they run together like two gears, each day being a tooth on the respective gears.

J. Eric Thompson's paper:

J. T. Goodman wrote of the 360-day period, now called the Tun: “This period is the real basis of the Maya chronological system.”

Furthermore, every known unit in the Maya calendar has in its composition the symbol for the 360-day year....

C. J. Calleman's statements:

The real point to get for the study of the Mayan calendar is however that in its prophetic uses it is based on the 260-day tzolkin or the 360-day tun, cycles that do not have an origin in the physical universe.

18 "spells" of xiantian magic square

Xiantian Magic Square
The XMS arrangement comprises eight columns, eight rows, and two diagonals for a total of 18 groups linearly-arranged.  We can also refer to the groups as octets or "spells."  Each of the eighteen "spells" comprises a unique collection of eight numbers all arranged in a line on the grid.  Additionally, each octet sums to 260, the same number of days as in the tzolkin.

• Each octet may stand for a winal (20-day tun month) since both octets and uinals relate to  eighteen
• Since an octet represents 20 days (winal) and sums to 260 (tzolkin year), it  associates each day of an octet with the value 13

Considered this way, XMS can be considered as relating to both tun and tzolkin calendars, though our use of metaphor may somewhat exaggerate these relations.  It should be noted that the number 20 is not yet directly discernible within the XMS arrangement, though it is a demonstrable feature of the 64 hexagrams (q.v. yao-groups).  The equatorial plane of the spherical representation of Change comprises twenty complementary pairs. 

Notes:

Complementary pairs on the XMS grid sum to 65; any four such pairs sum to 260, the same number of days in the tzolkin calendar.  Four pair is an octet, an octet is 20 days; therefore one pair is five days (value 65) and one day has value 13.  QED

Coincidentally, 13 / 8 * 360 (tun) = 585, a fair approximation to the Venus cycle of 584.  Admittedly, 8 / 5 * 365 (haab) = 584; a precise fit.  Both fractions (13/8 and 8/5) are common approximations to the golden ratio, phi (~1.618).

Scientists have calculated that approximately 1 billions of years ago, the Moon was ~25% closer than it is today, the Earth having an ~18-hour day and a 18 - 20-day month as marked by the Moon's circuit.

Linear octants are also called "spells" in acknowledgement of the 18 spells gained by Odin through his self-sacrifice on the World Tree Yggdrasil: two for each day he was hanged.