The Tzolkin, or sacred calendar, is a 260-day matrix used both by the ancient and present day Maya. This Tzolkin matrix is based on the permutation table, called the Buk Xoc in the Chilam Balam tradition. It reveals a pattern or sets of patterns of 13 numbers and 20 signs that repeat their sequences of permutations every 260 days.
The 13:20 frequency is the universal constant of time from whose mathematics the Tzolkin is derived. This 13 x 20 template is a device that provides us with a lens to view the whole. The entire historical cycle of 13 baktuns (3113 BC - 2012 AD) can be mapped within this matrix. This 260-day cycle synchronizes with the 365-day solar cycle precisely every 52 years, to create the measure of the solar galactic cycle.
"... The Tzolkin matrix is a Harmonic Module, a fractal yardstick of radial time with multiple applications, something analogous to the periodic table of elements, but of the synchronic order."
José Argüelles, Time and the Technosphere
"The Tzolkin is the simplest possible mathematical matrix to accommodate the largest possible number of harmonic transformations, transmissions and transductions - a veritable periodic table of galactic frequencies."
The 13 Moon 28-day calendar can be found within the Tzolkin matrix's Loom of Maya - the 52. This loom can naturally be broken down to its components of thirteen sets of four units each, starting with the corners and moving inward. Thus the first set of numbers is 1, 7, 13, 7; the second set is 9, 13, 5, 1; the third set is 4, 6, 10, 8; until we get to the center 6, 7, 8, 7. Each of the thirteen sets of four numbers adds up to 28, demonstrating the harmony of the 13 Moon 28-day template (28 x 13 = 364). 364 can also be factored as 7 x 52.