The Lunar Series was the first Maya original contribution to the calendar and was incorporated early in the 3rd century
AD. It was displayed just after the long count and tzolk'in in a sequence of four to eight glyphs. Using lunar day
counts of 29 or 30 days, the Maya grouped Moon cycles into sets of six lunations (a lunation being the time between
two, successive new Moons).
Also within, or at least connected to the Lunar Series is a 9-day cycle called the Lords of the Night. Little is known about the significance or origin of this 9-day cycle, but it is recognized as the smallest cycle the Maya recorded. An interesting modern Maya use of nine days is connected to the Tzolk'in and the day of one's birth. In Maya communities of the Guatemalan highlands, it is said that counting nine days forward and nine days backwards from one's tzolk'in birthday gives the identities of their protector nawals, or protector spirits. Together, scholars refer to the Lords of the Night and the Lunar Series collectively as the Supplemental Series.
In each of the over 250 known inscriptions containing a Lunar Series, a few standard points of information are provided. Those are; how many days have passed during the current lunation, which of the cycles of six lunations this Moon is in, the name of the current Moon, and how many total days this lunation has (29 or 30). Individually, the glyphs representing these points of information were labeled by Morley as glyphs A, B, X, C, D, E, F and G. Glyphs Y and Z were added as reading methods became more refined. Rarely does a single text display all of these glyphs, usually conflating them into pairs or omitting a few for textual space considerations.
There is good evidence to say that the Maya were able to calculate the actual length of an average lunation very accurately. The Lunar Series chooses 29 or 30 days, following the Maya penchant for expressing only whole numbers, while modern science calculates the synodic period of the moon as 29.53059 days. When they chose to pick a formula of six lunations the average day count came out to 177 days, or 6 x 29.5 days, which was close to true but still incurred an error of about .36 days per year. While a count of 177 days was not as accurate as the Maya could get, it was probably used because it is the most common interval of time in between eclipses.
More accurate multiples of the lunar months were sometimes used for long range calculations. Comparison of Classic Period lunar data in Palenque monuments with the mythological lunar data from the Temple of the Sun suggests that the latter was calculated using the formula 81 moons = 2,392 days. This gives an average length of the lunar month as 29.53086, accurate to within 7 minutes per year. While not accurate enough to calculate a lunar age over two thousand years in the past, this formula would have produced accurate results when used to calculate lunar ages in the Classical era. At Copan, a formula that was almost as accurate seems to have been known: 149 moons = 4400 days. This gives a value of the lunar month as 29.5302 days.
John Teeple, a chemical engineer who chose the astronomy of Maya inscriptions as his hobby, uncovered the mechanics of the Lunar Series in the 1920's. Spending much of his time travelling on trains, he entertained himself by pouring over hieroglyphics texts and pondering their meanings. The first important clue noticed by Teeple was the fact that the last glyph of the lunar series always counted 29 or 30 days, close to the 29.53 day length of the lunar month. Next he noticed that the first numbers in the series were always between 0 and 29 days, suggesting that they were days in the lunar month.
Teeple tested his hypothesis by comparing inscriptions from the Temple of the Sun and the Temple of the Foliated Cross at Palenque. The Temple of the Sun records an event from mythological time, on the long count 126.96.36.199.6, long before the Classic Period. The Temple of the Foliated Cross records a long count date just 14 days later. Both are followed by a lunar series. If his hypothesis about the meaning of the lunar series was correct, he expected to find that his readings of the moon ages would be 14 days apart. Indeed, the Temple of the Sun text records of a moon age of 26 days, in a 4th lunar month of 30 days and the Temple of the Foliated Cross text records a moon age of 10 days in the 5th lunar month. This was his confirmation and he went on to translate almost 200 examples of the Maya Lunar Series and published them in two extensive manuscripts, one in 1925 and the other in 1930.