In addition to having three calendars, namely, the long count, the tzolkin and the haab, the Mayas further complicated matters by occasionally using different systems to number the days in the haab months and by shifting the haab one or two days in relation to the tzolkin.

The Classical Mayas apparently numbered the days in a month from day 0 to day 19, after which came day 0 of the next month. Sometime shortly before the Spanish Conquest a system came into use in Mayapan in which days were numbered from 1 through 20. Thus the "month base" can be either 0 or 1.

The matter of the shift of the haab in relation to the tzolkin can be explained in terms of what are known as "yearbearers". A "yearbearer" is a tzolkin day name that can occur on the first day of the year. Assuming that the month base is 0, the first day of the year is 0 Pop. Every 0 Pop is also some tzolkin date, for example, 1 Ik 0 Pop. Since there are twenty tzolkin day names, and the haab year has 365 (= 20*18 + 5) days, the tzolkin name for each succeeding new year's day will shift by 5 in the cycle of day names, as in the following sequence of new year's days:

1 Ik	0 Pop
2 Manik	0 Pop
3 Eb	0 Pop
4 Caban	0 Pop
5 Ik	0 Pop
...

Only four of the tzolkin day names can coincide with 0 Pop, and these four are called the "yearbearers".

In the historical records are found three different systems of yearbearers. The most common is the system Ik, Manik, Eb, Caban, as shown above. This system is found at Tikal, and in the Dresden Codex. According to Bricker and Bricker:

"Another set of yearbearers, Akbal, Lamat, Ben and Edznab, were occasionally employed during the Late Classic period. They are called Campeche yearbearers after the region where they were first identified ... A third calendar, based on Kan, Muluc, Ix and Cauac, was introduced in Yucatan during the Postclassic period and is documented in the Chronicle of Oxkutzcab ..." ([14], p.S4)

These authors also note that it was "in Mayapan on the eve of the Spanish conquest" that the Mayas began to number their months from 1 to 20, instead of from 0 to 19. For these Mayas the first day of the year was not 0 Pop but rather 1 Pop. In such a system the yearbearers are the tzolkin day names that can occur with 1 Pop. Such a system is used in the Madrid Codex, where the yearbearers are Kan, Muluc, Ix, Cauac.

A third system of yearbearers, namely, Akbal, Lamat, Ben, Edznab has been reported. Three systems of yearbearers and two month bases (0 and 1) gives six possible systems for relating haab dates and tzolkin dates. Some tzolkin/haab dates are possible within some systems and not within others, and no tzolkin/haab date is possible within all six systems.

Thus when interpreting tzolkin/haab dates it is necessary to be aware as to whether the month base number is 0 or 1 and which are the yearbearers. Of the six logically possible systems, only four were actually used, as shown in the following table.

Year bearers	Month base 0	Month base 1
Ik Manik Eb Caban	Tikal (Dresden Codex, Paris Codex)	System A (not used)
Akbal Lamat Ben Edznab	Campeche	System B (not used)
Kan Muluc Ix Cauac	Yucatan (Madrid Codex)	Mayapan

Some scholars, notably Sir J. Eric S. Thompson ([70], p.127), state that the Dresden and Paris Codices use the Akbal/Lamat system of yearbearers. This results from interpreting "the first of Pop" to mean 1 Pop rather than 0 Pop. If this interpretation of "yearbearer" is adopted then the Dresden Codex does use the Akbal/Lamat system, for the fact that only Ik, Manik, etc., can occur with 0 Pop implies that only Akbal, Lamat, etc., can occur with 1 Pop. Thompson adduces some evidence that the 0 day of a month was really the last day of the preceding month, so that 0 Pop was really the last day of the old year, not the first day of the new year, but suggests that the Mayas themselves (at this late stage in their history) may have become careless in drawing such distinctions. Be that as it may, the system of yearbearers used in this software interprets the 0 day of a month to be the first day of that month, implying that the system of yearbearers used in the Dresden Codex is Ik/Manik and not Akbal/Lamat.