Leo Wiener, in Africa and the Discovery of America also discussed the fact that the West African zodiacs are of 13 months like that of the Amerindians ( Vol.3, p.279). This information is based on the work of F.Bork, Tierkreise auf westafrikanischen Kalebassen, in Mitteilungen der vorderasiatischen Gesellschaft, Vol.21, p.266.Wiener wrote: “In the first place, the central square contains the Mandingo tutelary god with his attributes and appurtenances. The numerical calculations based on 20 and 13, which is the essence of the American calendars, is surely built on African models. Here again we possess but the scantiest material for verification, but just enough to be startling and unique”(p.270).
Coe and Stone, Reading the Maya Glyphs wrote : "The first part of a Calendar Round is the 260-day Count, often called in the literature by the ersatz Maya name "tsolk'in". This is the eternally repeating cycle , and concist of the numbers 1 through 13, permuting against a minicycle of 20 named days. Since 13 and 20 have no common denominator, a particular day name will not recur with a particular coefficient until 260 days have passed. No one knows exactly when this extremely sacred calendar was invented, but it was certainly already ancient by the time the Classic period began. There are still highland Maya calendar priests who can calculate the day in the 260-day Count, and it is apparent that this basic way of time-reckoning has never slipped a day since its inception" (pp.41-42).
This sacre calendar has 13 months of 20 days (13x20=260). John Montgomery, How to Read Maya Hieroglyphs, wrote "The Tzolk'in or 260 day Sacred Almanac, was widely used in ancient times for divinatory purposes. Guatemalan Maya and other cultures in Mexico still use it as a means of "day keeping". The origins of the 260-day calendar are debatable although a number of scholars have suggested it corresponds to the nine month period of human gestation" (p.74).
Wiener has already shown that the Mande probably had a calendar with 13 months of 20 days as evident from the Calabash zodiacs.Mande calendrics are the result of a combination climatic, social andastronomical factors. The moon, seasons and stars are used for reckoning time. The major star studied by the Mande is Sirius.
The Mande have several calendars, lunar, ritual and etc. The Mande system of notation is based on 20, 60 and 80 according to M. Griaule & G.Dieterlen. Aspects of the Mande notation system is found among most West Africans. Griaule in Signes grapheques des Dogon, made it clear that the number 80 also represented 20 (80÷20=20; 20 x 4=80) and probably relates to the Mande people (see: R. Temple, The Sirius Mystery, (1976) p.80).
The base of the Mande calculation is 60 (60÷20=3; 3x20=60). The Malinke-Bambara term for 20 is muġa . The Malinke-Bambara term for 60 is debė ni- muġa or 40+20 (=60).The Dogon claim they got their calendric system from the Mande. The importance of the number 20 is evident in the discussion of the trajectory of the star Digitaria around Serius, as illustrated in Figure iii, above. Note the small cluster of 22 dots (DL) in the figure that represent the star when it is furtherest from Sirius (R. Temple, Sirius Mystery (1976) p.40)
In this figure of Kanaga sign above Figure i, also illustrates the base notation 20 and 60. The head, tail and four feet each represent 20 ,i.e., 6 x 20=120; 120÷60=2. The calculation of Sigui also indicates the Mande notation system of 20 and 60 as illustrated in Figure ii.Further confirmation of the base 20 notation in relation to the Sirius system is the kosa wala. For example on the koso wala we have 10 sequences made up of 30 rectangles (10x30 =300), which can be divided by 20: 300÷20=15; and 60: 300÷60=5. And as noted by Griaule & Dieterlen in addition to the above, 20 reactangles in the koso wala represent stars and constellations (R. Temple, The Sirius Mystery (1976) p.48).
The Mayan system like the Mande system is also based on 60 and 20. For example as you note in your question the basic part of the Haab year is the Tun 18 month 20 day calendar, plus the five day month of Wayeb.The basic unit of the calendar is the Tun made up of 18 winal (months) of 20 k’in (days) or 360 days. Thus we have 18x20=360; 360÷60=6.Next we have the K’tun,(20 Tun) which equals 7200 days, 7200÷60=120÷60=2; or 7200÷20=360÷20=18.After K’tun comes Baktun (=400 Tun) 144,000 days, 144,000÷60=2400÷60=40; or 144,000÷20=7200÷20=360÷20=18.Yes the Mande had the zero.
The Mayan symbol for ‘zero’ means completion. M. Griaule in Signes d’Ecriture Bambara, says the Malinke-Bambara sign for zero is fu ‘nothing, the emptiness preceding creation’ (see Signes graphique soudanais, (eds) Marcel Griaule & Germaine DieterlenIn conclusion, Mayan calendrics are probably based on the Mande notation system of 20 and 60. And the Malinke-Bambara people possessed the zero.
Mayan groups record successfully time only using the 13 month 20 day calendar so there was no need for the Olmec to record a date and use a system like the Haab (Tun+ Wayeb ) to determine its actual time. A similar calendar of 13 months and 20 days was recorded on West African calabashes.As illustrated above the Mande notation system of 20 and 60 is also the system of the Maya.
The Mayan name for day k’in, may also be of Mande origin since it agrees with the Malinke-Bambara term kenè that means ‘day light, day’. The Mayan term for series of 360 days is tun, this corresponds to the Mande term dõ-na ‘an arrangement of dates/days’, the Mande term for calendar is dõ-gyãle-la. The Mayan speakers probably used tun, because they learned the Mande calendar in association with ritual days of the Mande speaking Olmecs..
Lets recap Wiener noted the existence of 13 month 20 day zodiacs in West Africa, and the American sacre calendar of 20 days and 13 months. Coe and Montgomery says the 13 month 260-day calendar continues to be used in Guatemala and other cultures up to today.