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Nahua/Maya Number system

The Zuni and Hopi Calendar
World Tree Axis: Dzibilchalt˙n
On the Mexican Calendar and its Cycles
The Maya Cycles
The Maya Creation
The Zuni and Hopi Calendar
On the Maya number system
Codex Mendoza / Mexican Numbers
The Calendar Wheel
The Calendar, The Seasonal Round, and Moon Ceremonies
Sun Calendars of U.S. First Americans
Maya numbers / Maya Mathematics
The "Five Suns', the Mexican Calendar, and Mexican Creation Story
The Skull Motif and the Mayan Discovery of Zero
Roman Numerals
On Numbers, the Syllabary, and Symbols
Oldest Known Maya Mural
Index of Links to Mexican and Mayan Codexes [& on the Number System]

IV.  The Calendar

Agriculture makes a people not only non-migratory, but close observers of the seasons, and hence of the yearly stations of the sun.  The count of time by moons is sufficient for nomadic peoples, or for tribes whose subsistence is mainly by the chase, but in a settled agricultural community the primitive lunar year is sooner or later replaced by a solar year, determined by the passage of the sun through the substantial and equinoctial points.  The lunar measure of time will not be abandoned, but it will be corrected by the solar, and gradually give way to the latter.  Such, indeed, is the outline of all calendric development.
The Zuni year is divided into two seasons, inaugurated by the solstices, each of which is composed of six months--lunations, subdivided into three ten-day periods.  The significations of the month names are interesting: the month of the winter solstice, which is the beginning of the year, is called Turning-Back, in reference to the Sun Father’s return from the south; it is followed by Limbs-of-the-Trees-Broken-by Snow, No-Snow-in-the-Road, Little-Wind, Big-Wind, and No-Name.  For the remaining half of the year, these appellations, though now inappropriate, are used again, the months of the second half-year being, strictly speaking, nameless.  A similar duplication occurs in the Hopi calendar, where the names of five moons are repeated, but in summer and winter rather than in the substantial division, which, however, plays an important role in the ferial calendar.  Fewkes records an interesting remark that may give the true reason for the arrangement: “When we of the upper world are celebrating the winter Pa moon,” said the priest, “the people of the under world are engaged in the observance of the Snake or Flute [summer festivals], and vice versa.”  The priest added that the prayer-sticks which were to be used by the Hopi in their summer festivals were prepared in winter during the time when the underworld folk were performing these rites.  “From their many stories of the under world,” writes Fewkes, “I am led to believe that he Hopi consider it a counterpart of the earth’s surface, and a region inhabited by sentient beings.  In this under world the seasons alternate with those in the upper world, and when it is summer in the above it is winter in the world below.”  Ceremonies are said to be performed there, as here.
Both Zuni and Hopi have priests whose special duty is to observe the annual course of the sun, and hence to determine the dates for the great festivals of the winter and summer solstices.  The Zuni sun priest uses as his gnomon a petrified stump which stands at the outskirts of the village, and at which he sprinkles meal and makes his morning prayers to the sun, until, on the day when that luminary rises at a certain point of Corn Mountain, the priesthood is informed of the approaching change.  Every fourth morning, for twenty days, the sun priest offers prayer-plumes to the Sun Father, the Moon Mother, and to departed sun priests; on the twentieth morning he announces that in ten days the rising sun will strike the Middle Place, in the heart of Zuni, and the ceremony will begin.  This rite occupies another twenty-day period, beginning with prayers to the gods and ending in days of carnival and giving; during this time the gods are supposed to visit the town, images and fetishes are brought forth and adorned, prayer-plumes are deposited by each family in honor of its ancestral rain-bringers, boys are initiated by ceremonial flogging, the sacred fire is kindled by the fire-maker, and there is a great house cleaning, moral as well as physical, for personators of the gods make it a part of their duty to settle family quarrels and to reprimand the delinquents, young and old.  At each solstice the sun is believed to rest in his yearly journey (the Hopis speak of the solstitial points as “houses”); when the sun strikes a certain point on Great Mountain five days in succession, the second change of the year takes place.  The ceremonies of the summer solstice include pilgrimages to shrines and elaborate dances, and this is also the season when it is especially lucky to fire pottery, so that all the kilns are smoking.  An instructive feature is the igniting of dried grass and trees and bonfires generally; for the Zuni believed clouds to be akin to smoke, and by means of the smoke of their fires they seek to encourage the Uwannami to bring rain.  The ceremony of the summer solstice, in fact, is the inauguration of the series of masques in which they, in common with the other Pueblos, implore moisture from heaven for the crops that are now springing up.
The Hopi sun priests make use of thirteen points on the horizon for the determination of ceremonial dates.  Their ritual year begins in November with a New Fire ceremony, which is given in an elaborate and extended from every fourth year, for it then includes the initiation of novices into the fraternities.  Other ceremonies are similarly elaborated at these same times; while still other rites, as the Snake- and Flute Dances, occur in alternate years.  The Hopi year is divided into two unequal seasons, the greater festivals occurring in the longer season, which includes the cold months.  Five and nine days are the usual active periods for the greater festivals, though the total duration from the announcement to the final purification is in some instances twenty days.  Of the greater festivals, the New Fire ceremony of November is followed at the winter solstice by the Soyaluna, in which the germ god is supplicated and the return of the sun, in the form of a bird, is dramatized; the Powamu, or Bean-Planting, comes in February, its main object being the renovation of the earth for the coming sowing and the celebration of the return of the Kachinas, to be with the people until their departure at Niman, following the summer solstice; the famous Snake Dance of the Hopi alternates with the Flute-Dance in the month of August.  These are only a few of the annual festivals, a striking feature of which is the arrival and departure of the Kachinas.  The period during which these beings remain among the Hopi is approximately from the winter to the summer solstice, and it may be supposed that their absence is due in some way to their function as intercessors for rain during the remaining half-year.  A secondary trait, found only in Kachina ceremonies, is the presence of clowns or “Mudheads”--a curious type of fun-maker whose presence in Zuni Cushing ascribes to the ancient union of a Yuman tribe with the original Zunian stock.
Neither Zuni nor Hopi succeed in entirely coordinating the primitive lunar and solar years.  The lunations and sun stations are observed, rather than counted in days; apparently no effort is made to keep a precise record of time nor to correct the calendar, unless indeed the uncertainty which Fewkes found among the Hopi priests as to the true number of lunations in the year, twelve according to some, thirteen and even fourteen according to others, may represent such an attempt.  On a sun shrine near Zuni there are marks said to represent year-counts; certain that few North American Indians have a more ancient and verifiable tradition than is possessed by the Pueblo dwellers.
Analogies between the Pueblo periods and festivals and those of the more civilized peoples of ancient Mexico seem to point to a remote identity--the five, nine-, and twenty-day periods, the general character of many of the rites and mythological beings, the significance of the heart as the seat of life.  But one in search of parallels need not confine himself to the New World.  The great summer solstice festival of the Celts, with its balefires, is of a kind with that of the Zuni, while the purification ceremonies of the winter solstice have points of identity with the Roman Lupercalia, the Anthesteria of the Greeks, and similar festivals, which close analysis would multiply.  The quadrennial and biennial character of many Pueblo ceremonies, as well as the division into greater and lesser rites, are still other noteworthy analogues of Greek usage. 
Taken From

The Zuni year begins with the winter solstice

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