a binding of the years; a calendrical concept; this happened every fifty-two years; originally, 1 Tochtli (One Rabbit) was recognized as the beginning of the first cycle of fifty-two years; but it was changed to 2 Acatl (Two Reed) in 1455 as a result of 1454 being a year of troubles (see attestations)
According to Gordon Whittaker (personal communication 4/19/2023), xiuhtlalpilli was the real term that we should be using in place of xiuhmolpilli to refer to the marking of the 52-year calendar period.
Ye anquimati yn quitotihui in tocolhuan yn iquac toxiuhmolpiliz ca centlayohuaz hualtemozque yn tzitzimime in techquazque yhuan yn iquac necuepaloz. (Anales de Juan Bautista, f. 8r–8v) = You all know what our grandparents said, that when the end of the year count was tied, that all would become dark and the tzitzimime would come down to eat us. Then many people would be transformed.
"The Aztec world was governed by 3 different types of calendar. These were called ‘tonalpohualli’, ‘xiuhpohualli’ and ‘xiuhmolpilli’. The ‘tonalpohualli’, commonly used for prediction and prophecy, comprised 260 days, made up of the 20 fate/day signs and numbers from 1 to 13 - giving rise to the idea of ‘trecenas’ or 13-day periods. The ‘xiuhpohualli’ was a civil as well as religious calendar comprising 365 days. These were divided into 18 ‘months’ of 20 days each, giving a total of 360 days. To complete the year, a group of 5 days called ‘nemontemi’ or seriously unlucky days was added. Finally, they had another calendar for counting the years, the ‘xiuhmolpilli’, which comprised 4 signs combined with the numbers 1 to 13. In this way, the ‘xiuhmolpilli’ consisted of a cycle of 52 years, at the end of which a new cycle began.
Ie vncan, ie ipan in toxiuhmolpilia... inic otlaiaoalo nauhcampa matlacxiuitl omeey = When [came] the time of the binding of our years... thirteen-year [cycles] had four times made a circle (central Mexico, sixteenth century)
in mitoa, toximmolpili, anoço inic molpilia xiuitl: yn icoac matlatlacpa omeexpa otlauicac, yn inauhteixti cecentetl xippoalli: inic onaci vmpoalxiuitl ipan matlacxiuitl omume = what was called "The Binding of Our Years," or "When the Years are Bound," [which occurred] when one by one the four year signs had each reigned thirteen years and when fifty-two years had passed (central Mexico, sixteenth century)
2. acatl xihuitl. 1299. años. ypan in toxiuhmolpilli = The year Two Reed, 1299, in which our years were bound. (central Mexico, early seventeenth century)
oncan yn xiuhmolpilli chiuhcnahui anoço ome acatl yn inxiuhtlapohual yn huehuetque = there there was a binding of the years: Nine or Two Reed [in] the ancient ones' year count (central Mexico, early seventeenth century)
Toxiumolpilli ycpac huetz in tlecuahuitl cohuatepetl = our years were bound; the fire drill was wielded on Mt. Coatepetl (central Mexico, early seventeenth century)
xiuhmolpilli = the "tied-up years," or a fifty-two year series, "often ordered into four groups of thirteen years"
"Up to the time of the great famine, the first of any fifty-two year period was always called one-Rabbit. But one-Rabbit happened to be the year 1454, when Apizteotl, the god of starving, was commanding the land. For such an unlucky year to initiate the new series of years was unthinkable. One-Rabbit was always followed by two-Reed, and in this latter year (1455), the rains came back plentifully" and so "it was decided by the Aztec cities to declare it and not the previous year to be the opening year of the present cycle and all future ones."
ye anq'[ui]mati yn quitotihui in tocolhua[n] yn iquac toxiuhmolpiliz ca ce[n]tlayohuaz hualtemozque yn tzitzimime in techquazque yhua[n] yn iquac necuepaloz = ya saben lo que decían nuestros abuelos, que cuando se atara la cuenta de los años, se iba a obscurecer del todo y bajarían los tzitzimime a comernos y entonces habría una transformación de la gente. (ca. 1582, México)