The Barxáw week does not have a seven day cycle; it does not even have a reasonably short cycle, although it has some subcycles. The repeating bit goes like the schematic below, underlines inserted where the non-cyclical element goes:
___, wík bir, tàx bir, ŋùx bir (but also ___), fát bir, tabí bir, nèm bir, ___
Four of these form a cycle. The initial day has different names in each subcycle: (bán) bán bir, wík bán (bir), tàx bán (bir), sòq bàn (bir) - the form essentially being "(one) one day, two one day, three one day, last one day". The last day of the subcycle is bán sòq (bir), wík sòq (bir), tàx sòq (bir), sòq (bir) or sòq sòq (bir) - the form essentially being "one last day, two last day, three last day, last last day". The fourth ŋùx bir is generally by lùjun ìsta bir ('big house day'), due to religious celebrations that usually occur on this day.
Days take no counters, and usually are not marked with prepositions or anything, except in the following construction: to specify which X bir in this cycle one is referring to, the first number before the initial day of that week can be presented after ðo. So, day three week three is tàx bir ðo tàx.
A cycle of four 'weeks' is called a 'bùcə', and the week itself is a 'dàqáw'.
The cycles are numbered - there's years of 11 of them, interspersed with years of 12 (but the average length is 371, roughly the length of the year on the relevant planet). Different regions have different naming conventions for the 'months' which is why numbers are widely used in writing. The first month is generally the first month after harvest.
Further, there are a number of specific additional names for particular months' lùjun ìsta bir and also for a few particular sòq sòq bir, as well as the first bán bán bir of the year. Local names vary.
Finally, the last lùjun ìsta bir of the year is sòq lùjun ìsta (bir), which is the largest celebration of the year.