Quarters of nobility
The power arrangements in the continental Europe prior to the 20th century gave preference to nobility. Some civil, ecclesiastical, and military positions had required the holder to be sufficiently noble, with quarters of nobility being a numerical measure of one's nobility. The quarters term is related to the quarterings in heraldry.
The number of noble quarters was associated with the number of nobles in previous generations of the family (ahnentafel), in which noble status has been kept regardless of whether a title was actually in use by each person in the ancestral line in question. For example, a person having sixteen quarterings (formally in heraldry "Seize Quartiers"), might have exclusively noble ancestry for the four previous generations (i.e., to the great-great-grandparent level): Given two parents per generation, four generations of uninterrupted nobility = 24 = 16. Alternatively, such a person might have exclusively noble ancestry for the five previous generations on one side, but have a commoner for their other parent, such that the latter side of that person's ancestry would "dilute" by half the nobility they derived from the former side: (25)/2 = 32/2 = 16.
If the family tree was perfect (all-noble) it was declared that the "House was Full", a defective quartering was called a window.
The number of noble quarters required for admission differed based on the country of origin, for example, to join the Knights of Malta at the turn of the 19th century, four quarters were sufficient for a Frenchman, eight were required from a German or Spanish postulant. This discrepancy was due to the fact that few French courtiers were not able to provide a long uninterrupted noble lineage due to frequent mesalliances with members of merchants' or financiers' families. A canon position at the Strasburg Cathedral required sixteen quarters.
In most cases, four quarters were enough, occasionally sixteen were required, the largest number ever required in France was 32, in Germany, 64.
Contemporary use of noble quarters is rare, although the Bailiwick of Utrecht until 2006 required a proof of four quarters from a knight candidate. This requirement had survived from ancient times (when the main branch of Teutonic order required 16 quarters), but in 2006 was lowered to one paternal and one maternal quarter, with paternal quarter lineage dating to at least 1795. The rule was established to keep out burghers and the new aristocracy (Catholics were ineligible due to another rule).