The Number Family System is the system where when a family is recognized to have substantial magical abilities, it gains a number in its name. This system replaced the 'Elements' families that came before. The respective families or members of members thereof are called Numbers (数字付き).
They are the Magicians created and modified by the 10 Magic Institutes. Their positions can change dependent on what occurs at the Ten Master Clans Conference. They stand at the pinnacle of Japans' Magicians.
They are the Families, which were also the products of the 10 Magic Institutes, but only the 10 most powerful are called the Ten Masters Clans, the remainder becoming the 18 Assistant Houses.
The Families which are not from the 10 Magic Institutes, but are recognized as powerful Magicians' lineages.
Families which were formerly part of the Number Family System. Magicians or their descendants that have been stripped of their family ‘number’. The reasons for stripping off their number could be from causes such as:
- The crime of treason.
- The crime of failure to perform an important duty, and "incompetence".