So let's get some terminology out of the way:
Master = Controller where you can make changes to the global configuration. It also has the database with all of the APs, access points neighbors and ARM calculations of all of the controllers. It can terminate APs for client traffic. If the master goes away, local controllers can still run, authenticate people, etc. It just means that you have no way of changing the global configuration. There is only one master in a master-local "system" at a time. A master can be the "primary" for access points and a "backup" for others at the same time. A master cannot be a master and a local at the same time.
Backup Master = Controller that backs up the master controller BUT only when the master controller goes away. It cannot terminate access points while the master is still up. If the master goes away the Backup Master becomes the master and you can make changes to the global configuration, as well as terminate APs on this new master. It has to be in the same layer 2 VLAN as the master, because they must have a VRRP between them that determines who is the master. There is at most only one Backup master in a master-local "system" at a time
Local Controller = A controller that has a read-only copy of the global configuration. It can terminate access points and pass user traffic. If the master goes away, and there is no backup master in the picture, you cannot make any changes to the global configuration. There can be many, many locals in a master. A local can be the "primary" for access points and a "backup" for others at the same time.
A controller is designated a master, backup master or local depending on whether or not you can change the global configuration on it. It has nothing to do with HA, specifically.
Based on your statement below, you can do your configuration with just two controllers: A master and a local.