Mathematics of Master Keying This small handout cannot possibly address the many complexities of master keying and the capacity of one specific master key system relative to another.  Rather, this simplification is designed to provide the architectural hardware consultant and sales person enough basic technical and mathematical principles to be comfortable handling a keying conference and submitting expansion specs to the factory for new systems and additions to existing systems. All numbers referenced here are theoretical and are based on one keyway.  The are offered for comparison and general understanding only.  Actual numbers will be smaller due to physical limitations in certain cylinders and in cutting keys.  Cross keying and selective master keys reduce the numbers further.  Master ring cylinders, on the other hand, use totally different rules and yield much larger systems. If you are planning a new system and find that the expansion numbers are a ‘close fit’ for one or more levels of keying, check with the Corbin Russwin Key Systems Department before committing to the expansion with you customer. System 70 Pre-System 70 In System 70, the increment between depths is large enough that you can use every depth in each cut position of keys within the same system. There are 6 depths total.  Removing one for the top master key leaves 5 for progression.  Therefore, the multiplier for System 70 is 5. In Pre-System 70, the increment between depths is so small that you must skip every other depth in each cut position of keys within the same system. Each cut uses either odd or even depths, totaling 5 for any one cut. Removing one for the top master key leaves 4 for progression.   Therefore, the multiplier for Pre- System 70 is 4.