We now get to the heart of the matter, of applying these concepts to actual conflict determination. There are three distinct ways of checking conflict, numbered for convenience #1, #2, and #4. No, that doesn't make a great deal of sense. All will be explained in the fullness of time. The important idea is that one need only accomplish one of these three. Note also that only the third involves the familiar counting of CDs. This is an important and underappreciated concept: counting CDs is the last method to apply, to be used only if the first two methods have failed.
The rest of this post will explain #1, Addition of Primary Charge. This is from RfS X.1.: "Armory does not conflict with any protected armory that adds or removes the primary charge group." This is such a pervasive rule that it is rarely actually explicitly cited, but without it life would be bad. What does it mean? When comparing two armories, if one has a primary charge group which is absent in the other, then they do not conflict.
This takes two forms. One coat may not have a primary charge group at all. Note that a peripheral charge is never considered primary. Examples of armory with no primary charge include "Paly gules and Or", "Per fess argent and sable", "Argent, a bordure sable", "Vert, on a chief Or three mullets azure." These are therefore respectively clear of "Paly gules and Or, a tower argent.", "Per fess argent and sable, two lions passant counterchanged.", "Argent, a crescent within a bordure sable.", and "Vert, three eagles, on a chief Or, three mullets azure." Heraldry with no primary charge group is fairly rare in SCA heraldry, but quite common in period. This makes it fertile ground for enterprising consulting heralds.
The second pattern is a little trickier: when one coat's primary group is demoted in the other coat to a "lesser" group. This is best explained by example: "Argent, three billets sable" is clear of "Argent, a chevron between three billets sable." "Purpure, a bend argent" is clear of "Purpure, a lion Or surmounted by a bend argent" (since the lion in the second case is the primary charge).
What does this rule mean for actual practical conflict checking? It creates vast areas which you don't need to check. If you are checking "Bendy Or and sable" for conflict, you don't need to check anything with a primary charge. You can still have a conflict with, e.g. a bordure or a chief, but not with a lion. In practice the place to look in the Ordinary is "Field Division - Bendy". Looking there I find "Bendy Or and sable, a cross quarter-pierced counterchanged." In a conflict check I wouldn't read past "Bendy Or and sable, a cross" since at that point I know a primary charge has been added, so it is clear.
As a second example, suppose you were checking "Sable, two lions combattant Or." This would not conflict with "Sable, a pale between two lions combattant Or", so there is no need to check the Ordinary under "Pale". Checking under "Beast - Cat - 2 - Or" I find "Sable, on a pale between two lions combattant Or, three fleurs-de-lys sable." In a conflict check I wouldn't read any further than "Sable, on a pale".
My third example is a bit trickier. Suppose you were checking "Gules, a fess between two lions passant guardant Or." Naturally you would check for conflicts under "Fess". There is a temptation to also check under "Beast - Cat - 2 - Or". This is not necessary. This is clear of "Gules in pale two lions passant guardant Or." and indeed for reasons which will be explained in Part V there are no possible conflicts which don't have a fess. That being the case there is no reason to look anywhere beyond fesses.
The key thought in practical conflict-checking is to limit your search to possible conflicts. I will expand on this idea in Part V. For now, remember that if the potential conflict has an added (or removed) primary charge group then you need go no further: it is clear.
In terra pax,