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Mid-capitals (also called medium capitals) are a larger form of small capitals.
By strict definition small capitals (or small caps) come to the top of the x-height of their roman counterparts. Designers' aim with mid-capitals is to make the small caps slightly larger so that the overall difference between the small caps and the roman, in a given setting, is more subtle and therefore more unified. Mid-caps then simply refers to striking a balance somewhere between the x-height and the cap height.
The term mid-capitals could be the nitpick of purists to simply put a name on slightly enlarged small caps to run more cohesively in text. Some would argue that it is therefore appropriate (and more practical) to refer to what might technically be mid-capitals as a variant on small capitals.
In recent years mid-capitals are becoming more common, especially for types that are geared toward use at smaller sizes. Some designers believe that at smaller sizes a less noticeable difference between the roman and the small capitals is desirable.
The OpenType specification admits the small caps feature smcp,c2sc and a petite caps feature pcap,c2pc. Fonts providing both often have petite caps that match the x-height while the small caps are somewhat larger, thus filling the mid-caps role.