CHROMATIC MEDIANTS
As explained in Scales and Keys, the third scale degree is named “mediant” because it is mid-way between tonic and dominant (ascending). The sixth scale degree is named “submediant” because it is mid-way between tonic and subdominant (descending). In context, “mediant” means “third,” either above or below.
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site
Modulation.
If one desired to indicate the mediant relationship of the chord roots, the analysis would have to include the preposterous designation of #I6 for the second triad! Since the second chord is not functioning as any type of tonic, analysts must use judgment in choosing the best label (in this case, N6).
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the following section.
It is not always possible to avoid writing false relations without breaking a law of voice leading. For example, there is a false relation that could not be avoided in the example provided in assignment 15.01. This, along with the very awkward melodic interval of a diminished third, is a significant reason why Neapolitans rarely resolve directly to dominant—
especially in voice leading.
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Audio/video of various assignments:

Assignment 16.03
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