Principle 17.2.2. Secondary Dominants.
The Roman numeral after the slash is the chord being tonicized by the \(\left.\text{V}\right.\) chord before the slash.
Section 17.2 Tonicization
In this chapter and the next, we will study tonicization, which means treating a chord other than the \(\left.\text{I}\right.\) chord like a tonic by approaching it with its dominant. In diatonic harmony, the \(\left.\text{V}\right.\) chord (the dominant) resolves to the \(\left.\text{I}\right.\) chord (the tonic). A secondary dominant is a major triad or dominant seventh chord that resolves to (or tonicizes) a chord other than the \(\left.\text{I}\right.\) chord.
Sing the bass line of the example above and notice that a secondary chord, through its chromaticism, intensifies the drive to the next chord.
You may find that you want to analyze the \(\left.\text{D}^{7}\middle/\text{F}^{♯}\right.\) in the example above as a \(\left.\text{II}^{6}_{5}\right.\) instead of a \(\left.\text{V}^{6}_{5}\middle/\text{V}\right.\) (which we pronounce as “\(\left.\text{V}^{6}_{5}\right.\) of \(\left.\text{V}\right.\)”), and the \(\left.\text{E}^{7}\middle/\text{G}^{♯}\right.\) as a \(\left.\text{III}^{6}_{5}\right.\) instead of \(\left.\text{V}^{6}_{5}\middle/\text{vi}\right.\) (“\(\left.\text{V}^{6}_{5}\right.\) of \(\left.\text{vi}\right.\)”). Notice, however, that a \(\left.\text{ii}\right.\) chord is typically minor in a major key and diminished in a minor key (\(\left.\text{ii}^{\circ}{}\right.\)), making uppercase \(\left.\text{II}\right.\) a chromatic harmony for which the proper label is \(\left.\text{V}\middle/\text{V}\right.\).
While labeling \(\left.\text{D}^{7}\right.\) as \(\left.\text{II}^{7}\right.\) in C major makes the root clear, it does not communicate the function of the \(\left.\text{D}^{7}\right.\), which is to progress to a G major chord (the \(\left.\text{V}\right.\) chord, or the dominant in C major).
Also, notice that \(\left.\text{vii}^{\circ}{}\right.\) is not tonicized with its secondary dominant in the example above. Listen to the following example to understand why diminished chords such as \(\left.\text{vii}^{\circ}{}\right.\) and \(\left.\text{ii}^{\circ}{}\right.\) in minor are not tonicized.
