Definition and Notation
The regular major scale contains seven basic chords, designated with Roman numerals in ascending order. Since the seventh degree is a diminished triad, it is not considered tonal and therefore, classical theory sees only the first six chords as eligible for an applied dominant. For instance, in the key of C major, those six chords would be:
Of these chords, V (G major) is said to be the dominant of C major (the dominant of any key is the chord whose root is a fifth above the tonic). However, each of the chords from ii through vi also has its own dominant. For example, vi (A minor) has an E major triad as its dominant. These extra dominant chords are not part of the key of C major as such because they include notes that are not part of the C major scale. Instead, they are the secondary dominants.
Below is an illustration of the secondary dominant chords for C major. Each chord is accompanied by its standard number in harmonic notation. In this notation, a secondary dominant is usually labeled with the formula "V of ..."; thus "V of ii" stands for the dominant of the ii chord, "V of iii" for the dominant of iii, and so on. A shorter notation, used below, is "V/ii", "V/iii", etc. The secondary dominants are connected with lines to their corresponding tonic chords.
Note that of the above, V/IV is the same as I. However, as will become clear shortly, they are significantly different.
Like most chords, secondary dominants can be classified by whether they contain certain additional notes outside the basic triad; for details, see Figured bass. A dominant seventh chord (notation: V7) is one that contains the note that is a minor seventh above the root, and a dominant ninth chord (notation: V9) contains the note a ninth above the root. For instance, V7/IV, although it is a C chord, is distinct from regular C major because it also contains the note B flat, which is a minor seventh above the root of C, and not part of the C major scale.
To illustrate, here are the secondary dominants of C major, given as dominant seventh chords. They are shown leading into their respective tonics, as given in the second inversion.
Chromatic mediants, for example vi is also a secondary dominant of ii (V/ii) and III is V/vi, are distinguished from secondary dominants with context and analysis revealing the distinction.
Read more about this topic: Secondary Dominant
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