This week we secondary or substitute functions. These are chords that can stand in for primary functions (tonic or predominant) for various purposes – most often variety, voice-leading, or to keep the phrase moving forward. The quality of a chord (major or minor) is always shown by the last letter of a functional label.
These chords can function in a similar way to their primary chord because they share 2 notes in common, so our ear can almost imagine the primary chord in some ways. Some substitutes are stronger than others.
Relative chords (Tonic Relative, Predominant Relative) share the same relationship to their primary chord as relative keys. This means that in major (ex. C major), Tonic Relative (Tr) has a root a diatonic third below tonic and is a minor chord (a minor). However, in minor the relationship is opposite, so that for minor tonics (ex. c minor) the Tonic Relative (tR) is a diatonic third above tonic and a major chord (Eb major).
If we instead keep a different 2 notes in common, we get the variant relationship. In major Tonic Variant (Tv) is a the chord with the root a diatonic third above tonic (C major-e minor), and in minor, Tonic Variant (tV) is the chord with the root a third below tonic (c minor-Ab major).
Similar relations can be made with predominants, so that in major the Predominant Relative (Pr) and Predominant Variant (Pv) are below by third and above by third just as with the tonic substitutes. In minor, a Predominant Relative (pR) is a diatonic third above, but the Predominant Variant is a chromatic chord, so we won’t cover it here.
An interesting relationship to note: A variant and a relative of the same primary function (Tv and Tr) share a fifth relationship between their root pitches (e minor to a minor) and can sound like a weak embedded cadence if one after the other.
I have posted both staff notations of these relations (in C major and a minor) and a Tonnetz graphic earlier this week.
Dominant chords will be altered instead of substituted.
Dr. Kit Music 
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