Functions are an abstract level of harmony that exists over the level of individual chords. Functions in harmony are like a “zoomed out” version of the music.

Table of common chords by function

Function types

Chords can be categorized into three functions:

• Tonic (T) – the foundation of the key, centered around the tonic note (scale degree ^1) and the triad built over it (^1, ^3, and ^5)
  examples of tonic chords: I (strong), I6 (weaker), vi (weak)
• Dominant (D) – the opposite of tonic, centered around the fifth (scale degree ^5) and the leading tone (^7)
  examples of dominant chords: V (strong), viio7 (weaker), V42 (weak)
• Predominant (PD) – centered around ^2 and ^4, used to prepare dominant or expand tonic/dominant
  examples of predominant: IV, ii6

The basic phrase model has the following form:

T, PD, D, T

where PD, and either the first or the last T, are optional. Each phrase in common practice music does this exactly once. Here are some examples of possible phrases:

• T-D-T (example: I-V-I)
• T-D (example: I-V)
• D-T (example: V-I)
• T-PD-D (example: I-ii-V)
• PD-D-T (example: IV-V-I)

Expansion

Each function area can be further expanded using weaker functions. These expansions are like mini-phrases, and usually follow the form of the basic phrase model. However, they are weaker because they use chords with weaker function. For example, chords in inversions are usually weaker than chords in root position. Chords that don’t have strong bass motion between ^1, ^4, and ^5, are usually weaker.

• Tonic expansions:
  • T (I) becomes T-T (I6-I)
  • T (I) becomes T-D-T (I-V43-I6)
  • T (I) becomes T-“PD”-T (I-IV64-I): PD is actually a passing or neighbour motion, and non-functional
  • T (I) becomes T-PD-D-T (I6-ii6-V43-I6)
• Predominant expansions:
  • PD (IV) becomes PD-PD (IV-ii6)
  • PD (ii) becomes PD-T-PD (ii-I6-ii6)
• Dominant expansions:
  • D (V) becomes D-D (viio7-V7)
  • D (V) becomes D-T-D (V64-I6-V7)
  • D (V) becomes D-“PD”-D (V6-IV6-V64): PD is actually a passing or neighbour motion, and non-functional
  • D (V) becomes D-T-PD-D (V-vi-IV-V)

An example of how a phrase can be expanded:

• Start with the basic phrase model: T-PD-D-T, realized as I-IV-V-I
• Expanding tonic, we can get T (PD-T)-PD-D-T, realized as I (IV-I6)-IV-V-I
• Expanding predominant, we can get T (PD-T)-PD (PD-T-PD)-D-T, realized as I (IV-I6)-IV (ii-I6-IV)-V-I
• Expanding dominant, we can get T (PD-T)-PD (PD-T-PD)-D (T-PD-D)-T, realized as I (IV-I6)-IV (ii-I6-IV)-V64 (vi-ii6-V7)-I
• Expanding the final tonic, we can get T (PD-T)-PD (PD-T-PD)-D (T-PD-D)-T (T-T), realized as I (IV-I6)-IV (ii-I6-IV)-V64 (vi-ii6-V7)-I (I6, I)

The amazing thing is, each of the functions created by expansion can be expanded further! This is how a large piece of music is understood, as a hierarchy of functions and their expansions, in which some chords are more important than others.

There is only one illegal motion in common practice music: D – PD. This motion is never functional. If it appears to occur, either the chords have been incorrectly identified, or one of the two areas is actually non-functional (perhaps because it is part of an expansion).