Tag Archives: harmony

Basic Harmony Terms

Melodic motion

There are two ways for notes to behave in a melody.

  • Step: the next note in a melody is one scale degree (difference of one letter name) or the interval of a (2) second away.
  • Skip (leap): next note is not a step away

Contrapuntal motion

A voice in music refers to an independent line of melody. In actual music voices can be doubled (played by multiple instruments) or harmonized (played with multiple pitch levels), but this does not mean additional voices have been created. A line of music must be sufficiently unique in its contour (pitches) or rhythm to be noticeable as a separate voice. Counterpoint is the technique of writing multiple voices that are distinct from one another.

Here is a list of ways that two voices can move relative to one another from most alike (least contrapuntal) to least alike (most contrapuntal).

  • Parallel motion: both voices move in the same direction and distance (creating parallel intervals)
  • Direct motion (similar motion): both voices move in the same direction (creating hidden parallels)
  • Oblique motion: only one voice moves, the other stays stationary
  • Contrary motion: the voices move in opposite directions (inward or outward)

Consonance and Dissonance

Here are commonly found intervals listed from most consonant to most dissonant. To compare compound intervals (intervals greater than an octave), first reduce to simple intervals.

  • Consonant
    • Perfect
      • (1/8) perfect unison and octave
      • (5) perfect fifth
      • (4) perfect fourth (sometimes)
    • Imperfect
      • (3/6) major and minor third and sixth
  • Dissonant
    • (4) perfect fourth (sometimes)
    • (2/7) major and minor second and seventh
    • (x4/°5) augmented fourth or diminished fifth, plus all other augmented or diminished intervals

An interesting note: composer Paul Hindemith further divided dissonances into perfect and imperfect dissonances. According to him, dissonant intervals that occur naturally in a piece of music’s scale or mode are perfect, while intervals that have been modified (augmented/diminished) are considered imperfect. Hindemith describes this theory in his book The Craft of Musical Composition.

While the (P4) perfect fourth is objectively consonant, it has a subjective reason for being a dissonance. In the Renaissance and Baroque eras it was treated as dissonant because harmonies resolved to triads, which do not contain strong intervals of a fourth. In later periods fourths were used more often as consonants. Hindemith also suggests an objective explanation for a dissonant fourth: the combination tones (another property of overtones) of a perfect fourth produce a pitch that reinforces the upper note instead of the bass, whereas the combination tones of a perfect fifth reinforce the lower note. This makes the fourth sound less stable, as it wants to be heard in terms of the upper note.

Chord Function

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)


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).

What is Music Theory?

Music: where physics and philosophy collide

Sound is the compression and expansion of air. Musical notes are produced when something (usually an instrument) vibrates and produces sound. This vibration is a wave, meaning it has the related properties frequency and wavelength. Frequency corresponds to the pitch of the sound. Wavelength is the distance taken up by the wave’s motion, and is inversely proportional to frequency, meaning higher frequencies have smaller wavelengths and vice versa. In short, larger vibrating parts produce lower pitch. More…