This chapter provides an introduction to the harmony section of Open Music Theory, then begins a discussion of how to create a sense of ending in a phrase. We focus exclusively on using I and V for now.

Two larger concepts inform the way we present harmony here: harmonic function and the phrase model.

Endings are often marked by cadences, of which there are two primary types: authentic cadences and half cadences.

Authentic cadences involve the progression V–I. They are perfect when both harmonies are in root position and do (\hat{1}) is in the soprano over tonic. If either of these conditions is not met, the authentic cadence is imperfect.

Half cadences involve the progression x–V, where "x" is any of a variety of harmonies.

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In this section, we'll focus on how composers of common-practice Western classical music use harmony in a phrase. Harmony is one important component (among others) of creating a phrase's sense of forward motion toward a goal. As we study harmony, it's important to keep two larger related concepts in mind: harmonic function and the phrase model.

Harmonic function refers to three categories of chords:

Tonic (T): Chords that sound stable, providing a sense of home or center. In Western classical music, the only chord that belongs to this category is I (in minor: i).

Predominant (PD): Chords that transition away from tonic function toward dominant function. This category can be split into two groups:

Strong predominants signal that a dominant function chord is imminent: IV and ii (in minor: iv and iio).

Weak predominants transition away from tonic, typically moving to a stronger predominant: iii and vi (in minor: VII, III, and VI).

Dominant (D): Chords that provide a sense of urgency to resolve toward the tonic chord: V and viio (the same in minor).

The phrase model refers to the typical order and flow of harmonic functions in a phrase. The principle of the phrase model is that a phrase needs at least tonic function and dominant function harmonies in order to exhibit a sense of trajectory. More often, phrases also include a predominant harmony to heighten the sense of trajectory toward closure. Phrases almost always progress from left to right in the phrase model, not from right to left, although we'll discuss some exceptions later. This is summarized in Example 1.

[](https://viva.pressbooks.pub/app/uploads/sites/12/2019/09/Phrase_Model.png) Example 1. The phrase model: (a) the minimum functions needed to create forward motion, (b) more common functional layout for a phrase (the final tonic is optional), (c) harmonic functions do not progress right to left.

One way to create a sense of closure at the end of a phrase is through cadences—melodic and harmonic patterns that create goals, kind of like punctuation marks in literary sentences. They're important not only because they can help you determine phrase endings, but also because they help establish a key. As a result, listening for potential cadence points is typically a good first step in analysis.

Example 2 shows two phrases and the two main categories of cadence: (1) inconclusive and (2) conclusive. The first phrase ends in m. 4 with a half cadence (HC) that sounds inconclusive. The second phrase begins in m. 5 and ends in m. 8 with an authentic cadence that sounds conclusive. The label PAC marks this as a particular kind of authentic cadence called a perfect authentic cadence, discussed below.

Example 2. Two cadences in Joseph Boulogne, Chevalier de Saint-George's "Ballet No. 6" from L'amant anonyme, Act II (0:00–0:07).

Authentic Cadences (they sound conclusive!)

An authentic cadence occurs when the harmonic progression V–I (or V–i in minor) marks the end of a phrase. There are two kinds of authentic cadence:

A perfect authentic cadence (PAC) occurs when both of the following conditions are met (Example 2, m. 8):

Do (\hat{1}) is in the soprano over the tonic chord

Both V and I are in root position

An imperfect authentic cadence (IAC) occurs if either of the above two conditions isn't met, but V–I is still involved (Example 3). For instance, an IAC can occur when:

Mi (me in minor) (\hat{3}) is in the soprano over the tonic chord (as in Example 3), or

V, I, or both harmonies are inverted

Example 3. An imperfect authentic cadence (IAC) in Fanny Hensel, "Ferne" Op. 9, No. 2 (0:00–0:14).

Half Cadences (they sound inconclusive!)

A half cadence (HC) occurs when a phrase ends on V (Example 2, m. 4). A variety of chords can precede V, so we often refer to the harmonic progression that marks HCs as "x–V."

For now, we'll restrict our vocabulary to only I and V chords (or i and V in minor) so we can learn some basic techniques of voice-leading.

Cadential Strength and the IAC

PACs are the strongest kind of cadence available to a composer because of the sense of finality they can create, and HCs are the weakest kind of cadence because of their unfinished sound. IACs are special because they occupy the space between HCs and PACs in terms of cadential strength (Example 4).

[](https://viva.pressbooks.pub/app/uploads/sites/12/2019/09/Example_3_Cadence_Strength_Spectrum.png)

Example 4. Spectrum of cadential strength.

Since there are many ways to compose an IAC (a composer can theoretically use various combinations of inverted chords and scale degrees in the melody), a composer can choose to make an IAC more or less strong.

The cadence in Example 3 above is relatively strong: it uses root position V–i with me (\hat{3}) in the soprano, it comes at the end of a sentence in the lyrics, it uses a half note, it's followed by a rest, and the music that follows sounds like a new phrase.

The potential IAC in Example 5 is comparably weaker: it uses V6–I, the moment goes by relatively quickly