V. Diatonic Harmony, Tonicization, and Modulation

Introduction to Harmony, Cadences, and Phrase Endings

John Peterson

Key Takeaways

  • This chapter provides an introduction to the harmony section of Open Music Theory, then it begins a discussion of how to create a sense of ending in a . We focus exclusively on using I and V for now.
  • Two larger concepts inform the way we present harmony here: and the .
  • Endings are often marked by , of which there are two primary types: and
    • 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 are untrue, the authentic cadence is imperfect.
    • Half cadences involve the progression x-V, where “x” is any of a variety of harmonies.

Introduction to Harmony

In this section of open music theory we’ll focus on how Western classical music composers use harmony in a . 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:

  1. refers to three categories of chords: , , and . Click on each category to see which chords belong to that category, and more importantly, what it means for a chord to be part of that category (really! Please click on each and read what pops up! This is important!).
  2. The refers to the typical order and flow of harmonic functions in a phrase (Example 1). More specifically, 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 (Example 1a). More often, phrases also include a predominant harmony to heighten the sense of trajectory toward closure (Example 1b). Phrases almost always progressed from left to right in the phrase model, not from right to left (Example 1c), although we’ll discuss some exceptions later.
diagram

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.

Introduction to Cadences

One way to create a sense of closure at the end of a is through , which are 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, we typically advocate listening for potential cadence points as a 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 (HC) that sounds inconclusive. The second phrase begins in m. 5 and ends in m. 8 with an that sounds conclusive. This authentic cadence is labeled “PAC” because it’s a particular kind of authentic cadence that we discuss below.

Example 2. Two cadences in Joseph Boulogne, Chevalier de Saint-George’s “Ballet No. 6” from L’amant anonyme, Act II. Audio Excerpt: 0:00–0:07.

Authentic cadences (they sound conclusive!)

An 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 (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 (IAC) occurs if either of the above two conditions aren’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


Ferne by openmusictheory. A (CC0) transcription of the full song is available here.

 

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

Half cadences (they sound inconclusive!)

A (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,” where the “x” refers to a variety of chords we’ll discuss in later chapters. 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. Imperfect authentic cadences are special because they occupy the space between HCs and PACs in terms of cadential strength (Example 4).

Diagram

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 a host of scale degrees in the melody), a composer can choose to make an IAC more or less strong.

  • The cadence in Example 3 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, and it’s followed by material that could easily be understood as continuing a phrase that’s under way or as referencing the beginning of a phrase that has just concluded, something that would strengthen reading m. 5 as an IAC. Performers may disagree on whether Example 5 contains an IAC or not, and they may adjust their playing accordingly.
Annotated score

Example 5. A potential IAC in Schubert’s Piano Sonata D. 845, III.

An additional complication is that composers often avoid creating a PAC using progressions that fit the description of an IAC, but which don’t mark the end of a phrase. In Example 5, m. 8 contains a potential IAC, but when m. 9 begins to repeat the material from m. 5 (compare the bass voice in m. 9 with the soprano in m. 5) it sounds like the passage is trying the run up to the cadence again to achieve something stronger than the potential IAC at m. 8. We indicate that the cadence in m. 8 is subverted by crossing the label out on the score. With so many possibilities, how can we determine what counts as a true IAC? The next section (“hearing cadences”) offers some help.

Annotated Score

EXAMPLE 6. Avoiding a cadence in Beethoven’s Piano Sonata Op. 2, No. 3, I, mm. 1–13.

Hearing Cadences

While there is certainly a degree of intuition involved with hearing cadences, it’s also a skill that can be honed over time. We recommend doing the following when you listen for cadences:

  • At first, listen and mark potential points of rest, goal, or closure
    • It’s common for students to initially mark too many cadences. One rule of thumb is that unless an excerpt’s tempo is quite slow, it’s not common for phrases to be two measures long.
  • Next, check the harmonies involved in these potential cadence points:
    • x-V = potential HC
    • V-I = potential AC
      • If Do (\hat{1}) is in the soprano over I and both harmonies are in root position, it’s a potential PAC.
      • If something else is in the soprano over I; or V, I, or both harmonies are inverted, it’s a potential IAC.
    • If it doesn’t involve one of the above two progressions, then it’s not a potential cadence.
      • Note that this doesn’t mean it doesn’t represent some kind of ending. It just means it’s not a cadence.[1]
  • Finally, listen for what happens after each potential cadence point.
    • Since true cadences mark the end of a phrase, it’s very common for cadences to be followed by a sense of . This “beginning” may be a repetition of the beginning of the phrase that just ended, or it may be new material that starts a new phrase. Hearing a sense of beginning following a cadence point is a great way to help verify that what you’ve marked as a potential cadence is indeed a true cadence point.
    • If, instead, you hear repetition of material from the middle of the previous phrase, it’s less likely that your potential cadence represents a true cadence. Instead, it likely represents a potential cadence point that has been .

Summary: steps for hearing cadences

  • Mark potential cadence points
  • Analyze the harmonies involved
  • Listen for a sense of beginning after each potential cadence point

 

Writing Authentic Cadences (TRIADS ONLY!)

The steps for writing a PAC or IAC are summarized in the box below. Examples 7 and 8 illustrate the steps for writing a PAC in major and minor, respectively; Examples 9 and 10 illustrate the steps for writing an IAC in major and minor, respectively.

Writing a PAC or IAC

  1. Determine the key
  2. Write the entire bass: sol–do (\hat{5}\hat{1})
  3. Write the entire soprano:
    1. PAC: re–do (\hat{2}\hat{1}) OR ti–do (\hat{7}\hat{1})
    2. IAC: re–mi (\hat{2}\hat{3}) OR sol–sol (\hat{5}\hat{5})
  4. Fill in the inner voices by asking:
    1. What notes do I already have in the bass and soprano?
    2. What notes do I need to complete the chord?
    3. What note will I double (remember in root position chords, it’s common to double the bass)?
  5. If you’re writing in minor, remember that you need to use the leading-tone, Ti (↑\hat{7}) in your V chord to give it momentum toward the tonic. In other words, V should be a major triad, not a minor triad.


EXAMPLE 7. Writing a PAC in a major key.

EXAMPLE 8. Writing a PAC in a minor key.

EXAMPLE 9. Writing an IAC in a major key.

EXAMPLE 10. Writing an IAC in a minor key.

Writing Half Cadences (using I and V only)

The steps for writing a HC are summarized in the box below. Examples 11 and 12 illustrate the steps for writing a HC in a major and minor key, respectively.

Writing a HC:

  1. Determine the key
  2. Write the entire bass: do–sol (\hat{1}\hat{5}) [note: for now, we’ll use only I and V chords, although later we’ll see that other chords more commonly precede V]
  3. Write the entire soprano: do–ti (\hat{1}\hat{7}) OR mi–re (\hat{3}\hat{2}) [note: sol–sol (\hat{5}\hat{5}) is possible, but not common]
  4. Fill in the inner voices by asking:
    1. What notes do I already have?
    2. What notes do I need to complete the chord?
    3. What note will I double (remember in root position chords, it’s common to double the bass)?
  5. If you’re writing in minor, remember to use the leading-tone, Ti (↑\hat{7}) in your V chord. In other words, your V chord should be a major triad, not a minor triad.

Example 11. Writing a HC in a major key.

EXAMPLE 12. Writing a HC in a minor key.

Assignments
  • Assignment 1: Asks students to write and identify cadences using only I (or i) and V chords in major and minor

Media Attributions

  • Phrase_Model © John Peterson is licensed under a CC BY-SA (Attribution ShareAlike) license
  • Example_3_Cadence_Strength_Spectrum
  • Example_4_Potential_IAC_Schubert_845_III
  • Example_5_Beethoven_op_2_3_I

  1. Sometimes, for example, the melody suggests an ending, but the harmony doesn't participate. Or, sometimes the harmony suggests an end but the melody refuses to close. Cadences are special goal points because they represent places where both the melody and harmony agree on a phrase ending.

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Open Music Theory by John Peterson is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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