IV. Diatonic Harmony, Tonicization, and Modulation
44
John Peterson
Key Takeaways
- 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 [latex](\hat{1})[/latex] 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.
Introduction to Harmony
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 .
Introduction to Cadences
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.
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.
shows two phrases and the two main categories of cadence: (1) inconclusive and (2) conclusive. The first phrase ends in m. 4 with ahttps://musescore.com/user/32728834/scores/6827779/embed
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 ( , m. 8):
- Do [latex](\hat{1})[/latex] 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 ( ). For instance, an IAC can occur when:
- Mi (me in minor) [latex](\hat{3})[/latex] is in the soprano over the tonic chord (as in ), or
- V, I, or both harmonies are inverted
https://musescore.com/user/32728834/scores/6617197/embed
Half Cadences (they sound inconclusive!)
A half cadence (HC) occurs when a phrase ends on V ( , 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 (
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
above is relatively strong: it uses root position V–i with me [latex](\hat{3})[/latex] 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
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 contains an IAC or not, and they may adjust their playing accordingly.https://musescore.com/user/32728834/scores/8391384/embed
An additional complication is that composers often avoid creating a PAC using progressions that fit the description of an IAC, but that don’t mark the end of a phrase. In subverted by crossing the label out on the score.
, 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 ishttps://musescore.com/user/32728834/scores/8391423/embed
With so many possibilities, how can we determine what counts as a true IAC? The next section (“Hearing Cadences”) offers some help.
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 listening for cadences following this process:
- 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 [latex](\hat{1})[/latex] is in the soprano over I and both harmonies are in root position, it’s a potential PAC.
- If something else like mi [latex](\hat{3})[/latex] or sol [latex](\hat{5})[/latex] is in the soprano over I, it’s a potential IAC.
- If 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 beginning. 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, your potential cadence may not be a true cadence. Instead, it likely represents a potential cadence point that has been subverted.
Writing Authentic Cadences (with triads only)
The steps for writing a PAC or IAC are summarized in the box below and illustrated in
.Writing a PAC or IAC
- Determine the key
- Write the entire bass: sol–do [latex](\hat5-\hat1)[/latex]
- Write the entire soprano:
- PAC: re–do or ti–do [latex](\hat2-\hat1[/latex] or [latex]\hat7-\hat1)[/latex]
- IAC: re–mi or sol–sol [latex](\hat2-\hat3[/latex] or [latex]\hat5-\hat5)[/latex]
- Fill in the inner voices by asking:
- What notes do I already have in the bass and soprano?
- What notes do I need to complete the chord?
- What note will I double? (Remember, in root position chords, it’s common to double the bass.)
- If you’re writing in minor, remember that you need to use the leading-tone, ti [latex](\uparrow\hat7)[/latex], in your V chord (making it a major triad, not minor) to give it momentum toward the tonic.
https://musescore.com/user/32728834/scores/5772942/embed
https://musescore.com/user/32728834/scores/5772904/embed
https://musescore.com/user/32728834/scores/5772922/embed
https://musescore.com/user/32728834/scores/5772955/embed
Writing Half Cadences (using I and V only)
The steps for writing a HC are summarized in the box below and illustrated in
and .Writing a HC:
- Determine the key
- Write the entire bass: do–sol [latex](\hat1-\hat5)[/latex] (note: for now, we’ll use only I and V chords, although we’ll see later that other chords more commonly precede V)
- Write the entire soprano: do–ti or mi–re [latex](\hat1-\hat7[/latex] or [latex]\hat3-\hat2)[/latex] (note: sol–sol [ [latex]\hat5-\hat5[/latex] ] is possible, but not common)
- Fill in the inner voices by asking:
- What notes do I already have?
- What notes do I need to complete the chord?
- What note will I double? (Remember, in root position chords, it’s common to double the bass.)
- If you’re writing in minor, remember to use the leading-tone, ti [latex](\uparrow\hat{7})[/latex], in your V chord, making it a major triad, not minor.
https://musescore.com/user/32728834/scores/5772954/embed
https://musescore.com/user/32728834/scores/5772897/embed
- Introduction to harmony, cadences, and phrase endings (.pdf, .docx). Asks students to write and identify cadences using only I (or i) and V chords in major and minor.
- 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. ↵
A relatively complete musical thought that exhibits trajectory toward a goal (often a cadence).
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A melodic and harmonic goal. In classical tonal music, cadence types include Perfect Authentic (PAC), Imperfect Authentic (IAC), and Half (HC).
A cadence with the harmonies V–I. The harmonies are typically in root position. Authentic cadences can be further distinguished by their melody note in the I chord: an authentic cadence ending on 1̂ in the melody is a perfect authentic cadence, while one with 3̂ or 5̂ in the melody is an imperfect authentic cadence.
A kind of inconclusive cadence that occurs when a phrase ends on V. Occasionally, particularly in Romantic music, the final chord of a half cadence will be V⁷.
A category of chords that sound stable, providing a sense of home or center. The I chord is the paradigmatic tonic-function chord, but vi and iii occasionally have tonic function.
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A category of chords that provides a sense of urgency to resolve toward the tonic chord, including V and vii° (in minor: V and vii°).
A V–I cadence that ends with do (1̂) in the melody. Both harmonies must be in root position.
A V–I cadence in which V, I, or both harmonies are inverted, and/or do (1̂) is not in the soprano over the tonic triad. Additionally, IACs are often used to evade a cadence.
Occurs when a potential cadence point is declined by the material that follows it. A common strategy is for a composer to write music that proposes a cadence, but then to "back up" in the phrase and try the cadence again. See also the "one-more-time" technique in the chapter on phrase expansion.
One of three formal functions (with the other two being middle and ending). Beginnings are often signaled by establishment of a new melody or repetition of the beginning of a previously heard melody, emphasis on tonic harmony (especially root position), a melody that opens up musical space by ascending, a statement of a motive that is developed through the remainder of the phrase.