Harmony | Learning and Loving Music Theory

Understanding Key Changes

The concept of changing keys, or modulation, was introduced in this music theory lesson. Here we’ll see how it works in actual music.

The best way to explain modulation is to demonstrate it. We’ll do that with a simple example. But be sure to turn your ears on and listen. Changing keys is something you should hear. Once you hear it, then it’s easier to see it on the written score.

Listen to the following chord progression in D major. When it completes, sing what you hear as the tonic, or home key. If you’re not sure, click the play button below the score.

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Play tonic:

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Next, listen to the same chord progression, only this time it’s in A major. Again, sing what you hear as tonic.

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Play tonic:

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Now we’ll connect these two progressions with a couple of chords, thereby creating a passage of music that modulates from D major to A major:

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Determining if a Passage of Music Modulates

Do you hear how, in the foregoing example, the passage clearly starts in the key of D major, but when it concludes it cadences in the key of A major? As I said above, the best way to determine if a modulation has occurred is to use your ears.

Here are some other factors that help us to identify a modulation. We will continue to refer to the example above (modulating from D major to A major):

Recurring Accidentals

Notice that the passage does not change key signatures. You will discover that much traditional music will change keys but not change key signatures. Instead, the composer will use accidentals. (See further comments on this at the end of the lesson.)

On the third beat of measure 4 and onward, all of the G’s are sharp (there are no G naturals). In other words, the music from measure 4 until the end has 3 sharps (the key of A major), not 2 sharps (the key of D major).

Emphasis on the Dominant of the New Key

This fact, of course, is related to the recurring G-sharp, which is the leading tone of A major. And because these G-sharps are always part of a dominant harmony of A major, our ears are drawn to hear A major as the new key.

Cadential Pattern in the New Key

Finally, another good clue that the music has changed keys is a strong cadence (usually some type of authentic cadence) in the new key. In our example above, the last two measures contain a strong TSDT progression, ending with a perfect authentic cadence (PAC) in A major.

Pivot Chord Modulation

The example above (modulating from D to A) is one of the simplest and smoothest ways to change keys. It’s called a pivot chord modulation, and is quite common in traditional tonal music. The B minor chord on the third beat of measure 4 has a dual function: it is a vi in D and a ii in A, hence the term pivot chord. We will discuss pivot chords in detail in the next lesson.

The chord progression we’ve been using in this lesson is actually a simplified version of a passage from the third movement of Mozart’s Piano Sonata in D Major, K 284:

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A Note on Key Signatures and Modulation

When students first encounter modulation, there is often confusion. I am frequently asked something like this: “How can the music be in the key of A major (3 sharps in the key signature) when the key signature is D Major (2 sharps)?” The answer to that is simple:

The key signature does not always tell you the sounding key

As you begin to study more complex music (such as music with one or more modulations), you have to get used to the fact that the key signature does not always indicate the actual sounding key. Music literature is filled with pieces of music that wander around in several different keys without changing the key signature.

At this level of music theory, I tell my students that, when you see a key signature, you cannot assume that it is indicating a key. All the key signature is telling you is that, for example, all of the Fs and Cs are sharp. You have to figure out the key using other methods (those we studied in this lesson: sound, recurring accidentals, dominant chords, and cadential patterns). Only then, do you know for sure what key the music is in.

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Harmony Table of Contents

Lessons Table of Contents

Harmonic Rhythm

Harmonic rhythm is how often chords change in a passage of music, and is measured in note values. For example, if chords change every half-note, we say “the harmonic rhythm is a half-note.” Or, if the harmony changes every quarter note, we say “the harmonic rhythm is a quarter-note.” Sometimes the harmonic rhythm is a combination of note values that change at a regular rhythm, such as a half-note followed by a quarter-note:

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Introduction to Cadences

We have described tonal harmony as a hierarchy of pitches and chords where one pitch or chord has prominence over all the others. This tone or chord, as we learned in this music theory lesson, is the tonic scale degree. We might say that the tonic is the goal in a piece of tonal music. In order to reach that goal, the music progresses towards it (hence, the term harmonic progression).

Harmonic progressions set up expectations in our ears, expectations that are fulfilled only when the tonic chord is reached. Some of the greatest music ever written plays on this idea by setting up expectations, then denying them, creating tension in the music. This tension gives way to relaxation when the tonic chord is finally reached. When music comes to a point of relaxation or repose, it is called a cadence.

All of the elements of music (melody, harmony, rhythm, dynamics, timbre) contribute to cadence, but traditionally, we classify cadences according to their harmonic content. Most of the time, cadences are easy to identify because of the sense of culmination they create in the music. For example, cadences are often accompanied by longer note values, a slowing of the tempo, and a change in the harmonic rhythm.

But not all cadences end with the tonic chord. There are many cadences of varying degrees of strength. Some cadences sound complete, that is, the music comes to a rest, and we don’t hear a need for the music to continue. These types of cadences are called conclusive cadences. Then there are cadences that do not sound complete, that is, the music sounds like it needs to continue. We call these types of cadences inconclusive cadences.

For the remainder of this lesson we’ll show you how to identify and label the various cadence types. In future lessons, we’ll see how these cadences work in actual music. Use this lesson as a reference and to help you memorize the cadences.

Conclusive Cadences

Authentic Cadence

The authentic cadence is the most fundamental and final sounding of all cadences. It consists of a dominant triad or dominant seventh chord followed by the tonic triad (V-I, V7-I). There are two types of authentic cadences: the Perfect Authentic Cadence (PAC), and the Imperfect Authentic Cadence (IAC).

Perfect Authentic Cadence (PAC)

The perfect authentic cadence has specific requirments:

It is a V-I or V7-I progression.
Both chords, V and I, must be in root position.
Scale degree one () must be in the soprano of the I chord.

Here are two examples of a perfect authentic cadence.

Imperfect Authentic Cadence (IAC)

Any authentic cadence (V-I or V7-I) that does not meet the requirements above, is an imperfect authentic cadence. In the first example, scale degree one () is not in the soprano. In the second example, the V chord is not in root position:

Plagal Cadence (PC)

The Plagal Cadence, a IV moving to a I, often is called the “Amen” cadence because of its frequent occurrence at the end of hymns:

Inconclusive Cadences

Half Cadence (HC)

Any cadence that ends with a V chord is a half cadence:

Phrygian Half Cadence (PHC)

A Phrygian half cadence is a iv6-V progression and occurs only in a minor mode. It is characterized by a descending half-step in the bass. The soprano usually contains scale degree 4 moving to 5, but this is not a requirement.

Deceptive Cadence (DC)

When we hear a dominant chord near the end of a musical phrase, we are expecting a resolution to the tonic chord. The deceptive cadence denies this expectation. The most common deceptive cadence is the dominant chord moving to a vi. A variant of the V-vi, and a favorite of Handel, is the V moving to a IV6: