Modulation Practice

Modulations are central to the art of tonal music. This article can get you started. 

This lesson builds upon the first lesson which you can find here: Modulation

Hearing and writing modulations

A modulation guides the ear smoothly from one tonality to another.

The exercise is where you progress from one tonic to a different tonic without any jumps or gaps in-between. It’s a bit like the 12 tone exercise in the sense that you're guiding the ear with the tones and working with the fifths at a deep and creative level.

A modulation is not necessarily a key-change. In a composition, modulations could take place before a key change, or during the development of a form, and writing a modulation is more than a way to replace one key with another. The practice is almost elemental in the way that it connects us to how music could be heard, built, expressed.

When listening, find the stable chords. Circle them, if you want. Each chord has a purpose to guide the ear. Look for the big structures in the modulation first. The beginning and end are stable points; try to find how the points of stability are connected in the middle. Ask yourself, where does each phrase end and begin? 

Eventually, and with the help of looking at the scores, you'll start to hear that each of the notes are constantly changing depending on their relation to so many things: the roots of the chord, tension and dissonance, on where each voice in the chord is leading. 

The modulations will activate every musical parameter, and writing one will first require your knowledge of cadences and chord progressions. 

Here are 6 modulations—5 new and 1 old—that all try to achieve the same goal: a smooth progression of chords from one established tonality to another. 

The function of the pivot chord 'turns' from being past-oriented to future-oriented once it is in the past. The Bb-F fifth in the IV6 chord reorients the ear to F, bringing the D minor along with it long after it is heard.

C major to F major via D minor.

This is the modulation we built in our last lesson (which you can check out again by clicking here).

Figure 1. The three moments of the modulation: opening tonality, neutral field, and final tonality. Two main moments of tension: the A major (yellow) and the G minor 7 (blue). The G minor is relatively less of a harmonic contrast than the A major.

Listen to the D minor. Can you hear the same chord in two keys at different times? Can you hear it switch from being heard as the ii of C, to then connecting to F? The revolution happens with only three chords.

Explode to the open position with intervals

Even though the modulation is written in the closed position, I usually think of it in the open position, with each voice singing a horizontal line, and only when sung together can they articulate the full harmony. 

Figure 2. The same modulation in the open position. All chord roots are labeled red, and the interval of the other voices to the root is indicated on some of the notes. Try hearing harmony in this way. 

Part of the reason why the A major chord (V/ii) is relatively unstable compared to everything that came before it is because the root is in an upper voice, no longer in the bass. 

Similarly, the soprano sings three F's in a row, but each F changes its function based on the root of the harmony underneath. Try and hear those changes in the quality of the soprano voice as it moves from an unstable seventh to resolving down to F functioning as a more stable third in the chord, to an open sounding fifth attached to the Bb, and finally to the root of the new central tonality. This is the key to understanding how to properly phrase and play a modulation.

The pivot is where the function of the chord changes inside the note. Nothing changes in the vibration itself, and yet the sound of the chord, from relating to C to relating to F happens after the chord connection from the D minor to the ii65 of F. It's as if the musical time of the D minor in the moment of the ii65 goes from flowing to the future, to flowing to the past.

The Renaissance Connection

The moments of tension and release articulates similar to how Lasso treated dissonances and consonances in his cadences. The dissonant chords are approached by consonant chords, and the resolutions are placed in descending order leading to stability. 

With this analysis, I hope you approach the remaining modulations in the same way. And further, you can begin to see all written music with this degree of living interconnectedness which can always be found rooted in our very experience. 

C major to F major via A minor.

Using the melodic parameter to improve a modulation.

Figure 3. This one goes to the neutral field of A minor via the deceptive cadence in C major. The A minor is confirmedwith its dominant (without it the modulation as a whole is much weaker) so that the second A minor chord is much less tense than the first one. 

Then the F is introduced in the soprano on the Gm7 chord, but the F is a seventh, a dissonance that wants it to resolve down to E. The second F in the soprano has much more stability since it's the root of the chord. Then we finally get that downward resolution of F to E as the third of the dominant. We are now in F major. 

Also, compare the right and left hands of this progression from C to F via A minor. What I like about this one is the strongest modulatory part is the bass—note how the right hand plays notes nothing but notes in C major (no accidentals). The bass helps move those notes to relate to a new dominant fifth. 

We could confirm the A minor with it's lower fifth in a plagal cadence with D minor instead of E major. You probably wouldn't want D major which has an F#, and we're aiming for the key of F natural. D minor would bring us close to F at the same time, while creating a more introverted feel to the modulation. 

Figure 4. Overall it's a more introverted sounding modulation, compared to using the E major chord. The ear doesn't have that fifth between E-B like it does with the E major, so we never hear those 4 and 5 sharps above the notes. Instead the A is enforced by its minor subdominant, D minor, so the D-A fifth brings us near to F. It's a lower fifth, we don't have any of that same harmonic contrast with the upper fifths. So the modulation is improved by raising some of the upper voices by inversion to add contrast with the line and activating a different parameter to help us: the melodic.

Now I would hardly consider the soprano, alto, or tenor voices here a melody, but the way that the voices work together with the bass to modulate from C to F is made stronger by activating some degree of the melodic parameter in the ear (by using a lot of horizontal major seconds). 

G minor to Ab major via C minor

How I picked the neutral field from G minor to Ab major.

If you look at the circle of fifths between G minor and Ab major, there are a bunch of keys in between that can connect. I chose C minor, the fifth right in between. That way, I could go to my target key of Ab major via the subdominant key of Db major, which is the Neapolitan of C minor.

Figure 5. Note the audio starts from the V of G minor.

Where are the stable points in this modulation? Where are the chords leading? The arrows in Figure 5 give a clue as to how to phrase the modulation. Those are the harmonic impacts that are necessary to live the modulation from g to Ab. 

G minor to F major via A minor

Using octavation and dissonant sevenths to improve a modulation.

Hear this one first and then look at the score:

Did you notice the bass spans an entire octave? Also instead of the ii7 chord I usually use in the final cadences, I replaced it with a IVmaj7 which forms that dissonance you heard toward the end. 

Figure 6. Here's the score so you can see the voicing of the magical IV7; the seventh between Bb and A pull each other in to form the strong dominant of F (C-G). 

C major to D major via B minor

Here is a visual on how I think about fifth relations. 

The harmonies of the modulation from C major to D major via B minor are mapped out here on the circle of fifths. You can see how the smooth progression of chords maps out on the circle, and you can get a sense that you can go "anywhere" once you know how the fifths can be approached. 

Figure 7. The circle of fifths with the modulation from C to D mapped out on it. You can listen along and follow the tones along the map from C to b to D. Thinking this way can help you come up with new ways of modulating between the keys. Study each modulation by tracing the chords freely along the circle of fifth relations. Remember, if you're modulating to a major key use a minor neutral field, and vice versa. 

Figure 8. C to D via b. 

F major to Bb minor via Gb major

Using the Neapolitan twice with two functions in one modulation.

Figure 9. Here is another example where the Roman numerals sort of break down—here it's just best to think of the modulation in the three big moments, the opening tonality, F major, the neutral field, and the final cadence in Bb minor. 

The neutral field is established: I7-II-V-I in Gb major. The connection from the beginning F to Gb is the Neapolitan relation. It's a drop of 5 fifths but it's surprisingly smooth this way. Thanks to the Cb major chord (falling yet another fifth from Gb), our ears find the stability in Bb minor, again a Neapolitan relation, this time bringing us to our new home from Cb to Bb. 

Experience from beginning to end

Each modulation is an experience that must be played from beginning to end if you want to know how the tones all relate to you. You should analyze them to find the tempo of each modulation; i.e., how are all the tones connected, not with logic, but how do they live in you?

The most direct way to study this information is to listen with a very open mind, free from labeling or judging, and just letting yourself be moved by the musical forces that move you. The main and direct 'intangible' parameters to hear are the moments of tension and resolution in the modulation.

Your mods could be very different from mine, but in my experience the ones that follow the cadence - neutral field - cadence schema are the ones that function the best. Within those limits already you can do so much. You can, for example, establish an opening cadence with V6-I-V-I. 

At first, writing a functional modulation is a challenge but once you get it, then you've got it. The exercise of modulation is not a composition, and it's an exercise about navigating through worlds of harmonic possibility. The journey is most important.

A true modulation is when you hear no trace of the original tonic. You have essentially escaped the gravitational field of the tonic, drifted in space, and entered the orbit of a new center of gravity. Doing so requires harmonic energy, and a path-trajectory to guide the ear from one structured sound to another.

Summary, and more to come

The purpose of this post is not to dazzle beginning harmony students into feeling overwhelmed with learning Neapolitan chords in 24 keys. No, it actually it is to get us excited about the possibilities of harmony. So many musicians want to know how to use chords better and this is the answer that worked well for me: practice modulation. Through repetition, you're set on the way to mastering the tonal relations and make it possible to write any music you want. And when you write/compose one, feel free to send it in and I'll share one with you too: Jordan [at] jordanali.com. 

The modulation exercise

1. Hear a modulation and write it down. Or, choose one of the prompts below. You can use logic to think it through but write down at least the names of the chords that are modulating. In the beginning, use lots of trial and error and stick to the fundamentals that we learned about fifth relations.

2. Arrange the chords in closed position with smooth voice leading (like in figure 1). 

3. Rearrange for 4 voices (like in figure 2). 

4. Record each voice on your instrument or sing them, phrasing the modulation to achieve what you have in your mind. Share them on your YouTube and use the tag #modulationmagic. 

Modulation Exercise Prompts (Studies from simple to more advanced)

1. Write a modulation from D major to G major via e minor. If you never wrote one before, this is a good start. Study the modulation that we made in the last post from C to F via D, and you can even follow the same pattern.

2. Write one from D to C major using a German cadence. 

3. Write one from g minor to Ab major. 

4. Try writing one with two neutral fields. For example, modulate from D major to Bb major using C major and g minor as your neutral fields. 

5. Create a modulation that circles back to the starting key. Essentially 2 modulations: one leaving a key to a new one, and then a second modulation leaving the new key and returning to the first. If you want to you can combine your modulation from prompt 3 and combine with mine from C to D and see what happens.

The day 11 lesson on harmonic reduction marks the moment where we start to head home in the course. So far we've been building larger and more complex structures, but tomorrow we'll be starting from the complex and simplifying it to understand how we hear and live the music that we love.