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Modulation

1 French composer Charles-Henri de Blainville (1767). Quoted from Forte, Allen (1979). Tonal Harmony in Concept & Practice , p.265.

Modulation is a shift of key. The Wikipedia article on the subject opens with a nice quote from the 18th c. which I will now gleefully purloin:

Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.1

This was certainly true of main-stream performance music in the author's own day, what we now call "classical music," but not so much for his contemporary folk music. The latter is, truth-be-told, the real great-great-grandmother of modern pop (in spite of numerous cross-influences). Indeed, many modern listeners still find modulations to be confusing, irritating, or both. Some of that distaste, to be sure, comes from bad modulations, but much of it comes from the fact that not everyone listens to music the same way. In spite of all that, prepare to dive in.

Short-term modulations

2 'Brief' is a keyword here; neighbor modulations are quite common for the refrain (see below). A 'neighboring key' is one that only moves one step (either direction) on the circle of fifths. Put another way, it is one that requires only a single accidental to be added or removed from the key signature.

Brief modulations to neighboring keys2 are fairly common in older music, but less so in modern pop. Hymns are a good place to look for them. Rockingham (Edward Miller), one of the tunes used for "When I survey the wondrous cross," (although probably not the one you are thinking of) has a good example:

Edward Miller, Rockingham (Lyrics: "When I survey the wondrous cross," Isaac Watts) Numeric notation styles
If the audio button is screwed up, try the MIDI

Technically, the only out-of-key chord is a secondary dominant on the F7, but if you listen to it you can hear that the whole section shown in orange sounds like a new key. It is the key of the dominant chord (and when you hear this sort of thing, that is often where it is taking you), but it then returns to the original key with the A♭ chord. IMHO, this passage is not really long enough to earn the term "modulation"; rather, it serves as a sort of elongated dominant chord.

Neighbor keys

3 Dominant key if the primary key was major. If it was minor, it was more likely to be the relative or parallel major.

4 See the later page on Standard Forms.

In contrast, in the early 19th century, composers would, as a matter of course, modulate into the dominant key3 for a significant portion of the piece. This was an expected feature of what is called "sonata allegro" form.4 It is relatively easy to do, you simply go to the five throw in a few secondary dominants until the new key sounds normal to the listener, and you are there (there are other ways as well, as we shall see). It was, in fact even easier for these composers, since the audience was expecting it. Part of the challenge for the composer doing this in the early 19th c. was how to get back, since that was also an expected part of the form, but only after wandering around key-wise for a while.

5 Note that some on-line chord sheets get this one wrong, but this one seems to have it right.

The dominant and subdominant (both one accidental away) are called neighbor keys, and going to one of them is a neighbor key modulation. Carl Carlton gave us one of these in the refrain of "Everlasting Love" (1974). In fact, this kind of modulation is a common enough move that I could waste your time with plenty of examples from modern songs, but one more will suffice: Sia (Furler) does one of these going into the refrain of "Chandelier." It is slightly different, though, moving from E♭→Fm. What makes it a neighbor key modulation is the fact that Fm is the relative minor of A♭(the 4 of E♭), so if you remember how a relative minor relates to its relative major, you will see that this still differs by only one accidental from the original E♭.5

Moving into remote keys is also possible, and we will look at various ways to do it. If you are writing a piece of any significant length (longer than the radio three-minute limit) it is a good way to keep the listener's interest.

Truck-driver gear change

Never-the-less you do actually hear modulation in pop all the time. The most common, to the point of being commonplace, is the shift in the coda (tag, outro) up by some interval, most frequently a step or a half-step. It is usually a sudden shift, and is generally successful in increasing the energy of the piece as it progresses toward its conclusion. It is so common that it has a (not particularly complementary) name: "the truck driver gear change" (because it suddenly shifts to a new energy level), but then, it wouldn't be so common if it didn't work. Not satisfied to do it just once, REM gives us two in "Stand," jumping up one step for the next to last refrain, and then again on the last one. If Beethoven were writing millennial pop songs, here is what "Ode to joy" might sound like:

Beethoven's "Ode to Joy" with "Truck-driver gear change" and fade. If the audio button is screwed up, try the MIDI

Still, a number of writers make more sophisticated use of modulation, even within the three-minute limit.

Visiting the relatives

Another common mid-song (i.e. non-coda) modulation is between relative keys. It is also the simplest because it doesn't even require a signature change. Brief modulations are so common as to sometimes raise the question of whether they are modulations at all. In fact, the only challenge, such as it is, is to establish that the key has changed. This is often accomplished by restating a recent melodic fragment in the new mode, or, if going from major to relative minor, by throwing in a major dominant in the new key (making it harmonic minor). But after all, you may not really care if your listeners think, "Oh, a key change!" You just want it to sound good.

Numeric notation styles
If the audio button is screwed up, try the MIDI
The chords without the viola part:
If the audio button is screwed up, try the MIDI

Here is an example modified from one we saw a couple of pages ago (when we talked about modal shift). You may recognize the melody, although it is slightly changed. The piece begins in major. The orange section represents the shift to relative minor, after which it returns to major. Obviously, you can have longer shifts, but this is a short example.

Justin Timberlake's "Mirrors" modulates from the minor key in the verses to its relative major in refrain. Lionel Ritchie does the same in "Hello." The Beatles manage to go the other way (much rarer in pop) in "When I'm Sixty-Four" (i.e major to relative minor in the refrain/bridge). Radiohead pulls of an interesting variation in "Sulk": the verses are in D Mixolydian, and the refrains are in G major. Technically, these are the same key signature, but like a relative minor/major modulation, the tonal center shifts (I suppose this would be a shift to relative Mixolydian). Then they do the 'truck-driver' thing for the last refrain.

Secondary dominants (again)

5 By "local key," I mean one rooted in one of the in-key chords (i.e. relative modes).

We have already seen the secondary dominant route to a modulation, if you happen to want to go to a local key.6 Here is the first in a long series of otherwise boring, but thankfully short examples of a complete modulation. Let's listen, and analyze:

C  G  C  F/a  G (7)  C (7)  F  B7  Em
Am/c  Em F♯ B (7) C Em Am/c B (7) Em
Use of secondary dominant (B7) to get from the key of C to Em If the audio button is screwed up, try the MIDI
7 F does have a https://www.youtube.com/watch?v=XJCvPhqcY9A relationship with B, although it is not a secondary dominant because the third of F (a) is not a leading tone to b. But it still leans towards it, as we talked about on the last page. In this context we could have used an F7 for a true secondary without changing the result dramatically. You can, of course, use a stream of secondary dominants to make your way to some distant keys.

8 In standard usage in the 18th & early 19th centuries, the composer was expected to return to the original key before the piece ended, as I mentioned earlier. By the middle/late 19th century, composers had rebelled against this convention, and felt free to modulate wherever and whenever they wanted. Modulations in modern pop are likely to return home if they were for a refrain. Otherwise, only occasionally (e.g. The Flaming Lips in "Do you realize??," mentioned below).

In the first four measures, the piece is simply establishing the key (C major). Then in the sixth measure you can hear the tonic being used as a secondary dominant by adding the flat seven and resolving on the F, but without changing keys. But the F takes us to a B7,7 which is clearly out of key (the B in the key of C is diminished), and is the secondary dominant for the keys of E (both major and harmonic minor). The next chord is Em. We could stay in the key of C at this point, but instead we start playing chords that emphasize our new home in the key of Em, including a deceptive cadence (the C) followed by an authentic one. At this point we are firmly in Em. Unlike the Miller piece, above, the idea is to stay here for a while.8

Pivot chords

Simple pivot chords make use of the fact that any given chord can exist in different keys, usually having different functions, of course. You can use this multiple functionality to shift from one key to another. You are playing along in G major, for example, and you come to a Bm chord (the 3m chord), you happen to know that Bm is also the 6m of D. This sort of relationship is called a "common chord." You can take the opportunity to jump from G to D off of the Bm using that commonality. Since there is only one sharp difference (it happens to be a neighbor key), this simply involves salting in a few c♯s and you are there! If you were jumping to A, where Bm is 2m, you have a little more work to establish your new key, since it is two sharps away rather than one, but it is still fairly easy. You can hear a shift like this between the refrains (key of C) and verses (key of F) in "The Three Bells (Little Jimmy Brown) by The Browns (both tonics are represented in the other key). Alternatively, or as well here is another boring example.

C  G  C  F/a  G (7)  C  F  Dm7  Gm/b♭
Am/c  Dm  Gm/b♭  A() (7)  Dm
Use of a pair of pivot chords (F & Dm7) to get from the key of C to Dm If the audio button is screwed up, try the MIDI

As before, the first four measures establish the starting key of C (up to the third C chord). The F and Dm7 are both pivot chords (4→2 in C = 3→17 in Dm). Then the rest of the short piece is establishing the new key. It is particularly strengthened by an authentic cadence using the harmonic minor's 57 (A major→A7→Dm).

9 If it is a minor key, its 2 is diminished, which cannot be the root of a key, unless we were to include the Locrian mode. If we are going to go modal, though, this list is going to get quite long. It should be noted that in this paragraph, I am not generally distinguishing major and minor. These relations will be true in both modes with the caveat that 1, 4, & 5 are either all major or all minor (in the case of the natural minor). Other modes will have the same relationships, without the handy minor/major consistency, and you will have to keep track of that pesky diminished chord.

Any given in-key chord (except diminished) will exist, at least enharmonically, in two other like keys—five if you include relative majors/minors. 1 can be the 5 of its 4, or the 4 or its 5 (plus 3 of its 6, 6 of its 3, and, if it is major,9 7 of its 2), etc. But you can get to much more remote keys by using some of the following methods.

Diminished pivot

We saw on the last page that diminished chords can serve as secondary dominants. When you are using them to modulate, they have some extra flexibility. Diminished chords have a destabilizing quality because they add an extra level of dissonance coming from their tritone fifth. Also, except for the 7 (not doubly) diminished in majors (or the 2 in minors) they are unnatural to the key. This endows them with a handy feature is that allows you to use any of the notes in the chord as a leading tone. That quality is increased when you add the diminished 7 to get a doubly diminished 7 chord. You can use this to modulate remotely to four different keys per diminished chord, and of course, you can get to any of the three doubly diminished 7 chords from any key fairly smoothly with a little practice. Consequently you can use these chords to get to any key from any other key.

Part of the reason for this is that doubly diminished chords are symmetrical, by which I mean that every note is separated by an interval of a minor third from the notes on either side of it, and by a tritone from the one remaining note in the chord. Because of this, if you build one in, say, the key of A rooted on the g♯ (g♯-b-d-f), that chord happens to be enharmonically equivalent with the 77 in the key of E♭ (d-f-a♭-c♭). So, you can simply reassign it and slide up to the E♭. Then you play enough chords to establish your new key, and you are in the new groove.

Augmented chords have the same unstable nature, since they are not natural to any key, and are also symmetrical. Of course, you only have three leading tones per augmented chord, but to make up for that you have four chord possibilities, rather than three. It is also worth noting that the leading tone feature is not as strong with augmented chords, perhaps because they do not occur naturally. Here are a couple of my boring examples, but try as I might, I could not find an example of this type of modulation in any modern popular songs (feel free to write if you know of one). These chords are rare enough as it is.

C  G  C  F/a  G (7)  C  Am  Am7  B7(=D7)
E♭  B♭  Cm  Fm/a♭  B♭  B (7)  E♭
Use of diminished seven (B7(=D7)) as a pivot chord to get from the key of C to E♭ If the audio button is screwed up, try the MIDI

Once again, we establish the key (up to the second Am7), but this time we go to a B7. We are still in key, except for the ♭7, but now we are going to redefine it, kind of the same way we did with pivot chords, as a D7, which we can do because of its symmetrical nature. Now it is the 7 of E♭, so we simply move there. The rest of the piece is simply establishing the new key.

C  G  C  F/a  G  G (7)  C  Dm  D♭  A♭/c 
E♭  A7/c  A♭ E♭  A♭  B♭m  E♭  E♭7/g  A♭ 
F/a♭  Bm  E♭/g  E♭7  A♭
Use of an augmented chord (D♭) as a pivot chord to get from the key of C to A♭ If the audio button is screwed up, try the MIDI
10 Two stories are told about the early 20th century composer, Igor Stravinsky. In one, a reporter asked him if he composed at the piano. He indignantly replied, "What? Do you think I have no ear?" [Most composers can write by simply hearing the notes in their heads, and just writing them down.] In the other story, he was booked into a hotel suite that didn't have a piano. He complained, "How do you expect me to discover new chords?" So, apparently he was indignant frequently, but did he need a piano or not? [Note: both of these quotes are strictly from memory, and neither one is likely to be completely correct. I'm pretty sure I heard them from the late Nicolas Slonimsky.]

11 I have seen the label "pivot note" to denote repetition of parallel scale steps on top of new chords (so, for example, in guitarmasterclass.net). This is a common feature of melodies and lead parts in both classical and modern music (we saw Beethoven doing it in his 5th symphony), but doesn't have much to do with modulation. It can however be used for modulation if the melodic statements are in different keys, as discussed in the text but, for obvious reasons, I will call it something else (a mirrored melody).

In this case the modulation is on the D♭ to the remote key of A♭. It is slightly different because it resolves down. Augmented chords don't always do this, but it is not uncommon to continue the voice movement in the same direction that got you there. If you are coming from a minor chord, movement is easiest down from the tonic. If it is major, it is easiest upward from the fifth. In both cases the already present major third is kept in tack.

You can hear augmented chords in the verses of Ben Folds Five's "Underground," and somewhere on any Beatles' album starting with "Rubber Soul," (I first encountered them in "I'm fixing a hole"), but I was not able to find anyone using one for modulation. In general, you are more likely to see diminished and augmented chords in songs written on the piano (although that doesn't have to be the writer's primary instrument) for the simple reason that piano makes it easier to see the relationships between chords and melody, and much easier to break the 'rules.'10

Pivot notes

Another common method used to smooth transition to another key is the pivot note. This does not require any intermediate chords, but it does require a cooperative melody (which does not, however, need to be in the vocal). Let's imagine that you are now in A♭ from the previous modulation. Your melody moves along in the new key and it hits and holds an e♭ on top of a Cm. At this point, with the note still ringing, you play a B chord. Your e♭ suddenly becomes an d♯, and is now the 3 of a B in a completely different key. This is a pivot note.11 In order for it to work, the note has to be common to both chords in some level of enharmonic equivalence, although it does not have to be part of the core triad (i.e. it can be a seventh or something). Here is a variation on an example we did on the last page, with a sustained pivot note across the modulation (at the Bm→A).

D♭  A♭7  B♭m  G♭  D♭  A♭7  Bm 
A  E  Bm7  C♯m  D♮
Use of a sustained pivot note to get from the key of D♭ to D If the audio button is screwed up, try the MIDI
The chords without the sax part:  If the audio button is screwed up, try the MIDI

The pivot note can also be an expected melodic note, rather than a held one. You can hear a number of these expected-note pivots in verse section of Bonnie Tyler's "Total Eclipse of the Heart. The following example, rooted in the same melodic idea as the last one, also illustrates this sort of thing. Listen how the melody set up in the first four chords is repeated, through the key change (C♭ G♭/b)—same notes; new key.

D♭  A♭  B♭m  G♭  D♭  A♭
C♭  G♭/b  A♭m  F♭  C♭  D♭m
Use of an expected melody to get from the key of D♭ to D If the audio button is screwed up, try the MIDI
The chords without the sax part:  If the audio button is screwed up, try the MIDI

Finally, in this category, we should mention mirrored melodies. They can be the exact same melody, given different tonal significance by the new key (as is common with relative key shifts), or simply the same melody, transposed to the new key, but recognizably connecting the two segments. This is basically going on in The Flaming Lips, "Do You Realize??," (around 2:25), and in Bach's double violin concerto, to which I have already referred twice. And yet another example, this time a somewhat more familiar tune:

C  Am  Dm  G/b  Dm/f  Am  G/b  C 
Bm/d  F♯m  E/g♯  A
Use of an repeated melody to connect a new key A to the old one C If the audio button is screwed up, try the MIDI
The chords without the violin part:  If the audio button is screwed up, try the MIDI

Parallel minor and modal shifts

A modal shift is a movement to a parallel mode. For example, you are playing along in A major and you, for a short or longer ter,m shift to A Dorian, or A Lydian, A Aeolian, or whatever. This would be called the parallel Dorian/Lydian/Aeolian mode. The most common would be A Aeolean (usually called the parallel minor). We saw this in Creep earlier and I blessed you with one of my extremely exciting (cough) examples (which I will put here as well).

12 I hope you can make sense of my repeat signs, imported from score notation.
 G  Gm  C  Cm  F♯/a  D 12  G
Mode change within a melody (major-minor) If the audio button is screwed up, try the MIDI
The chords without the sax part:  If the audio button is screwed up, try the MIDI

Both the Gm and the Cm are highlighted here because it shifts first from major (G) to minor (Gm), back to major (C), then to minor again (Cm), and finally to major (at the F♯).

Elton John shifts from a major key to the parallel minor during both refrain and bridge in "I'm Still Standing."

Parallel modes differ from relative modes. Relative modes do not involve a change in key signature, only a shift in emphasis. Parallel modes always involve a key signature change.13 If you are in G, which has one sharp, the relative minor (Em) is still one sharp, but the parallel minor (Gm) has two flats. If you are confused, listen and compare the above example to the same basic melody using the relative minor shift above under 'Visiting the relatives,' above. I hardly even notice (it is so common) when I hear mixing and matching the Mixolydian with the Ionian (regular major) or Aeolian (natural minor) in modern pop (as in "Then Came You," by Dionne Warwick and The Spinners). Other modal shifts are a bit more surprising. The following familiar sounding example goes back and forth between Ionian and Mixolydian, but doesn't ever really modulate.

D♭  A♭7  B♭m  C♭  B♭m  Fm  C♭  D♭
Mixing modes: Ionian (major) & Mixolydian If the audio button is screwed up, try the MIDI
The chords without the sax part:  If the audio button is screwed up, try the MIDI

This one starts off the same as all the rest of the similar sounding examples, but then jumps to a C♭ (♭7). The A♭7, earlier, has a regular C♮, as does the Fm, so the piece is going back and forth between the two modes willy-nilly. The B♭m→Fm could be viewed as temporary shift into the relative minor, but it is really too short for that.

Abrupt remote shifts

The aphorism, "rules are there be broken," may not work so well when you are driving, but in art and music it is often the driving force behind creative change. So it is not so surprising when you see it. Sometimes songwriters and composers just go where they want without any sort of preparation. One of the best-known songs that does this unapologetically is Derek & The Dominos' "Layla." The verse is in E?, but the refrain is a step lower in D?. Actually, these two keys are only two apart on the circle of fifths, which isn't usually a huge jump. What makes it surprising is the direction. Most jumps like this go up for the refrain rather than down. Furthermore, it is completely abrupt. Maybe that is why some charts put the refrain in C? (the enharmonic equivalent), emphasizing its apparent remoteness. "The Youth," by MGMT makes the exact same move, but without any abrupt feeling. Unexpectedly, this makes it less successful.

The Flaming Lips make a sudden remote jump, and then back, a few measures later, in "Do you realize??" (around 2.25). Elliott Smith makes the same jump (1 steps), although less briefly, in the refrains of "Miss Misery." All of these are abrupt—no preparation in terms of secondaries, modes, pivots, or anything else. I am going to refrain from boring you with an example of this. Technically, 90% of the "truck-driver gear changes" I mentioned earlier fall into this category.

Final thoughts on modulation

Generally speaking, skilful modulations manage to pull it off without the listener's awareness. There exceptions, like "Layla," but this may be one of those cases where that other aphorism, "the exception proves the rule" comes into play. Most listeners to popular music are musically conservative. They don't seem to mind hearing the same progression over and over, in song after song. So if you are going to play with modulation, you have to do it carefully. The less your mass audience knows what is going on, the better. Your handful of more sophisticated listeners will not be fooled, and they, generally, will appreciate it.

Next up…

Stay tuned for Special chords and chromaticism.

© 2015 Alan Humm