Learning to follow key changes is not easy for many students, especially when they are asked to locate modulations themselves and distinguish between different methods of modulation. Here is a step-by-step guide that uses a charming example of Romantic music: Edward Elgar’s Moths and Butterflies from The Wand of Youth Second Suite. More practice is also available on this site in “Modulation Practice: Beethoven’s Violin Concerto.”
Step One: Get to know the music
Begin by hearing a recording [here’s one on YouTube] while reading the sheet music [it’s on imslp.org — Moths and Butterflies is the third movement]. Please note that this piano reduction has two mistakes! The right hand chord on beat 1 of bar 3 should have a D♯, not a C♯. In that same bar, the left hand should return to bass clef; its two notes are both E, and the bass clef continues until treble is restored in bar 5 as shown.
Step Two: Divide the music into phrases
Dividing music into phrases helps to show when modulations occur, and if they do, what is the method of modulation being used. To find the music’s phrases, locate its cadence points. Mark up the music, and if it’s not too difficult to do by ear, identify cadence types. Here’s my breakdown of this piece:
- Section 1 (A)
- Phrase 1: bars 1-4
- Phrase 2: bars 5-8
- Phrase 3: bars 9-17
- Phrase 4: bars 18-21
- Section 2 (B)
- Phrase 5: bars 22-29
- Phrase 6: bars 30-37
- Section 3 (A)
- Skip it. This is identical to bars 1-21 except for the very end, which doesn’t modulate… we can safely leave it out of this analysis.
Step Three: Identify harmonies and keys
Following modulations doesn’t require the labeling of every single chord. Instead, listen to each phrase individually, tuning in to the audible shifts that come with the introduction of accidentals. When you find one, examine the music to see if the accidental is persistent (indicating a change of key or mode) or fleeting (related to a chromatic chord like a secondary dominant, or a chromatic melody tone).
Identify the starting key of the music, paying close attention to how it starts and how it cadences. Working from phrase-to-phrase makes far more sense than working chord-to-chord for several reasons:
- If a phrase begins and ends without modulating, you can ignore it (as far as modulation is concerned).
- If one phrase cadences in a key and the next begins in another, you can confidently identify it as a direct modulation.
- If one phrase begins in a a key and cadences in a different one, you can fairly confidently identify it as a pivot modulation. Be careful to notice the difference between a cadence in a new key and a non-tonic cadence (like a half cadence). Also be careful when a phrase begins with a non-tonic chord; this can be confusing.
Your turn: Study Moths and Butterflies
Take some time now to examine the music, identifying each key area and labeling each modulation on the sheet music. Here’s a note to you millennials: YOU HAVE TO DO THIS ON PAPER! Print out the sheet music and mark it up as you go along. Bring your computer to a piano and go back and forth between listening to a recording and playing chords and melodies (especially bass lines) on the piano.
My turn: Compare your work with mine
Here’s the phrase-by-phrase breakdown of Moths and Butterflies:
- Phrase 1 is entirely in A Minor. Note how it begins with an A Minor arpeggio and ends with a A Minor chord. There are some accidentals in the phrase, but nothing is substantial enough to change the key: the sharped notes in bar 2 are all chromatic neighbor tones, and the chord that begins bar 3 is a secondary chord: vii°7/V.
- Phrase 2 is very much like phrase 1, but it ends with an emphasis on the E Major chord, which is strongly tonicized in bars 7 and 8 with the D♯dim7 (vii°7 of E) and B7 (V7 of E) chords. Do these indicate a modulation to E Major? It’s possible, but it’s equally valid to consider this a half cadence in A Minor.
- Phrase 3 begins with an abrupt shift to a new key. The harmonies implied in bars 9-10 are (one chord per beat) Dm7 – G7 – C – F, with a fleeting chromaticism on the second eighth of bar 9. The pattern repeats in Bars 11-12. This is certainly not in A Minor! I realize that, for many students, it is not enough to be told “it sounds like it is in a key.” One could be confused by several complicating factors: that the new phrase starts with a non-tonic chord (Dm7), and further complicating matters, it ends with a non-tonic, non-dominant chord, too (F). The G7 chord, however, is powerful and it makes the whole phrase sound like it is in C Major.
- Since the previous phrase ends in one key (A Minor or E Major, whichever interpretation you prefer) and this phrase begins in a new key, the modulation is direct. You can label this phrase in the new key; there is no pivot chord. These bars are in C Major: ii7 – V7 – I – IV (then repeated). The tonic chord may technically be CMaj7(#5), but the sonic effect is that of a C Major chord with a chromatic embellishment, the G# leading up to A.
- Phrase 3 continues with a B♭/D harmony in bars 13-15, oscillating against a harmony that is difficult to label because of a pair of melodic non-chord tones; I would call this chord F7/E♭. The “main” harmony, nevertheless, is B♭, and when it changes to E7 on beat 2 of bar 15, it signals a return to A Minor. Since this modulation occurs during the progress of a phrase, it is a pivot modulation. The most common modulating pivot is a common chord — the last chord that works well (diatonically, usually) in both the old and new keys. So what is the common chord here? Work backwards from the end to find it. The E7 chord does not belong in C Major (it is V7 in A Minor)… now go back one. The B♭ chord does not belong in C Major (it is the Neapolitan in A Minor)… now go back one more. The F chord DOES work in C Major, and it has the added advantage of working as dominant of the B♭ “Neapolitan.” This will do! Use the standard “bracket notation” to label how the pivot chord works in both keys, continuing one extra chord to show the function of B♭/D.
- Phrase 4 is a repetition of phrase 1, and is entirely in A Minor.
- Phrase 5 begins with a sudden, unambiguous shift to C Major, and features a “descending tetrachord” progression I – V6 – IV6 – V before, at bar 24, it begins a strange and meandering modulation: a modulation by sequence.
TIME OUT: What’s a modulation by sequence? A sequence is a melodic figure that is repeatedly transposed up or down a step coupled with a pair of chords that are likewise repeatedly transposed up or down (usually) a step. As it moves, the melody can either stay within a key (this is a “tonal sequence”) or rigidly maintain its internal intervals (this is a “real sequence”); this provides an opportunity for modulation. A modulation by sequence can often be labeled as a pivot or direct modulation, but sometimes (rarely) the modulation can’t be explained any other way than as the by-product of the sequential motion. Fortunately, Moths and Butterflies contains both approaches for us to examine.
- Back to phrase 5. Notice how the modulating sequence transposes each bar down by step (follow the high notes as they descend D – C – B♭) as the chord roots ascend by fourths each half-bar: D7 – G7 – C – F7 – B♭and on to Em7(♭5). Notice that all of these motions are up by perfect fourth except for the last one, which is an augmented fourth; that’s because at this point the music has settled into its key of D Minor, and another perfect fourth chord root ascent would have resulted in an E♭chord – that would note have settled the music into the desired key.
- Another modulation in phrase 5 occurs at the very end. This is what jazz players would call a turnaround (Elgar would definitely not have used this term!): a change of chord that comes after the point of cadence (here at bar 29). At bar 30, Elgar makes a modulation by change of chord quality, changing the Dm tonic to a D7 chord, which functions as dominant of G, which begins the next phrase.
- Phrase 6 has the other kind of modulation by sequence — the kind that isn’t a variety of pivot or direct modulation. The music begins as a repetition of phrase 5, transposed up a fifth to begin in G Major. The phrase modulates differently, though; whereas phrase 5 modulated up to the minor supertonic (from C Major to D Minor), this one modulates to the parallel minor (G Major to G Minor). The chord progression begins the same in both phrases, but diverges in the fourth bar: whereas the bass in phrase 5 (this is bars 25-26) moves from scale degrees 1 to 6 up to ♭7, the bass in phrase 6 (this is bars 33-34) moves from scale degrees 1 to 6 down to ♭6 before resuming the pattern more or less as before. This returns the music to a tonal center of G, though now G Minor. After the cadence, the same shift of chord quality occurs, changing the Gm tonic chord to a G7 dominant, looping the music around to C Major for the repeat of the section.
- How did the sequence in phrase 5 have a pivot chord but not the one in phrase 6? The pivot in phrase 5 was shown above. This sequence, rather than forming a “proper” modulation, mimics the sequence from before but substitutes a chromatic shift in bar 33 for the pivot chord. This chord (marked with a ?) is a half-diminished seventh chord on scale degree 6; it is diatonic in neither G Major nor G Minor. Instead, it forms a sort of chromatic incomplete neighbor-tone in the bass, anticipating two notes of the next chord (E♭) before moving the bass down into it.
- The second ending of phrase 6 also has a modulation, one that leads back to A Minor. It’s another turnaround (again… Elgar wouldn’t have used that term). The G Minor chord that ends phrase 6 is used as a pivot chord to the new key — i in G minor is VII in A Minor. The modulation is made particularly smooth by the stepwise descent in the bass from Gm to Gm7/F to Am/E, starting the new phrase distinctively with a second inversion harmony. It is also possible to consider this a direct modulation rather than a pivot modulation since the Gm chord isn’t quite a chord in the key of A Minor — it’s the chord that results from the natural minor scale. I would consider both to be valid choices.
