Modulation, in the wild

"Modulation" sounds like a special event — a double bar, a new key signature, a fanfare. Most of the time it's quieter than that: a run of bars whose harmony correlates far better with some other key than with home. We slid a window across every piece in our library corpus and matched it against all twenty-four keys — 82 spans across 45 real pieces came back a strong match for somewhere other than home, each with the bar range, the destination key, and how confident the match is.

Practice with the pieces that use it →

The census

How often each piece in the corpus leaves its home key, ranked by how much it wanders:

piece	home key	modulation spans
Prelude 8 in D-sharp minor (BWV 877)	D-sharp minor	6
Sonata in C, K. 545	C major	5
Arabesque No. 1	A major	4
Clair de Lune	D-flat major	4
Sonata No. 11, K. 331 — Alla Turca	A major	4
Prelude 3 in C-sharp major (BWV 848)	C-sharp major	4
Prelude 13 in F-sharp major (BWV 882)	F-sharp major	4
Prelude 4 in C-sharp minor (BWV 873)	C-sharp minor	3
Prelude 24 in B minor (BWV 893)	B minor	3
Nocturne in C-sharp minor (Op. posth.)	C-sharp minor	2
Für Elise	A minor	2
Waltz in A minor, B. 150	A minor	2
Prelude 7 in E-flat major (BWV 852)	E-flat major	2
Prelude 5 in D major (BWV 874)	D major	2
Prelude 6 in D minor (BWV 875)	D minor	2
Prelude 12 in F minor (BWV 881)	F minor	2
Prelude 15 in G major (BWV 884)	G major	2
Prelude 18 in G-sharp minor (BWV 887)	G-sharp minor	2
Invention No. 1 in C, BWV 772	C major	1
Lullaby (Wiegenlied)	D-flat major	1
Arabesque, Op. 100 No. 2	A minor	1
Arabesque No. 2	G major	1
Clair de Lune (Easy Arrangement)	A minor	1
The Entertainer	C major	1
Minuet in C (Notebook for Wolfgang)	C major	1
Liebestraum No. 3	A-flat major	1
The Wild Horseman (Album for the Young, Op. 68 No. 8)	A minor	1
Prelude 6 in D minor (BWV 851)	D minor	1
Prelude 8 in E-flat minor (BWV 853)	E-flat minor	1
Prelude 9 in E major (BWV 854)	E major	1
Prelude 10 in E minor (BWV 855)	E minor	1
Prelude 11 in F major (BWV 856)	F major	1
Prelude 13 in F-sharp major (BWV 858)	F-sharp major	1
Prelude 14 in F-sharp minor (BWV 859)	F-sharp minor	1
Prelude 15 in G major (BWV 860)	G major	1
Prelude 16 in G minor (BWV 861)	G minor	1
Prelude 17 in A-flat major (BWV 862)	A-flat major	1
Prelude 19 in A major (BWV 864)	A major	1
Prelude 20 in A minor (BWV 865)	A minor	1
Prelude 23 in B major (BWV 868)	B major	1
Prelude 2 in C minor (BWV 871)	C minor	1
Prelude 7 in E-flat major (BWV 876)	E-flat major	1
Prelude 14 in F-sharp minor (BWV 883)	F-sharp minor	1
Prelude 20 in A minor (BWV 889)	A minor	1
Prelude 23 in B major (BWV 892)	B major	1

Prelude 8 in D-sharp minor (BWV 877) moves the most — 6 distinct spans away from D-sharp minor. Most of the rest wander less: a handful of bars into the dominant or the relative minor before finding their way home again.

Hear the key changes

Each link opens the piece in the harmony player. Bar ranges below show where the window matched, the key it matched, and the correlation coefficient (closer to 1.0 is a stronger match).

Prelude 8 in D-sharp minor (BWV 877) J. S. Bach home: D-sharp minor bars 0–4: e-flat minor (r=0.86) · bars 6–11: F# major (r=0.91) · bars 12–16: b-flat minor (r=0.92) · bars 17–21: e-flat minor (r=0.96) · bars 22–25: g# minor (r=0.94) · bars 26–36: e-flat minor (r=0.93)
Sonata in C, K. 545 W. A. Mozart home: C major bars 11–19: G major (r=0.97) · bars 20–24: a minor (r=0.94) · bars 25–28: G major (r=0.86) · bars 33–38: d minor (r=0.93) · bars 39–50: F major (r=0.97)
Arabesque No. 1 C. Debussy home: A major bars 8–23: c# minor (r=0.94) · bars 65–69: C major (r=0.92) · bars 89–95: f# minor (r=0.94) · bars 96–103: E major (r=0.99)
Clair de Lune C. Debussy home: D-flat major bars 1–8: C# major (r=0.93) · bars 25–36: C# major (r=0.97) · bars 40–43: c# minor (r=0.87) · bars 56–69: C# major (r=0.96)
Sonata No. 11, K. 331 — Alla Turca W. A. Mozart home: A major bars 13–21: a minor (r=0.88) · bars 31–37: f# minor (r=0.87) · bars 49–60: f# minor (r=0.93) · bars 77–86: a minor (r=0.88)
Prelude 3 in C-sharp major (BWV 848) J. S. Bach home: C-sharp major bars 14–17: A-flat major (r=0.85) · bars 22–25: e-flat minor (r=0.88) · bars 30–33: b-flat minor (r=0.91) · bars 44–55: F# major (r=0.91)
Prelude 13 in F-sharp major (BWV 882) J. S. Bach home: F-sharp major bars 8–19: C# major (r=0.92) · bars 31–43: e-flat minor (r=0.93) · bars 44–51: g# minor (r=0.86) · bars 52–55: C# major (r=0.9)
Prelude 4 in C-sharp minor (BWV 873) J. S. Bach home: C-sharp minor bars 11–19: g# minor (r=0.95) · bars 20–30: E major (r=0.95) · bars 31–37: f# minor (r=0.91)
Prelude 24 in B minor (BWV 893) J. S. Bach home: B minor bars 14–24: D major (r=0.97) · bars 25–35: e minor (r=0.96) · bars 40–46: f# minor (r=0.93)
Nocturne in C-sharp minor (Op. posth.) F. Chopin home: C-sharp minor bars 19–26: A major (r=0.94) · bars 32–45: A-flat major (r=0.91)
Für Elise L. v. Beethoven home: A minor bars 25–29: F major (r=0.91) · bars 30–37: C major (r=0.95)
Waltz in A minor, B. 150 F. Chopin home: A minor bars 5–15: C major (r=0.92) · bars 33–40: A major (r=0.93)
Prelude 7 in E-flat major (BWV 852) J. S. Bach home: E-flat major bars 49–53: c minor (r=0.89) · bars 54–58: f minor (r=0.94)
Prelude 5 in D major (BWV 874) J. S. Bach home: D major bars 8–24: A major (r=0.93) · bars 25–35: b minor (r=0.93)
Prelude 6 in D minor (BWV 875) J. S. Bach home: D minor bars 27–36: a minor (r=0.87) · bars 54–57: g minor (r=0.85)
Prelude 12 in F minor (BWV 881) J. S. Bach home: F minor bars 13–28: A-flat major (r=0.95) · bars 36–43: b-flat minor (r=0.96)
Prelude 15 in G major (BWV 884) J. S. Bach home: G major bars 10–19: D major (r=0.93) · bars 33–38: e minor (r=0.94)
Prelude 18 in G-sharp minor (BWV 887) J. S. Bach home: G-sharp minor bars 14–21: e-flat minor (r=0.92) · bars 38–41: c# minor (r=0.9)
Invention No. 1 in C, BWV 772 J. S. Bach home: C major bars 1–10: G major (r=0.93)
Lullaby (Wiegenlied) J. Brahms home: D-flat major bars 1–10: C# major (r=0.87)
Arabesque, Op. 100 No. 2 F. Burgmüller home: A minor bars 8–12: C major (r=0.9)
Arabesque No. 2 C. Debussy home: G major bars 39–46: C major (r=0.85)
Clair de Lune (Easy Arrangement) C. Debussy home: A minor bars 32–39: F major (r=0.88)
The Entertainer S. Joplin home: C major bars 69–75: F major (r=0.93)
Minuet in C (Notebook for Wolfgang) L. Mozart home: C major bars 11–16: G major (r=0.96)
Liebestraum No. 3 F. Liszt home: A-flat major bars 54–59: f minor (r=0.92)
The Wild Horseman (Album for the Young, Op. 68 No. 8) R. Schumann home: A minor bars 10–16: F major (r=0.87)
Prelude 6 in D minor (BWV 851) J. S. Bach home: D minor bars 1–6: g minor (r=0.87)
Prelude 8 in E-flat minor (BWV 853) J. S. Bach home: E-flat minor bars 11–19: b-flat minor (r=0.91)
Prelude 9 in E major (BWV 854) J. S. Bach home: E major bars 11–16: f# minor (r=0.86)
Prelude 10 in E minor (BWV 855) J. S. Bach home: E minor bars 12–30: a minor (r=0.96)
Prelude 11 in F major (BWV 856) J. S. Bach home: F major bars 1–5: d minor (r=0.87)
Prelude 13 in F-sharp major (BWV 858) J. S. Bach home: F-sharp major bars 9–16: e-flat minor (r=0.97)
Prelude 14 in F-sharp minor (BWV 859) J. S. Bach home: F-sharp minor bars 10–13: c# minor (r=0.93)
Prelude 15 in G major (BWV 860) J. S. Bach home: G major bars 8–15: D major (r=0.93)
Prelude 16 in G minor (BWV 861) J. S. Bach home: G minor bars 9–15: c minor (r=0.88)
Prelude 17 in A-flat major (BWV 862) J. S. Bach home: A-flat major bars 10–24: E-flat major (r=0.95)
Prelude 19 in A major (BWV 864) J. S. Bach home: A major bars 10–18: f# minor (r=0.96)
Prelude 20 in A minor (BWV 865) J. S. Bach home: A minor bars 10–16: C major (r=0.95)
Prelude 23 in B major (BWV 868) J. S. Bach home: B major bars 1–12: g# minor (r=0.93)
Prelude 2 in C minor (BWV 871) J. S. Bach home: C minor bars 6–12: E-flat major (r=0.89)
Prelude 7 in E-flat major (BWV 876) J. S. Bach home: E-flat major bars 13–17: B-flat major (r=0.86)
Prelude 14 in F-sharp minor (BWV 883) J. S. Bach home: F-sharp minor bars 15–24: A major (r=0.94)
Prelude 20 in A minor (BWV 889) J. S. Bach home: A minor bars 8–12: G major (r=0.92)
Prelude 23 in B major (BWV 892) J. S. Bach home: B major bars 11–14: g# minor (r=0.92)

Go deeper

Train your ear to catch it → Our ear-training site drills the moment a passage stops sounding like home — before you can name the destination key, you can hear that you've left.
The theory: chromatic modulation → Pivot chords, common-tone modulation, and how composers get from one key to another — the full chapter on our theory site.
A favorite modulation lever → An augmented sixth chord is enharmonically a dominant seventh in disguise — one of the cleanest pivots for slipping into a new key, surveyed on its own terms.
Learn a piece that uses them → The practice ladder loops eight bars at a time — hear the harmony slowly, read along, then play at tempo.