Introduction to Modulation
Most popular classical harmony books that I’ve read barely scratch the surface when discussing modulation, which can make it seem like a “dark art” even to experienced composers. This 3-part article series will attempt to demystify the subject by breaking down a dogmatic method of modulation developed many years ago at the Moscow Conservatory. This article assumes that you have at least an intermediate understanding of classical harmony. Let’s jump right in to it!
All key centers in Western tonal music can be said to relate to one another in one of three ways, which are referred to as “degree’s of kinship” (1st degree of kinship, 2nd degree of kinship, and 3rd degree of kinship). In this first article we will discuss what constitutes a key relationship as on the “1st degree of kinship”, and it’s corresponding modulation procedure. Parts two and three will discuss modulations to “distant keys” (key’s that do not share many common tones), referred to as 2nd or 3rd degree modulations.
What constitutes a “first degree” key relationship?
Keys that relate on the first degree of kinship are all diatonically related keys. “Diatonic keys” are derived from the diatonic triads of any given key (omitting diminished triads due to the unstable 5th). Keys derived from diatonic triads will share many common tones with the “home key” (key we are modulating from), which will make our modulation sound smooth and convincing. More common tones between two keys means the listener will be less likely to notice an abrupt change in the music.
In addition to diatonically related keys, the keys derived from iv minor* (in any given major key) and V major** (in any given minor key) are also said to be in first degree relation to their respective “home keys”. These two keys are included as non-diatonic exceptions due to their extremely common use; even though they technically contain non-diatonic notes, they don’t sound too foreign to “western ears”.
Keys that are in First Degree of Kinship to C major:
D minor (ii), E minor (iii), F major (IV) and F minor (iv minor)*, G major (V), and A minor (vi)
(diminished chords omitted due to unstable 5th)
Modulating from C major to D minor, E minor, F major, F minor, G major, or A minor would be considered a first degree modulation.
Keys that are in First Degree of Kinship to G minor:
Bb major (III), C minor (iv), D minor (v) and D major (V)**, Eb major (bVI), F major (bVII)
All of these keys are derived from the diatonic triads of G minor (D major [V major] being an exception)
The Pivot Chord
Our goal in any modulation is to make it truly convincing by suspending the listeners sense of tonic (key center) without sounding too far away from our “home key” at any given time. For first degree modulations, use a pivot chord diatonic to our “home key” (original key we are modulating from) and our “destination key” (key we are modulating to). Even though this pivot chord is diatonic to both keys, it will serve different functions in each key.
This pivot chord should ideally belong to the subdominant group chords of the destination key.
Subdominant Group Chords
ii(ii) strongest; IV(iv) strong; vi(VI) weak (minor key numerals in parentheses)
Ex. C major subdominant group chords: D minor (ii), F major and F minor (IV and iv), A minor (vi)
Ex. G minor subdominant group chords: A diminished (ii), C minor (iv), Eb major (VI)
While there are many chords belonging to each “functional group”, some chords in each group are “stronger” than the others. Ideally, you should choose the strongest chord from the given functional group that you are working with. While we’re at it, lets define the other types of “functional group” chords:
Dominant Group Chords
V and vii diminished equally strong (often combined into V7), iii(III) weak
Ex. C major dominant group chords: G major/ G7 (V or V7), B diminished (vii)
Tonic Group Chords
I(i) strongest, vi(VI) and iii(III) are equally weak (both functionally ambiguous)
Ex. C major tonic group chords: C major (I), A minor (vi), E minor (iii)
The best way to introduce our pivot chord is through the use of a secondary dominant, a non-diatonic dominant 7th chord a perfect 5th above any given diatonic chord root.
In the key of C major, A7 would be considered a “V7 of ii” (notated V7/ii) secondary dominant chord if it resolves to a D minor [ii] chord.
D minor is the ii chord in C major, and the root of A7 is a perfect 5th above the root of D minor.
A7 is a secondary dominant in the key of C, and should resolve to a D minor chord.
Following this same logic, in the key of C major, B7 would be considered “V7/iii” (resolving down a P5 to E minor [iii])
C7 would be “V7/IV” (resolving down a P5 to F major or F minor [our non-diatonic iv exception]) etc…
Through resolving this secondary dominant chord, we get a temporary suspension of tonic to a pivot chord that has functional meaning in both our home and destination keys, and we use this suspension to assign a different functional meaning to our pivot chord and eventually come to a full cadence in the destination key.
Major Key Modulation Examples:
*All examples will be given in terms of a 4 bar modulating consequent (the “back half” of an 8 bar phrase). Assume some 4 bar antecedent in the home key before each given example for an 8 bar antecedent-consequent phrase*
We will start with modulating from major keys:
Our pivot chord in this example is Am (measure 2 beat 1), which is vi in C major and ii in G major (our destination key). This is an excellent pivot chord because it is the strongest of the subdominant group chords in our destination key (ii in G), and it serves the alternate tonic function of “vi” in our home key of C major.
The secondary dominant used to “tonicize” (give the impression of a temporary tonic chord) our pivot chord happens on the 4th beat of measure one: a 2nd inversion E dominant 7th chord (5th in the bass, analyzed V 43/ii in G). This E7 is our first kind of momentum towards our destination key as it temporarily suspends the feeling of C major as the key center after resolving to an A minor chord. We use this resolution to treat the Am chord as ii in G major (instead of vi in C major), and we reinforce this in beats 1-3 of measure 2 by tonicizing it again with an inverted secondary dominant.
It’s important to only use inverted secondary dominants to tonicize pivot chords, as a root position secondary dominant might give the impression of a full tonal shift toward your pivot chord once resolved.
As the pivot chord is reinforced by another inverted secondary dominant in measure 2, the listener starts to lose the sense of tonal center while still feeling like they are in familiar harmonic territory. This sets up our “Double Dominant chord” on beat 4 (A “DD chord” is another word for Italian, French, or German augmented chord). DD chords work beautifully as a climactic dissonance right before a cadential I(i)6/4 passage in a new key.
What makes this DD chord so powerful is the half step motion from both above and below the 5th scale degree of our destination key:
C# ➞ D (in the bass voice), Eb ➞ D (in the alto voice)
There is also chromatic half-step motion in the soprano voice (A# ➞ B). B is the 3rd in a G major triad, which is the primary tonic of our destination key (G major). This half-step motion toward the 5th and 3rd of our new primary tonic chord leads the listener toward the new tonal center, G major.
We suspend the listeners sense of tonic by tonicizing pivot chords, then re-establish it with chromatic motion towards a I 6/4 ➞ V7 ➞ I cadence in our new key.
Here’s a modulation from a major key to minor again using a subdominant group chord from our destination key as a pivot (C#m, iv in G# minor):
This time we use a secondary diminished chord on beat 4 of measure 1 instead of a secondary dominant to tonicize our pivot chord. A secondary diminished chord is essentially the same concept as a secondary dominant; it is an inverted diminished chord a half-step below any given chord root, and serves a dominant function resolving 1 half-step upward.
Before I continue with more examples, let’s break this down with a “beat by beat” explanation for first degree modulations:
Beat 1-3: Establish “home key” (tonic ➞ dominant ➞ tonic motion)
Beat 4: Inverted secondary dominant/diminished chord (triad or 7th) of pivot chord
Beat 1: Resolve previous chord into tonic triad or first inversion chord of pivot chord
Beat 2-3: Either inverted cadential motion on the pivot chord (pivot chord ➞ secondary dominant ➞ pivot chord), or tonicize another, stronger pivot chord (if you first tonicized IV, next tonicize ii, the strongest subdominant group chord).
Beat 4: French, German, or Italian augmented chord of the key to which you modulate (aka Double Dominant chord).
** Make sure you resolve previous augmented chord correctly!**
Beat 1-2: Second inversion I chord of destination key (known as “cadential I 6/4 chord”)
Beat 3-4: Root position V7 of destination key
I will refer to the harmonic sequence in this measure as cadential I(i)6/4 ➞ V7 ➞ I(i) from here forward.
Tonic of destination key!
Minor Key Modulation Examples:
Here we use A7 (V major in the destination key d minor) as the pivot chord, and utilize a deceptive cadence to VI in our destination key as a stepping stone to get to the DD chord (Beat 4, measure 2; Gr+6). A7 functions as a secondary dominant in our initial home key of A minor, and the deceptive cadence in beats 2-3 of measure 2 suspends the feeling of being in the key of A minor while also subtly hinting toward the key of d minor. This is solidified by the DD chord in the next beat along with the cadential I(i)6/4 ➞ V7 ➞ I(i).
Sometimes, you aren’t able to pivot on subdominant group chords. Here are some tips on how to proceed no matter what your pivot chord is:
If your pivot chord is ii in the destination key (modulating to major keys only), after it use all cadential chords. This pivot chord is desirable because it serves a strong subdominant function in the destination key, and pivoting on this chord before cadencing to the new key give a very natural subdominant ➞ dominant ➞ tonic motion. Using a second inversion minor 7th chord (ii4/3) before cadencing on the V chord allows for very smooth voice leading.
If your pivot chord is iii(III) in the destination key, after it use IV, then ii, then cadential I(i)6/4 ➞ V ➞ I (i). You may want to tonicize the IV and ii subdominant chords to add harmonic motion.
If your pivot chord is IV(iv) in the destination key, after it use a Double Dominant chord. Before taking DD, you could also tonicize the stronger subdominant group chord ii (IV ➞ V/ii➞ ii ➞ DD ➞ I(i)64 ➞ V ➞ I(i) ). You can use triads or 7th chords.
If your pivot chord is V in the destination key, after you it should use a deceptive cadence to vi(VI), and then either tonicize subdominant group chords, or after vi(VI) go straight to DD ➞ I(i)64 ➞ V ➞ I(i).
If your pivot chord is v in the destination key (minor keys only), after it use V major, then proceed as outlined above.
If your pivot chord is vi(VI), after it use subdominant group chords in order of strength: ii (strongest) IV (strong) vi(VI) (weak). You may want to tonicize these chords. After that, use DD ➞ I(i)64 ➞ V ➞ I(i)
If your pivot chord is natural VII in the destination key (minor keys only), after it use a ii 4/3 chord then i 64 ➞ V ➞ i . After ii 4/3, you can also omit the i 6/4 and just take V ➞ i. Using III after the pivot chord is also an option (you may want to tonicize it), then iv ➞ i 6/4 ➞ V ➞ i.
All of these examples are extremely short 4 bar phrases, but can and should be applied to longer passages when writing your own music. I rarely find myself using the I 6/4 cadence to complete phrases in my own writing, but you can apply the same ideas of subdominant ➞ dominant ➞ tonic motion within a modal context to achieve a less “classical sounding” modulation. The most important idea to take away from first-degree modulations is the concept of tonicizing pivot chords to assign them a different harmonic function in our target key. As soon as the listeners sense of tonic is suspended, we can then use dominant chords to guide their ear toward a new tonic.
Next post we will talk about modulating to keys in “2nd degree” relation. See you then!
(All credit due to Professor Alla Cohen, who passed this information on to me as her mentor did)
About the Author
Nathanial Beltz is a composer and multi-instrumentalist currently living in Boston, Massachusetts. He earned a B.M. in Scoring for Film and Video Games at Berklee College of Music, and is now the owner and audio director of Interactive Audio Solutions, a Boston based music production company. He also plays with various bands in the New England area, including his original project GAIT.