In the first article of this 3 part series “Modulation Tips for Composers”, we discussed modulating to closely related keys (keys derived from the initial key’s set of diatonic triads). This key relationship is referred to as being on the “first degree of kinship”.
In part 2 we will discuss modulating to keys that are not derived from diatonic triads of the initial key, but are still within 5 “signs of difference“:
“Signs of Difference”
and D major (2 sharps)
would be said to have 2 signs of difference. The keys of Gb major (6 flats)
and A major (3 sharps)
would be considered to have 9 signs of difference and would not be a 2nd degree key relationship.
Throughout this article, I will use the abbreviation S.O.D. to refer to “signs of difference”. Let’s further break down what constitutes a 2nd degree key relationship:
Second Degree of Kinship
Any given key has exactly 12 keys that are said the be in second-degree relation. The process of finding these 12 keys is dependent on whether you are modulating from a major key or minor key.
Major Key Modulations
Each major key has 8 major keys plus 4 minor keys in second-degree relation. The major keys can be found following this rule: 4 keys are situated above the given major ascending by half steps in the range of a major 3rd, and 4 more major keys below the given major, descending by half-step in the range of a major 3rd.
Major keys in 2nd Degree relation to C major : (4 ascending) Db major, D major, Eb major, E major ; (4 descending) B major, Bb major, A major, Ab major
*IMPORTANT* The order of ascending/descending half-steps MUST follow this sequence: diatonic, chromatic, diatonic, chromatic.
C to Db is considered a “diatonic half-step“, and C to C# a “chromatic half-step“.
C# would NOT be considered in second degree relation to C major, but Db is. This is because the keys of C and C# don’t share any common triads at all.
The 4 minor keys in 2nd degree relation are found the following ways:
2 keys below the given major, descending by half-step in the range of a M2 (C major: B minor, Bb minor).
2 more keys can be found: minor dominant (C major ➞ G minor [v minor]), and parallel minor (C major ➞ C minor).
All of these keys are derived as relative minor keys to the major keys we previously found.
Keys in 2nd degree relation to:
C major – (8 major) Db major, D major, Eb major, E major; B major, Bb major, A major, Ab major
(4 minor) B minor, Bb minor, G minor, C minor
A major – (8 major) Bb major, B major, C major, C# major, G# major, G major, F# major, F major
(4 minor) G# minor, G minor, E minor, A minor
Minor Key Modulations
Keys in 2nd degree relation to:
Here we tonicize B minor as in intermediate key to modulate between F# and A major. B minor is the iv minor chord in our initial key of F#, and happens to belong to the subdominant group chords of our destination key. When modulating from a major key to a 2nd degree key with more flats (or less sharps), always use an intermediate key of iv minor from the initial key.
Notice that we are still using the same general beat-by-beat skeleton as first degree modulations, but have replaced “pivot chords” with “intermediate keys“.
2nd Degree beat-by-beat
Beat 1-3: Establish “home key” (tonic ➞ dominant ➞ tonic)
Beat 4: Inverted secondary dominant/diminished chord (triad or 7th) of intermediate key
Beat 1-3: Tonic of intermediate key (tonic ➞ dominant ➞ tonic to establish intermediate key)
Beat 4: French, German, or Italian augmented chord of the key to which you modulate.
Beat 1-2: Cadential I(i) 6/4
Beat 3-4: Root position V7 of destination key
Tonic of destination key!
2. Modulating from major, to sharps (a key with more sharps/less flats), 3 or more S.O.D:
To modulate “from major to sharps”, use an intermediate key of iv minor of the destination key (the key which we are modulating to):
We utilize the common use of subdominant minor to bridge the two unrelated keys and create a “pseudo-common triad” between them (C minor is iii in the key of Ab major and iv in the key of G major). Now that we have a common triad, we can change its secondary tonic iii function in Ab, and assign it a subdominant function in G by using a German augmented chord directly after it, and then cadencing in our new key.
In practice, you will most likely spend more time in the intermediate key for 2nd degree modulations than you would tonicizing pivot chords in first degree modulations (even though these examples show them occupying the same amount of time). 2nd degree intermediate keys should feel more like a “temporary modulation” rather than a single pivot chord when you are applying these techniques.
3. Modulating from minor, to flats (a key with more flats/less sharps), 3 or more S.O.D:
To modulate “from minor to flats”, use an intermediate key of V major from the destination key (key we are modulating to). We must also use a deceptive cadence to vi(VI) in our destination key before the final cadence:
Here we utilize a deceptive cadence (key of D minor) in measure 2 beats 2-3. This allows for very smooth voice leading because of the 3 shared common tones between the Bb major (VI) and Gr+6 chord.
Also, notice the parallel fifths in beats 2-3 of measure 1. This is a diminished fifth moving in parallel motion to a perfect fifth in a passing situation, which is acceptable because you are not losing a harmonic voice (and more importantly, Mozart did it). Some refer to this as “Mozart’s Fifths”.
4. Modulating from minor, to sharps (a key with more sharps/less flats), 3 or more S.O.D:
To modulate “from minor to sharps”, use an intermediate key of V major of the initial key (key we are modulating from):
This is the first time we’ve seen a modulation that doesn’t use a Gr+6 chord as the harmonic climax. Our intermediate key happens to function as bVII in our destination key, which doesn’t lend itself well to a cadential situation with an augmented chord. If your intermediate key happens to function as bVII, use a ii half diminished 4/3 (aka 2nd inversion minor 7 flat 5) before the cadential i 6/4 for a smooth stepwise modulation.
Here’s another example that uses the augmented chord:
I prefer to spell my German augmented chords with scale degree #2 as opposed to b3. I think this more clearly shows the direction of resolution up to scale degree 3 in the tonic triad in the next chord, and it isn’t really functioning as a “minor third” in the chord anyway.
5. Modulating to a key with only 2 signs of difference:
To modulate to a 2nd degree key that has only 2 signs of difference (major or minor), use an intermediate key of the key that is only 1 sign of difference from both keys.
Ex. F major (1 flat) ➞ Eb major (3 flats) = 2 signs of difference. Use Bb major/G minor (2 flats) as an intermediate key):
Here is another example that doesn’t use an augmented chord. Because the intermediate key ended up being iii in our destination key (secondary tonic), after it we can simply use IV ➞ I 6/4 ➞ V7 ➞ I. This gives us a very natural tonic ➞ subdominant ➞ dominant ➞ tonic motion, which is the nucleus of the tonal system and is the definition of “being in a key”.
I’ll reiterate that these short 4 bar examples are for learning purposes only; I don’t think this is exactly how you should approach your own writing. However you can take concepts from this method and make them your own in order to achieve a balance of structure and personality, whatever your style of writing.
Next article (part 3) will talk about modulating to distant keys, and will see how we can apply these techniques to formulate large form tonal plans for a piece.
(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.