Review

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”

“Signs of difference” means the number of changing accidentals between two key signatures. For example, the keys of C major (no accidentals)screen-shot-2016-10-08-at-9-45-10-pm

and D major (2 sharps)

screen-shot-2016-10-08-at-9-45-23-pm

would be said to have 2 signs of difference. The keys of Gb major (6 flats)

screen-shot-2016-10-08-at-9-45-32-pm

and A major (3 sharps)

screen-shot-2016-10-08-at-9-45-40-pm

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.

Example:

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.

Example:

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

Each minor key has 8 minor keys plus 4 major keys that are said to be in second-degree relation. The minor keys are situated exactly the same way that it is for major: 4 keys above the given minor, 4 below, ascending/descending by half-step. 4 major keys can be found the following way: 2 major keys situated above the given minor, ascending by half-step in the range of a M2. 2 more major keys can found on the major subdominant (IV), and parallel major.

 

Example:

Keys in 2nd degree relation to:

     A minor – (8 minor) Bb minor, B minor, C minor, C# minor, G# minor, G minor, F# minor, F minor
                    (4 major) Bb major, B major, D major (IV), A major (parallel major)
     D minor – (8 minor) Eb minor, E minor, F minor, F# minor, C# minor, C minor, B minor, Bb minor
                     (4 major) Eb major, E major, G major (IV), D major (parallel major)

 

The process of modulating to second degree keys is dependent on 2 factors: modality of initial key (coming for a major or minor key), and whether we are going to a key that has more sharps (or less flats), or to a key with more flats (or less sharps).

 

Imagine keys in the circle of 5th’s laid out on a linear plane, where C major is “0”:
screen-shot-2016-10-08-at-9-45-49-pm
Going to the left on the scale would be considered going “to flats”, and right on the scale “to sharps”.

 

With these two factors(modality and key signature), we get 4 possible scenarios (with an additional 5th special case scenario):
1. Modulating from major keys, to flats (a key with more flats/less sharps)
2. Modulating from major keys, to sharps (a key with more sharps/less flats)
3. Modulating from minor keys, to flats (a key with more flats/less sharps)
4. Modulating from minor keys, to sharps (a key with more sharps/less flats)
5. Modulating to a key with only 2 signs of difference. *

 

* All 2nd degree modulations assume that the given keys contain more than 2 signs of difference. There is a special method reserved (#5) for keys that only have 2 signs of difference between them. *

 

In order to modulate to a second degree key, we need to use an intermediate key between the initial and target to make the modulation more convincing. The intermediate key used is different depending on each of the 5 scenarios described above.

Case-By-Case Examples

1. Modulating from major, to flats (a key with more flats/less sharps), 3 or more S.O.D:

 

To modulate “from major to flats”, use an intermediate key of iv minor from the initial key:

F# to A

 

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

Measure 1

Beat 1-3: Establish “home key” (tonic ➞ dominant ➞ tonic)

Beat 4: Inverted secondary dominant/diminished chord (triad or 7th) of intermediate key

 

Measure 2

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.

 

Measure 3

Beat 1-2: Cadential I(i) 6/4

Beat 3-4: Root position V7 of destination key

 

Measure 4

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):

Ab to G

 

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:

F#minor to D minor

 

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):

Eb minor to C minor

 

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:

Bb minor to C

 

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):

 

F to Eb

 

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

nate_headshot_thumbnail

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.
Website: www.interactiveaudiosolutions.com 

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