Introduction to Modulation Tips – Part 3

This is the third and final article of the three part series titled “Modulation Tips for Composers”. I highly recommend reading part 1 and part 2 before continuing with this article.

 

3rd Degree of Kinship

So far, we’ve discussed ways to modulate to diatonically related keys (1st degree of kinship) and keys that are within 5 “signs of difference” (2nd degree of kinship). 3rd degree relationships are essentially “everything else”; keys are considered to be of the third degree of kinship if they are:

 

1. On the distance of a tritone*, any diminished/augmented or double diminished/augmented interval

(ex.) C major ➞ F# minor/major (Augmented 4th or tritone) ; C major ➞ Gb major (Diminished 5th) ;
Eb major ➞ C# major/minor (Augmented 6th); G# minor ➞ Db major (Double Diminished 5th)

* Relative keys of those situated on the distance of a tritone are also said to be in 3rd degree relation with the following exceptions:

– The relative major of any minor key situated a tritone away from any major key
(ex.) C major ➞ A major (A major is the relative of F# minor, but is in 2nd degree relation to C)

– The relative minor of any major key situated a diminished 5th from any minor key
(ex.)  D minor ➞ F minor (F minor is the relative of Ab major, but is in 2nd degree relation to D)

 

2. On the distance of a chromatic half-step

(ex.) C major and Cb major ; A minor and A# minor

 

3. Enharmonic keys

(ex.) F# major and Gb major; G# minor and Ab minor

 

4. Any key relationship with 7 or more signs of difference

 

The process of modulating to 3rd degree keys is a gradual one. We will need at least 2 (sometimes more) intermediate keys in between our “initial” and “destination” keys in order to achieve a smooth and convincing modulation. The process changes depending on 2 factors: 

1. Modality of initial key (major or minor),

2. 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”:

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Going to the left on the scale would be considered going “to flats”, and right on the scale “to sharps”.

Similarly to 2nd degree modulations, this yields a total of 4 different combinations:

1. Modulating from major keys, to sharps (a key with more sharps/less flats)
2. Modulating from major keys, to flats (a key with more flats/less sharps)
3. Modulating from minor keys, to sharps (a key with more sharps/less flats)
4. Modulating from minor keys, to flats (a key with more flats/less sharps)

 

Each of these combinations has it’s own set of rules for gradual modulation…

 

*In the preceding articles, modulation procedures were accompanied with a short 4 measure example. 3rd degree modulations should be thought of as a large form tonal plan for an entire piece, so short examples are not heplful as they sound too abrupt. *

 

1. Modulating from major keys, to sharps (a key with more flats/less sharps) in 3rd Degree

 

1. Find the 3 minor keys that are in 1st Degree relation to your initial (or “home”) key
(ex.) C major ➞ F# major
– The minor keys that are in 1st Degree relation to C major are: D minor, E minor, A minor 

 

2. Find the major dominants of those first degree minor keys you just found
(ex.) D minor, E minor, A minor (from step 1)
Major Dominants: A major (V in D minor), B major (V in E minor), E major (V in A minor)

 

3. Choose a pair of keys from the keys you just found that moves you closest to your destination
(ex.) D minor ➞ A major ; E minor ➞ B major ; A minor ➞ E major

 

Your goal is to choose a key pair that gets you in 1st or 2nd degree relation to your home key

 

Out of these pairs, E minor ➞ B major is the best choice, as B major is in 1st Degree relation to F# major (diatonic IV in F#) our destination key. From here, we can proceed with the method for keys in 1st degree relation to complete the modulation

 

So, our tonal plan for modulating from C major ➞ F# major is: C major ➞ E minor  ➞ B major ➞ F# major

 

C major ➞ E minor is a 1st degree modulation
E minor ➞ B major is a 1st degree modulation
B major ➞ F# major is a 2nd degree modulation

 

As you can see, 3rd degree modulations are really just 1st and 2nd degree modulations combined to reach a distant key. Our keys get “more sharp” as we progress, (C major = 0 sharps ; E minor = 1 sharp ; B major = 5 sharps ; F# major = 7 sharps) which makes the modulation gradual and convincing.
 
You won’t always be able to reach a 1st or 2nd degree key using the 3 step method described above. If this happens, simply repeat the process until you have a key that is in 1st or 2nd degree relation:

 

(ex.) Cb major ➞ C# major

 

 – 3 minor keys in 1st degree relation to initial key (Cb) and their major dominant keys:

 

Db minor ➞ Ab major
Eb minor ➞ Bb major
Ab minor ➞ Eb major

 

Ab major, Bb major, and Eb major are all still in 3rd degree relation to C# major. However, Bb major is “closest” to our destination key (it has the fewest number of flats), so lets repeat the process using Bb major as our initial key:

 

3 minor 1st degree keys from Bb major and their major dominants :

 

C minor ➞ G major
D minor ➞ A major
G minor ➞ D major

 

A major is in 2nd degree relation to C# major, so we should choose the D minor ➞ A major pair and can use the method of 2nd degree modulations to proceed.

 

Therefore, our tonal plan for modulating from Cb major ➞ C# major is:

 

Cb major ➞ Eb minor ➞ Bb major ➞ D minor ➞ A major ➞ F# minor* ➞ C# major

 

*We received F# minor as an intermediate key by following the method for 2nd degree modulations (A ➞ C# major)

 

That’s a lot of keys!

2. Modulating from major keys, to flats (a key with more flats/less sharps) in 3rd degree

 

1. Find the key of iv minor from our initial key

 

(ex.) C# major ➞ Ab minor

 

iv minor in C#F# minor

 

2. If still in 3rd degree relation from your destination key, find the 3 major keys in 1st degree relation from the key you found from step 1 (F# minor) and their minor subdominants (iv):

 

A major ➞ D minor
D major ➞ G minor
E major ➞ A minor

 

3. Choose the pair that gets you closest to your destination key (ideally in 1st or 2nd degree relation)

 

G minor is in 2nd degree relation to Ab minor (our destination), so choose the D major ➞ G minor pairing.
(If none of the keys are in 1st or 2nd relation, repeat the process with the key that gets you closest to your destination)

 

Therefore, our tonal plan for modulating from C# major ➞ Ab minor is:

 

C# major ➞ F# minor ➞ D major ➞ G minor ➞ Eb major* ➞ Ab minor

 

*We received this key by following the process of 2nd degree modulations (G minor ➞ Ab minor)

 

3. Modulating from minor keys, to sharps (a key with more sharps/less flats) in 3rd degree

 

1. Find the major dominant of our initial key

 

(ex.) A minor ➞ D# minor

 

The major dominant of A minor E major

 

E major is in 2nd degree relation to D# minor, so we can proceed with the 2nd degree method:

 

A minor ➞ E major ➞ B major* ➞ D# minor

 

*We received the key of B major by following the method for 2nd degree modulations (E major ➞ D# minor). Remember that for keys with less than 3 “signs of difference” in 2nd degree, you should take an intermediate key that has only 1 sign of difference between the two: E major = 4 sharps, D# minor = 6 sharps ; take an intermediate key with 5 sharps: B major.

 

2. If they key from step 1 is still in 3rd degree relation to your destination key, find the 3 minor keys in 1st degree relation to the key you found in step 1, and their Major Dominants:

 

(ex.) Eb minor ➞ D# minor
C minor ➞ G
D minor ➞ A
G minor ➞ D

 

All of these keys are still in 3rd degree relation to D# minor. Pick the key pair that gets you closest to your destination (in this case it is D minor ➞ A)and repeat.

 

(1st degree minor keys from A):

 

B minor ➞ F#
C# minor ➞ G#
F# minor ➞ C#

 

C# is in 1st degree relation to our destination key of D# minor (diatonic VII), so we can proceed with the 1st degree method. Therefore, our tonal plan for Eb minor ➞ D# minor is:

 

Eb minor ➞ Bb major ➞ D minor ➞ A major ➞ F# minor ➞ C# major ➞ D# minor

 

and lastly…

 

4. Modulating from minor keys, to flats (a key with more flats/less sharps) in 3rd degree

 

1. Find the key of IV minor from our initial key

 

2. If the key you find is in 1st or 2nd degree relation, proceed as necessary

 

3. If the key you find is still in 3rd degree relation, find the 3 major keys in 1st degree relation to the key found in step 1 and their minor subdominants

 

(ex.) C# major ➞ Ab minor 

 

IV minor in C# = F# minor

 

F# minor is still in 3rd degree relation to Ab minor, so follow step 3:

 

A major ➞ D minor
D major ➞ G minor
E major ➞ A minor

 

G minor is in 2nd degree relation to Ab minor, so proceed with the 2nd degree method. This makes our tonal plan for C# major ➞ Ab minor:

 

C # major ➞ F# minor ➞ G minor ➞ Ab minor

 

Now that we have a dogmatic way to modulate to keys relating on the 1st, 2nd, and 3rd degree of kinship, we can follow the rules in order to modulate from any given key to any other key possible in the western tonal system. Pretty cool!

 

Keys relationships to C major:

 

1st Degree of Kinship: D minor, E minor, F major, F minor, G major, A minor

 

2nd Degree of Kinship: Db major, D major, Eb major, E major, B major, Bb major, A major, Ab major, B minor, Bb minor, G minor, C minor

 

3rd Degree of Kinship: C# major, F# major, Gb major, Cb major

 

I hope this series was able to demystify modulation and provide you with methods that you can apply to your own writing. These modulations sound very “classical” in nature, but as you work with them you will find that there are ways to alter each process to make it fit the harmonic language you are working with.

 

Lastly, I want to once more thank professor Alla Cohen for all of her wisdom and dedication to music.

 

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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