Music Theory De-mystified Blogkey relationships

14. The Relationships Between Keys

This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.

The relationship between two keys is simply how many notes they have in common: the more notes in common, the closer their relationship.

Why do we care? Because this is not just true on paper. Theory reflects reality. Closely related keys actually sound close, musically. They sound compatible.

In the preceding lessons we have already seen two types of key relationships; the cycle of fifths and relative major and minor. Here’s a quick review:

The Cycle Of Fifths

The cycle of fifths is a list of the keys in the order of their key signatures, from every note being a flat through to every note being a sharp. In this list, any two adjacent keys have all but one note in common.

The effect of this close relationship is that the music can comfortably and cohesively shift from one key to the other and back.

This is most easily demonstrated with chords. We’ll look at chords in a later post, but for now we can say that a (basic) chord represents a key. Chord names mimic key names, just in a shortened form. A note name by itself implies a major chord/key. If it’s followed by ”m”, it’s a minor chord.

Adjacent keys in the cycle of 5ths can be visited in any order. Here’s a short example in C major with a simple melody and chords. As usual in my posts, the examples are purely for illustration, so they don’t sound as exciting as real compositions…

Here’s an example of a simple melody in C major visiting adjacent keys, as represented here by chords.

A large proportion of music in Western culture in most genres, whether fast or slow, rhythmic or free, accompanied or solo, is based on visiting closely related keys.

To find the next key in the cycle of 5ths, go up to the 5th letter in the key to find the root note, then sharpen the 7th note of the scale (add a sharp or lose a flat).
To find the previous key in the cycle of 5ths, go down to the 5th letter in the key (or up to the 4th letter) to find the root note, then flatten the 4th note of the scale (add a flat or lose a sharp).

You can also use the cycle of 5ths as a list to look up the root note of a key and its latest sharp or flat, or even the complete key signature. An example of this for major scales can be found in 12. Major Keys And The Cycle/Circle Of Fifths. The cycle of 5th for major and minor keys, with key signatures, is shown in The Cycle (circle) of Fifths.

Relative Major And Minor

Next we looked at another close relationship between keys, one where two keys have every note in common: relative major and minor. Having all notes in common, the difference is in which one is the root note. Of course, changing the root note changes the mode, hence the term relative major and minor.

Major and minor have different characters – different tonalities. Moving between one and the other feels a bit like going to an unfamiliar corner of a familiar room; like viewing the scene from a different angle.

Here is a simple melody in C major visiting the relative minor.

To find the relative minor of a major key, go up to the 3rd letter in the key and keep the same key signature (play the same notes starting on the 3rd note).
To find the relative major of a minor key, go down to the 3rd letter in the key and keep the same key signature.

For more on relative major and minor, please visit 13. Relative Major And Minor.

Parallel Major And Minor

There is a third type of key relationship which we haven’t yet visited; parallel major and minor. This means a major and a minor on the same root note.

The easiest way to see their relationship is by writing one on top of the other, literally parallel.

Here’s an example on C:

In the above graphic we can see that the parallel minor has three notes that are flattened compared to the parallel major, the 3rd, 6th and 7th notes.

Key signature wise, the parallel minor is 3 keys behind the parallel major (anticlockwise).

Parallel major and minor have only four of their seven notes in common so, as far as the cycle of 5ths goes, they’re not that closely related. However, because they share the same root note, their relationship feels closer than that.

Here is a simple melody in C major visiting the parallel minor.

Another Shortcut

Here’s another way to remember a few keys you don’t know…

Major to Parallel Minor

If you know the key signature of a major key then the minor on the same root note, the parallel minor, is 3 keys backward (anticlockwise) in the cycle of 5ths.
If you know the notes in the scale rather than the key signature, such as when playing by ear, flatten the 3rd, 6th and 7th notes. You’ll get the same result.

Minor to Parallel Major

If you know the key signature of a minor key, the major on the same root note is 3 keys forward (clockwise) in the cycle of 5ths.
If you know the notes in the scale, sharpen the 3rd, 6th and 7th notes.

Examples

Major to parallel minor

We know C major has no sharps or flats, so C minor has 3 flats (Bb, Eb, Ab)

Minor to parallel major

We know A minor has no sharps or flats, so A major has 3 sharps (F#, C#, G#)

Nothing In Common Is Still Something

On the far side of the relationship spectrum, two keys can have no notes in common. This is achieved by sharpening or flattening the root note and thus, every note. Musically, it’s a complete reset. Moving between two such unrelated keys can sound anywhere from refreshing to dramatic or mysterious.

In the case of C major, 0 sharps/flats, sharpening everything gives us C# major, 7 sharps.

Similarly, flattening everything gives us Cb major, 7 flats.

To sharpen everything, go forward (clockwise) 7 keys in the cycle of 5ths. All flats become naturals and all naturals become sharps. Every note is played 1 semitone higher than before.
To flatten everything, go backward (anticlockwise) 7 keys in the cycle of 5ths. All sharps become naturals and all naturals become flats. Every note is played 1 semitone lower than before.

Flattening D major (2 sharps) results in Db major (5 flats). All naturals become flats and all sharps become naturals.

Note: there is a practical limit to how many sharps or flats we can have. If there are more than 7, one or more notes in the scale will have a double sharp or double flat. These exist but are only used when necessary, usually as an accidental rather than as part of a key signature. For keys, it’s generally easier to respell (rename) the root note and avoid the issue.

If there are more than 7 sharps or flats, respell the root note. The key signature will go from lots of sharps to a few flats or from lots of flats to a few sharps.

For example, you probably remember by now that G major has 1 sharp, F#.

If we sharpen everything we get G# major, with 8 sharps. All the naturals are sharps and F is a double sharp.
However, G# is the same pitch as Ab. Ab major only has 4 flats so it’s much easier to read and doesn’t require a double anything.
Knowing G major does help you find Gb major though. By flattening everything we go from 1 sharp to 6 flats, no doubles there.

From The Known To The Unknown

Use your knowledge of key relationships to help learn the key signatures of more keys. Start with a couple of common or easy to remember keys and with a little thought, you’ll soon know most of them. At the same time you’ll become more familiar with the idea of keys being related to each other.

For instance, just by knowing C major (0 sharps/flats) you can quickly find its parallel minor, C minor (3 flats), 3 keys back in the cycle of fifths or flatten the 3rd, 6th and 7th notes.
You can also find C# major and Cb major by sharpening or flattening everything, as we’ve seen above.
From C minor you can find C# minor (sharpen everything: 3 flats becomes 4 sharps). Or you can find C# minor from C# major using parallel major to minor.
From C minor you can also find Eb major (still 3 flats), using relative minor to major (count up to the 3rd note in the key).
Similarly, from C# minor, using relative minor to major, you can find E major (4 sharps). Or you can find E major by sharpening everything in Eb Major (3 flats becomes 4 sharps).
We know A minor already, but if you forgot, you could find that from C major using relative major to minor (count down to the 3rd scale note, keeping the same key signature, 0 sharps/flats).

That’s 8 keys and key signatures just from remembering one key!

And I could keep going: From E major you can find E minor and so on… Not to mention using the cycle of 5ths to find the next key (add 1 sharp or lose 1 flat) or previous key (add 1 flat or lose 1 sharp), and then their relative minors or majors, etc.

Try this yourself with another common key like A minor or G major.

Try These…

Test your ability to think in key relationships! Name the following keys and list either their notes as a scale or their key signatures:

A major has 3 sharps; F#, C#, G#. What is the next key in the cycle of fifths after A major?
Bb major has 2 flats; Bb, Eb. What is the previous key in the cycle of fifths before Bb major?
D major has 2 sharps; F#, C#. What is the relative minor of D major?
D minor has 1 flat; Bb. What is the relative major of D minor?
E major has 4 sharps; F#, C#, G#, D#. What is the parallel minor of E major?
F# minor has 3 sharps; F#, C#, G#. What is the parallel major of F# minor?
You worked out the key of D minor. Now sharpen it.
G major gas 1 sharp; F#. What is the key of Gb major?

Answers at the end of this post.

Key Relationships Are Real

Being able to work out key signatures by using the various key relationships not only helps you with the odd unfamiliar key but it also reinforces your understanding of these relationships. As mentioned earlier, key relationships aren’t just musical arithmetic, they are real: when listening, you can hear the connection between related keys.

Try This…

For any key, the next and previous keys in the cycle of 5ths and their relative minors or majors are the most closely related. Choose a key whose key signature (or scale notes) you remember and work out these closely related keys.

If you play chords, try changing between the chords of these keys. If you play melodies, play their scales or triads. Either way, you’ll find that you can mix them up into any order and they will feel like they belong together.

(Sib simple chord sequence as chords, then triads, then as rapid scales)

You can also use closely related keys to work your way progressively to a distant key without really noticing, such as in the classic chord progression of Jimmy Hendrix’s Hey Joe, a cascading sequence of forward steps in the cycle of 5ths. In that song, the surprise comes when the sequence resets at the start of the next line: only then can you hear how far from home you ended up…

(Sib Hey Joe progression in scales and chords with repeat)

Note: we’ll investigate chords and triads later in this course.

If you play by ear, you can use any of the methods above to find how to play the scales of related keys. All you need to remember is the name of the key.

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NEXT LESSON: 15. Modes

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers to Try These…

E major (latest sharp is D#). 4 sharps; F#, C#, G#, D#
F major (latest flat is Bb). 1 flat; Bb
B minor: same key signature, 2 sharps; F#, C#
F major: same key signature, 1 flat; Bb
E minor: 1 sharp; F#
F# major: 6 sharps; F#, C#, G#, D#, A#, E#
D# minor: scale = D# E# F# G# A# B C# D#. 6 sharps; F#, C#, G#, D#, A#, E#
Gb major has 6 flats: scale = Gb Ab Bb Cb Db Eb F Gb. 6 flats; Bb, Eb, Ab, Db, Gb, Cb

A Melody Is A Journey

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

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This is a key tenet in my approach to music theory. However, if you disagree, feel free to comment.

Most music has both a melody and chords. Even a melody by itself is usually built on chords, it’s just that we don’t hear them. We call this an implied chord progression (when no chords are written, we can deduce the likelihood of potential chords by the evidence provided in the melody such as phrase structure, the actual notes used and the use of accidentals).

A chord represents a key- at least basic major and minor chords and their common variants do. How effective they are at establishing their key depends on low long they’ve got. Yes, time. The longer the time spent on a chord, the more it feels like THE key.

A melody is a journey. Typically it starts at home (in the home key) then travels to one or more visiting keys, represented by the main chords along the way, eventually arriving home again.

Just like a physical journey, the trip can be long or short, fast or slow, bumpy or smooth, visiting nearby or exotic places on the way. Everything that applies to a physical journey has its parallel in a musical journey.

There are three parts to any trip- the departure (including any prep such as packing), the travel and the arrival. Similarly, pieces (and the phrases within them) have a start, a middle and an end.

Time, Space and Culture Shock

A journey can be brief or extensive, or anything in between. The places you see can be familiar or exotic, near or far.

A trip to the local shop to get staples might be a 5-minute walk around the corner or up the street. You spend just long enough to do a common task in familiar surroundings and head back. This is the most basic journey; familiar and short.
You might drive across town to visit a close friend or family. Again, you are in familiar surroundings, yet you travelled beyond your immediate neighbourhood. This still feels like a small and safe journey yet you may spend hours on your visit and be surprised by the changed traffic or weather conditions coming home. A tiny bit more complex journey than the first example.
Maybe you’ve chosen to visit someone out of town or in another state. You might be invited to stay a few days. Longer distance means a little less familiarity: you don’t know the roads so well, where the post office is, the bed feels a bit different, etc. After a day or two, you start to get used to this. The longer you’re there, the more it feels like home.
While you’re there, you might take mini trips within the journey- go to the shop, the beach, maybe even camping out.
If you stay away long enough, when you come home it feels a bit strange at first. You almost turn the door key the wrong way, the colour of the wallpaper isn’t quite as you remembered it, you didn’t realise you were low on a few staples.
What if you set out on a grand adventure to visit strange and distant cultures? The journey is either massive, with strange and mysterious stops on the way, like an ocean journey, or super fast, almost like a blur, as in a flight. When you arrive, it’s almost alien. Everything’s different: the living conditions, the language, the food… Stay there for a while, however, and you gradually pick up a few basic words, learn a bit about the local neighbourhood and start to feel more settled.
Were you to stay in an exotic culture for long enough, it would start to feel like home, and your memories of your real home become less and less clear. Coming home after living there for years, home itself would feel like a very strange place at first. Stay somewhere long enough and you might even come home with a foreign accent!

All this can be mirrored in the way a piece of music progresses. The melody is the traveller, the main chords are the visiting points. Time is time.

The relationship between each chord and the home key (as well as between one chord and the next) is the relationship between home and the various places visited on our travels. As a (basic) chord represents a key, the main chords mark out the visiting keys in the journey.

Chord relationships are key relationships. A topic in itself, this is worthy of revisiting in at least one separate post. However, in general, keys (and chords) are related by how many notes they have in common. There are basically three types of key relationships:

The Cycle (or Circle) of 5ths

The cycle of 5ths is a sequence of all major and minor keys in increasing and decreasing key signature order, usually represented as a circle. Octaves are unspecified, as it’s just a list of keys. Adjacent keys in the cycle of 5ths have only one note different in their scales and both chords are made up of notes in the home key.

See my Beginner’s Tip for a graphic of the cycle of fifths, including relative majors/minors.

Adjacent keys in the cycle of 5ths are the closest companions. Many pieces only use 3 chords: that of the home key, previous key and the next key in the cycle, otherwise known as the Tonic, Subdominant and Dominant or I, IV and V. As we progress away from our neighbours, the keys sound less closely related and the chords a little more independent. Distant key relationships produce a startling or disorienting sensation in the listener.

Relative major and minor

All the common tonalities used in Western music have either a major 3rd or a minor 3rd from the root note. In this way, modes can be categorised as “like major” or “like minor” and be represented by a major or minor chord accordingly. It’s reasonable to talk in terms of major and minor chords, even if the piece is in another mode.

For every major scale, there is a minor scale with the same key signature (and vice versa). When the music changes between relative major and minor, the root note and tonality change but the notes all belong to the home key. As a chord progression, going from relative major to relative minor (and vice versa) feels more like taking a small step back rather than a significant change in key. Relative major/minor chords are often interchangeable in an accompaniment, depending on whether a more direct or a slightly indirect and more sophisticated effect is desired.

Major and minor on the same root note (parallel major and minor)

A major and a minor scale on the same root note have 3 notes that differ between them, so they only have 4 notes in common. In the cycle of 5ths that amounts to keys which are 3 steps apart, a relatively indirect relationship, yet they sound like they’re much more closely related. As it happens, only one of the three chord notes is different-the 3rd. The root note and 5th are both the same. The only thing that seems to change is the mood, the tonality.

Back to the present…

In short, closely related chords feel comfortable, almost predictable, as the melody arrives there – the friendly key next door…

Of course this is mitigated by the directness of the trip. We could potentially weave through a myriad of other keys before arriving next door, blindfolded and bedazzled, and it might then take us a while to realise where we are, but by and large, closely related keys can be freely visited in comfort.

More adventurous journeys use less direct key relationships or follow a cascading progression of keys in the cycle of 5ths to arrive in a new land.

When listening to a piece, try to feel not just the more rapid flow of the melody, but the deeper, underlying flow of the progression of keys through which the melody travels.

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The Cycle (circle) of Fifths

OK, this isn’t quite a beginner’s tip, but it’s a great hack for remembering key signatures, relative majors/minors and chord relationships.

The cycle of 5ths, or circle of 5ths if you prefer, is a list of all the major keys and their relative minors, ordered by their key signature. For convenience it’s usually written as a circle rather than a long, endless line. The keys are represented by chord names. A letter by itself is a major key or chord and a letter followed by “m” is a minor key or chord.

The pattern is centred around C major and A minor, which have no sharps or flats. Reading clockwise, you progress further into sharps. Reading anticlockwise, you progress “backwards”, further into flats.

At the bottom there is an overlap where two possible note names can be used to describe the same root note. The trade-off here between naming these keys as sharps keys or flats keys is minimal. In actual usage, the choice may become clearer when considering the natural (easily played) keys of the instrument(s) chosen to play the piece and what other keys are visited within the piece.

in theory, you could continue in either direction, beyond 7 sharps or 7 flats, but then you’re doubling up with much simpler key signatures for the same sounding key so you would need a very good reason to go beyond 7.

For a piece in a given key, say A major, the most closely related keys and the primary chords are found immediately to the left and right of the home key, and their relative minors or majors inside or outside the purple line.. In the case of A major that’s A, D, E, F#m, Bm and C#m.

Note: in most gentes, the chord on the next key (the dominant) is played as a major chord, even if the home key is minor. For example, for A minor, the chords are Am, Dm, E (rather than Em), C, F and G.

Primary school students are usually taught the sequence of letters as a mnemonic – at my school it was “Go Down And Enter By Fifths”, with a C at each end. It’s boring and it’s technically incorrect (the pattern goes up in fifths the way it reads, not down). I’m sure you could make up a better one…

The Cycle of 5ths is explained in more detail in 12. Major Keys And The Cycle/Circle Of Fifths.