How to form a diminished chord

A diminished chord has -like a minor chord- a minor 3rd interval from the first note (the root) to the second note of the chord. The difference with minor chords lies within the 3rd chord note as we will see below. Like with minor chords and major chords, we can have diminished triads and diminished 7th chords.

If you want to hear sound samples of the different chords, please refer to the lesson ‘What is a chord? How do different chords sound?’.

Diminished triads

A diminished triad is made of the root, the minor 3rd and the flattened 5th. So, in the case of the C diminished triad, this would be:   C   Eb   Gb

Another example is the G diminished triad: G   Bb   Db

The notation for a diminished chord is (in this case C diminished):     C O or Cdim. And in the case of G diminished: G O or Gdim.

Half diminished chords

As with major and minor chords, we can add the 7th. When we add the minor 7th to a diminished triad, we get a half diminished chord. Let’s see how that works in the key of C. The C diminished triad is C   Eb   Gb. The minor 7th in the key of C is the Bb, so C half diminished is: C    Eb    Gb    Bb

The notation for the C half diminished chord is: CØ or Cm7b5.

CØ is a nice and short notation, but Cm7b5 actually shows better what’s going on in the chord:

  • The ‘m’ stands for minor, since we have a minor 3rd
  • The ‘7’ stands for the 7th in the chord, in this case a minor 7th
  • The ‘b5’ stands for the flattened 5th in the chord

The G half diminished chord is: G   Bb   Db   F

So we can write G half diminished as: GØ or as Gm7b5

A half diminished chord can also be considered as a minor chord (but a minor chord with a flattened 5th).

Diminished 7th chords

Perhaps you noticed that a diminished triad is made of 2 stacked minor 3rd intervals. Look at the C diminished triad: from the root (C) to the minor 3rd (Eb) is a minor 3rd interval and from Eb to Gb is also a minor 3rd interval. Well, why not adding another minor triad? So, let’s do that!

What is a minor 3rd up from Gb? A minor 3rd consists of 3 semitones and 3 semitones up takes us to A. The only problem is that the 3rd note in the Gb minor scale cannot be an A.  Ab is the 2nd note, so the 3rd note must be written with the letter ‘B’ (see the rules in the major scale lesson). The only way we can do that, is with a double flat: Bbb (which is of course the enharmonic equivalent of A).

So, the C diminished chord is: C   Eb   Gb   Bbb

G diminished is a bit easier because it doesn’t contain any double flat: G   Bb   Db   Fb

The notation for diminished chords is as follows:

C diminished: C O7, Cdim7 or C O

G diminished: G O7, Gdim7 or G O

Even though diminished chords have a minor 3rd, they are, in contrast to half diminished chords, not considered as minor chords.

All the other diminished chords

Diminished 7th chords

And here comes the good news: there are only 3 different diminished 7th chords! Not 12, as was the case with minor and major chords (but this is only for diminished chords, not for half diminished chords since there are 12 different half diminished chords!). Only 3? Let me explain:

Look at the Eb diminished chord:

  • From Eb, up a minor 3rd to Gb
  • Then, from Gb, a minor 3rd up to Bbb
  • Finally, from Bbb, a minor 3rd up to Dbb (which is a C)

So, Eb diminished is: Eb   Gb   Bbb   Dbb (or C)

Compare this with the C diminished chord: C   Eb   Gb   Bbb

Even when not written totally the same (Dbb instead of C), the chords are exactly the same! And, indeed: a diminished chord of a note of the C diminished chord has the same notes as the C diminished chord itself. So this means that Cdim7, Ebdim7, Gbdim7 and Adim7 all are the same chord!

(Btw, notice that I wrote Adim instead of Bbbdim, because it would be a bit ridiculous to talk about the Bbbdim chord when we can simply say Adim.)

This enables us to finally make the table with the 3 different diminished chords:

Diminished chord: Chord notes:
C O7, Eb O7, Gb O7, A O7 C    Eb    Gb    A
Db O7, E O7, G O7, Bb O7 Db   E   G   Bb
D O7, F O7, Ab O7, B O7 D   F   Ab   B

Some remarks concerning this table:

  • Notice that the roots of the chords listed in the left column are the same as the notes of the diminished chords in the right column.
  • Instead of writing the correct notes for each individual diminished scale (like Bbb for Cdim), I wrote the easiest enharmonic equivalent (A instead of Bbb).
  • For the diminished chords with a black note root: I didn’t list the enharmonic equivalents, but you can find the notes of for example D# O7 at Eb O

Half diminished chords

Here’s the table with half diminished chords:

Half diminished chord: Chord notes:
CØ C   Eb   Gb   Bb
DØ D   F   Ab   C

 

EØ E   G   Bb   D
FØ F   Ab   Cb   Eb
GØ G   Bb   Db   F
AØ A   C   Eb   G
BØ B   D   F   A
DbØ / C#Ø Db   Fb   Abb   Cb  /  C#   E   G   B
EbØ / D#Ø Eb   Gb   Bbb   Db  /  D#   F#   A   C#
GbØ / F#Ø Gb   Bbb   Dbb   Fb  /  F#   A   C   E
AbØ / G#Ø Ab   Cb   Ebb   Gb  /  G#   B   D   F#
BbØ / A#Ø Bb   Db   Fb   Ab  /  A#   C#   E   G#

 

 

Please tell us what you think of this lesson about diminished chords by leaving a comment below.

Chord inversion: different ways to play the same chord

Let me start with a simple C major triad. You can play the C major triad in 3 different ways on the piano. All you need is a chord inversion. Let me explain…

Chord inversion in a triad

I will continue with the C major triad: C   E   G.  On the piano keyboard, it looks like:

C root

You can see that the C, the root of the triad, is at the bottom. We call the C major triad in this position the root position.

When we move the lowest note, the C, to the top, we get: E   G   C.

Or, on the piano keyboard:

C 1st inversion

We call this the C major triad in 1st inversion.

When we move now the lowest note (which is the E) to the top, we get: G   C   E.

We call this the C major triad in 2nd inversion (see next figure).

C 2nd inversion

When we move now the lowest note (which is the G) to the top, we’re back in root position, with the root (the C) at the bottom.

You can see that it’s possible to make three different ways to play a major triad:

  • Root position
  • 1st inversion
  • 2nd inversion

 

Now, you can imagine that all triads, whether they are major, minor, diminished or whatever, can be played in those 3 positions.

Chord inversion in 7th chords

We can apply the same ‘trick’ in 7th chords: always move the bottom note to the top to get to the next position.

Let me illustrate this with the C7 chord. In root position, this is: C   E   G   Bb (see figure)

C7 root position

Let’s move the root to the top to go to the C7 chord in 1st inversion: E   G   Bb   C (see figure)

C7 1st inversion

Move the bottom note (the E) to the top, and we’re in 2nd inversion:

C7 2nd inversion

Again, move the bottom note (now the G) to the top, and we’re in 3rd inversion:

C7 3rd inversion

And, as you guessed already, when we move now the bottom note (the Bb) to the top, we’re back in root position.

This means that the 7th chords have 4 possible positions:

  • Root position
  • 1st inversion
  • 2nd inversion
  • 3rd inversion

And, of course, you can apply the same trick to all other kind of 7th chords (minor 7th, major 7th, …).

 

It takes some time to really master the inversions of all kind of chords, that’s why it is important to practice a lot with it. You can do this by doing the exercises that are accesible via the links below. Do them in the order as they appear in this list, because they go from easy to more difficult. Do an exercise for about 5 minutes and then come back at the same or a next exercise later (or the next day).

Place the notes of the major triad on the piano (all the inversions)

Place the notes of the minor triad on the piano (all the inversions)

Place the notes of the dominant chord on the piano (all the inversions)

Place the notes of the minor 7th chord on the piano (all the inversions)

Place the notes of the major 7th chord on the piano (all the inversions)

Place the notes of the chord (dominant/minor 7th/major 7th) on the piano (all the inversions)

 

 

Please tell us what you think of this lesson and the exercises by leaving a comment below.

 

How to form a minor chord

Minor chords

How are minor chords formed? The most important characteristic of a minor chord is the minor 3rd interval from the root (starting note) to the second chord note. We can have minor triads and minor chords with a 7th.

If you want to hear sound samples of the different chords, please refer to the lesson ‘What is a chord? How do different chords sound?’.

Minor triads

A minor triad is made of the root (1st), 3rd and 5th note of the minor scale. For example, the C minor triad is formed by the root, the 3rd and the 5th note of the C minor scale. So, the notes of a C minor triad are: C, Eb and G. Notice the minor 3rd interval between the root (C) and the Eb. The Eb is therefore called the minor 3rd in the key of C.

Two more examples:

  • The A minor triad: the root, minor 3rd and 5th in the key of A are A, C and E, so the A minor triad is: A    C    E
  • The Db minor triad: the root, minor 3rd and 5th in the key of Db are Db, Fb (enharmonic equivalent of E) and Ab, so the Db minor triad is: Db    Fb    Ab

Minor 7th chords

Minor 7th chords are formed by a minor triad with an extra note: the minor 7th. The minor 7th is the note that makes a minor 7th interval with the root note. The minor 7th in the key of C is Bb. So, the C minor 7th chord consists of the notes C, Eb, G and Bb.

We write the C minor 7th chord as Cm7, Cmin7 or C-7

I will take the 2 other examples from above to give you 2 more minor 7th chords:

  • The A minor 7th chord: the A minor triad (A C    E) with the added minor 7th (G) gives us the A minor 7th chord:    A    C    E    G
  • The Db minor 7th chord: add the minor 7th in the key of Db to the Db minor triad to get: Db    Fb    Ab    Cb   (Cb being the enharmonic equivalent of B)

Minor major 7th chords

Minor major 7th chords are almost never used in rock/pop/blues music, but a lot in jazz.

A minor major 7th chord is made of a minor triad with an added major 7th note. At first sight, the name is a bit confusing: is it a minor chord or a major chord? Well, it is a minor chord because of the minor 3rd (it’s built on a minor triad!). The ‘major’ in the chord name refers to the 7th because it is a major 7th note.

We write a C minor major 7th chord as C-∆7 or Cm∆7.

A minor major 7th chord is easy to find when you know the minor 7th chord: just raise the minor 7th by a semitone.

Taking the same examples as before, we get:

  • The C minor major 7th chord: C    Eb    G    B
  • The A minor major 7th chord: A    C    E    G#
  • The Db minor major 7th chord: Db    Fb    Ab    C

All the other minor chords

With the information in this lesson, you can now find out all the other minor chords. Start with all the 12 triads, and then put the minor 7th or major 7th on top to find the minor 7th and minor major 7th chords. If you don’t remember well all the minor scales, then have a look at the lesson about minor scales. For the minor chords that have a ‘black key root’: take the roots that have a minor scale with not more than 6 sharps or 6 flats (see ‘How to form a minor scale’). For the sake of completeness, I will also add the enharmonic equivalents with more than 6 sharps or flats in parentheses.

When you’re finished, check your answers with the solutions below.

Triads

Minor triad Chord notes
Cm C    Eb    G
Dm D    F    A
Em E    G    B
Fm F    Ab    C
Gm G    Bb    D
Am A    C    E
Bm B    D    F#
C#m (Dbm) C#    E    G#    (Db    Fb    Ab)
D#m / Ebm D#    F#    A#  /  Eb    Gb    Bb
F#m (Gbm) F#    A    C#    (Gb    Bbb    Db)
G#m (Abm) G#    B    D#    (Ab    Cb    Eb)
Bbm (A#m) Bb    Db    F    (A#    C#    E#)

 

Minor 7th chords

Minor 7th chord Chord notes
Cm7 C    Eb    G    Bb
Dm7 D    F    A    C
Em7 E    G    B    D
Fm7 F    Ab    C    Eb
Gm7 G    Bb    D    F
Am7 A    C    E    G
Bm7 B    D    F#    A
C#m7 (Dbm7) C#    E    G#    B    (Db    Fb    Ab    Cb)
D#m7 / Ebm7 D#    F#    A#    C#    /    Eb    Gb    Bb    Db
F#m7 (Gbm7) F#    A    C#    E    (Gb    Bbb    Db    Fb)
G#m7 (Abm7) G#    B    D#    F#    (Ab    Cb    Eb    Gb)
Bbm7 (A#m7) Bb    Db    F    Ab    (A#    C#    E#    G#)

 

Minor major 7th chords

Minor major 7th chord Chord notes
C-∆7 C    Eb    G    B
D-∆7 D    F    A    C#
E-∆ E    G    B    D#
F-∆7 F    Ab    C    E
G-∆7 G    Bb    D    F#
A-∆7 A    C    E    G#
B-∆7 B    D    F#    A#
C#-∆7 (Db-∆7) C#    E    G#    B#    (Db    Fb    Ab    C)
D#-∆7 / Eb-∆7 D#    F#    A#    C##    /    Eb    Gb    Bb    D
F#-∆7 (Gb-∆7) F#    A    C#    E#    (Gb    Bbb    Db    F)
G#-∆7 (Ab-∆7) G#    B    D#    F##    (Ab    Cb    Eb    G)
Bb-∆7 (A#-∆7) Bb    Db    F    A    (A#    C#    E#    G##)

 

It’s really important to practice a lot in order to be able to quickly come up with the right minor chord when you’re play a song for example. The exercises below are an excellent way to practice your minor chord knowledge.

If you don’t know what chord inversions are, then do only the exercises in root positions. Otherwise, you can follow the lesson about inversions.

Minor triads:

Place the notes of the minor triad on the piano (only root positions)

Place the notes of the minor triad on the piano (all the inversions)

Minor 7th chords:

Place the notes of the minor 7th chord on the piano (only root positions)

Place the notes of the minor 7th chord on the piano (all the inversions)

Mix of all chords (also major!):

If you know how major chords work, you can do also the following exercises. If not, look first at the major chords lesson.

Place the notes of the chord (dominant/minor 7th/major 7th) on the piano (only root positions)

Place the notes of the chord (dominant/minor 7th/major 7th) on the piano (all the inversions)

 

I hope you learned a lot about minor chords. Please let us know what you think of this lesson and the exercises by leaving a comment below.

 

How to form major chords

Major chords

How are major chords formed? The most important characteristic of a major chord is the major 3rd interval from the root (starting note) to the second chord note. We can have major triads and major chords with a 7th.

If you want to hear sound samples of the different chords, please refer to the lesson ‘What is a chord? How do different chords sound?’.

Major triads

A major triad is made of the root (1st), 3rd and 5th note of the major scale. For example, the C (major) triad is formed by the root, the 3rd and the 5th note of the C major scale. So, the notes of a C major triad are: C, E and G. Notice the major 3rd interval between the root (C) and the E. The E is therefore called the major 3rd in the key of C.

Let’s try another example:  the A major triad. The root, 3rd and 5th in the A major scale are A, C# and E.

OK, one more example: the Eb major triad. The root, 3rd and 5th are Eb, G and Bb.

We write the major triad just with its root note, so the C major triad is simply written as C. The context will tell you if the symbol C refers to the single note C or to the C triad.

Major 7th chords

Major 7th chords are formed by a major triad with an extra note: the 7th note of the corresponding major scale. In the scale of C major, the 7th note is a B, so the C major 7th chord consists of the notes: C, E, G and B. Note that the interval of the root (C) to the 7th note in the scale (B) is a major 7th interval. That’s why we call this chord the C major 7th chord. So the word ‘major’ in the chord name refers to the major 7th (the B) of the scale, not to the major 3rd (the E). We write the C major 7th chord as: C∆7, CMaj7 or CM7.

Let me take the 2 other triad examples to show you 2 more major 7th chords:

The A major triad was: A, C# and E. Add the major 7th of the A major scale, and A∆7 consists of the notes A, C#, E and G#.

When you apply the same thing to Eb, you can see that Eb∆7 consists of the following notes: Eb, G, Bb and D.

Dominant or 7th chords

Instead of adding the major 7th to the major triad, we can also add the minor 7th to the major triad. The minor 7th in the scale of C is Bb (the minor 7th is the note that makes a minor 7th interval with the root). So the C dominant (or C seventh) chord consists of the notes C, E, G and Bb.

We write this chord as: C7.

Note: a major 7th chord is a major triad with a major 7th, but a 7th chord is a major triad with a minor 7th. So we don’t call this a minor 7th chord. A minor 7th chord is a chord based on a minor 3rd interval between the root to the second chord note. So here, the word ‘minor’ doesn’t refer to the 7th, but to the 3rd. A bit confusing, I admit, but things are like that…

So, A7 consists of the notes A, C#, E and G (since G is the minor 7th in the key of A). And Eb7 consists of the notes Eb, G, Bb and Db.

All the other major chords

With the information in this lesson, you can now find out all the other major chords. Start with all the 12 triads, and then put the minor 7th or major 7th on top to find the dominant (7th) and major 7th chords. If you don’t remember well all the major scales, then have a look at the lesson about major scales. For the major chords that have a ‘black key root’: take the roots that have a major scale with not more than 6 sharps or 6 flats (see ‘How to form a major scale’). For the sake of completeness, I will also add the enharmonic equivalents with more than 6 sharps or flats in parentheses.

When you’re finished, check your answers with the solutions below.

Triads

Major triad Chord notes Number of sharps/flats

in the major scale

C C   E   G 0
D D   F#   A 2 sharps
E E   G#   B 4 sharps
F F   A   C 1 flat
G G   B   D 1 sharp
A A   C#   E 3 sharps
B B   D#   F# 5 sharps
Db (C#) Db   F   Ab   (C#   E#   G#) 5 flats (7 sharps)
Eb (D#) Eb   G   Bb   (D#   F##   A#) 3 flats (9 sharps)
F# / Gb F#   A#   C#   / Gb   Bb   Db 6 sharps / 6 flats
Ab (G#) Ab   C   Eb   (G#   B#   D#) 4 flats (8 sharps)
Bb (A#) Bb   D   F   (A#   C##   E#) 2 flats (10 sharps)

 

Major 7th chords

Major 7th chord Chord notes Number of sharps/flats

in the major scale

C∆7 C   E   G   B 0
D∆7 D   F#   A   C# 2 sharps
E∆7 E   G#   B   D# 4 sharps
F∆7 F   A   C   E 1 flat
G∆7 G   B   D    F# 1 sharp
A∆7 A   C#   E   G# 3 sharps
B∆7 B   D#   F#   A# 5 sharps
Db∆7 (C#∆7) Db   F   Ab   C   (C#   E#   G#   B#) 5 flats (7 sharps)
Eb∆7 (D#∆7) Eb   G   Bb   D   (D#   F##   A#   C##) 3 flats (9 sharps)
F#∆7 / Gb∆7 F#   A#   C#   E#   / Gb   Bb   Db   F 6 sharps / 6 flats
Ab∆7 (G#∆7) Ab   C   Eb   G   (G#   B#   D#   F##) 4 flats (8 sharps)
Bb∆7 (A#∆7) Bb   D   F   A   (A#   C##   E#   G##) 2 flats (10 sharps)

 

Dominant (7th) chords

Dominant chord Chord notes Number of sharps/flats

in the major scale

C7 C   E   G 0
D7 D   F#   A 2 sharps
E7 E   G#   B   D 4 sharps
F7 F   A   C   Eb 1 flat
G7 G   B   D   F 1 sharp
A7 A   C#   E   G 3 sharps
B7 B   D#   F#   A 5 sharps
Db7 (C#7) Db   F   Ab   Cb   (C#   E#   G#   B) 5 flats (7 sharps)
Eb7 (D#7) Eb   G   Bb   Db   (D#   F##   A#   C#) 3 flats (9 sharps)
F#7 / Gb7 F#   A#   C#   E   / Gb   Bb   Db   Fb 6 sharps / 6 flats
Ab7 (G#7) Ab   C   Eb   Gb   (G#   B#   D#   F#) 4 flats (8 sharps)
Bb7 (A#7) Bb   D   F   Ab   (A#   C##   E#   G#) 2 flats (10 sharps)

 

And now it’s time to practice all that you’ve learned in this lesson. The exercises below are an excellent way to practice your skills.

If you don’t know what chord inversions are, then do only the exercises in root positions. Otherwise, you can follow the lesson about inversions.

Major triads:

Place the notes of the major triad on the piano (only root positions)

Place the notes of the major triad on the piano (all the inversions)

Dominant chords:

Place the notes of the dominant chord on the piano (only root positions)

Place the notes of the dominant chord on the piano (all the inversions)

Major 7th chords:

Place the notes of the major 7th chord on the piano (only root positions)

Place the notes of the major 7th chord on the piano (all the inversions)

Mix of all chords (also minor!):

If you know how minor chords work, you can do also the following exercises. If not, look first at the minor chords lesson.

Place the notes of the chord (dominant/minor 7th/major 7th) on the piano (only root positions)

Place the notes of the chord (dominant/minor 7th/major 7th) on the piano (all the inversions)

 

I hope that you learned a lot in this lesson about major chords. Please tell us what you find of this lesson and the exercises by leaving a comment below.

 

What is a chord? How do different chords sound?

What is a chord? How do the different chords sound?

So, what is a chord?

A chord is a group of notes (typically 3 or more) played simultaneously. When a sequence of different chords is played, we speak of a chord progression, like for example in a blues chord progression.

Different types of chords

Below, you can find a short description of the most widely used chords in Western music. For a more detailed description of all the types of chords, please refer to the articles about major chords, minor chords and diminished and augmented chords.

Triads

A special type of chords that we often use in Western music is the triad. A triad is simply a chord that consists of 3 notes: the first note (the first note is also called the root), the 3rd and the 5th note of a scale. This scale can be a major scale, a minor scale or another sort of scale.

Seventh chords

A seventh chord in its basic form consists of 4 notes:  the root, the 3rd, the 5th and the 7th note of a scale (minor, major , …). So it’s actually a triad with an added 7th.

How do the chords sound?

It’s important to give you an idea of how chords sound, and to hear the difference between the different sort of chords. Therefore, you can listen to the sound examples below:

The root of all the chords in the sound samples below is a C. Because in this way, it’s easier to compare the different chords.

Triads

Seventh chords

 

Listen well to the difference of the chords. So, start to listen to the difference between the major, minor, diminished and augmented triads to get a feeling for the major, minor, diminished and augmented sound. Then listen to what the 7th and the major 7th do to the sound by:

  • comparing a major triad with a dominant (or 7th) chord and with a major 7th  chord (so compare C with C7 and C∆7)
  • comparing a minor triad with a minor 7th chord and with a minor major 7th chord (so compare Cm with Cm7 and C-∆7)

 

Did you like this lesson on how different chords sound? Please tell us what you think of this lesson by leaving a comment below.

 

2

How to form a natural minor scale

First of all, why do I say ‘natural minor scale’, and not simply ‘minor scale’ (I also called a major scale just ‘major scale’ without any other specification)?

This is, because there exists only one type of major scales, but there are 3 types of minor scales:

  • the natural minor scale
  • the harmonic minor scale
  • the melodic minor scale

In this lesson, we talk only about the natural minor scale, in another lesson, I will talk about the other 2 minor scales.

The natural minor scale

When you know how to form a major scale, it’s very simple to form a natural minor scale. Before telling you the general rule, let me first show you this with an example:

In this example I will show you how to form the A natural minor scale. Well, as I promised, it’s very simple: the notes of the A natural minor scale are exactly the same as the notes of the C major scale, so only the white keys on the piano.

So the A natural minor scale is:

A  B  C  D  E  F  G  A

The only difference is the starting note, the root: A natural minor starts on an A, where C major starts on a C. And that’s all! Simple, isn’t it?

Since A natural minor and C major share the same scale (only another starting note), we say that ‘A minor is the relative minor of C major’ and ‘C major is the relative major of A minor’.

Now, every minor scale has its relative major scale, so the question now is: “How to find out which relative major scale belongs to a natural minor scale?”

Well, when you look at A minor/C major, you see that from A, when you go up a minor 3rd, you arrive at C.

So, when you want to find out –for example- what the C natural minor scale is, you have to go up a minor 3rd from C. A minor 3rd up from C brings us to Eb.

Eb major is the relative major of C minor and so they share the same scale. This means that the C natural minor scale is:

C  D  Eb  F  G  Ab  Bb  C

The other natural minor scales

As an exercise, you could now try to find out all the other natural minor scales. The best way to start is perhaps with our list of major scales. Then start with a certain major scale, find its relative minor, and start on the root of that relative minor scale and you’re done.

For example: start with the Db major scale. What’s the relative minor of Db major? Well, now you have to go down a minor 3rd!

A minor 3rd (3 semitones) down takes us to Bb (not A#, because in the scale of Db, it’s a Bb).

Another way to find the relative minor of a major scale is to look at the 6th note in the major scale: remember that the relative minor of C major was A minor. Well, A is the 6th note in the scale of C major.

OK, try to see if you can find the other natural minor scales. You will find the solutions just here below:

Tables with all the natural minor scales

First, the table with sharps:

Major scale Relative minor Natural minor scale Number of sharps
C Am A  B  C  D  E  F  G  A 0
G Em E  F#  G  A  B  C  D  E 1
D Bm B  C#  D  E  F#  G  A  B 2
A F#m F#  G#  A  B  C#  D  E  F# 3
E C#m C#   D#  E  F#  G#  A  B  C# 4
B G#m G#  A#  B  C#  D#  E  F#  G# 5
F# D#m D#  E#  F#  G#  A#  B  C#  D# 6

Followed by the table with flats:

Major scale Relative minor Natural minor scale Number of flats
C Am A  B  C  D  E  F  G  A 0
F Dm D  E  F  G  A  Bb  C  D 1
Bb Gm G  A  Bb  C  D  Eb  F  G 2
Eb Cm C  D  Eb  F  G  Ab  Bb  C 3
Ab Fm F  G  Ab  Bb  C  Db  Eb  F 4
Db Bbm Bb  C  Db  Eb  F  Gb  Ab  Bb 5
Gb Ebm Eb  F  Gb  Ab  Bb  Cb  Db  Eb 6

 

Notice that the D# natural minor scale (6 sharps) and the Eb natural minor scale (6 flats) are the same scales, only written differently (they are enharmonic equivalent).

 

Now, it’s important to practice the natural minor scales. I advice you to do the exercise below.

Place the notes of a natural minor scale on the piano

 

Please tell us what you think of the natural minor scale lesson and the exercise by leaving a comment below.

 

The circle of fifths

The circle of fifths (also called cycle of fifths) gives us a handy overview of the different scales and how they are related to each other.

How to form the circle of fifths

In the lesson ‘How to form a major scale’, I explained that starting from the C major scale, every time we take a major scale a fifth higher, the scale gets one extra sharp note. And, starting from C major, every time we go a fifth down (or a fourth up, which is basically the same), we get one more flat note in the major scale.

We could now display all the roots (starting notes) of the major scales in a row with C major (no sharps, no flats) in the middle. At the left of C, all the major scales with flats. Every step to the left would mean a fifth down (or a fourth up) and thus an extra flat note in the scale. At the right of C, all the major scales with sharps. Every step to the right would mean a fifth up (or a fourth down) and thus an extra sharp note in the scale.

Gb      Db      Ab      Eb      Bb       F        C        G        D        A        E        B        F#

It is important to realize that the most left scale (Gb) and the most right scale (F#) are actually the same scale, since Gb and F# are the same note, only written differently: they are enharmonic equivalent.

So that means that we could display this row with scales in a circle, as follows:

circle of fifths major

At the right side we have the major scales with sharps, on the left side the major scales with flats.

Every step clockwise in this circle (this would correspond with a step to the right in our row above) means a fifth up (or a fourth down). And every step counterclockwise a fifth down (or a fourth up). That’s why we call this circle the ‘circle (or cycle) of fifths’. Since a fifth up corresponds with a fourth down and vice versa, this circle is sometimes also called the ‘circle (or cycle) of fourths.

The minor scales in the circle of fifths

Since a natural minor scale has exactly the same notes as its relative major scale, we can also put the natural minor scales in our circle of fifths. So, for example: since the A minor scale and the C major scale share the same notes, we can put them in the same place in the circle of fifths:

circle of fifths major minor

And see here our circle of fifths, which gives us a quick overview of the number of sharps and flats in every major and minor scale, plus an overview of relative minor/major relationships.

Why would I need a circle of fifths?

As mentioned above, the circle of fifths gives a good overview of sharps/flats and relative minor/major.

The circle of fifths is among other things very handy for example in transposing a song (I’ll come back on this in a later lesson).

The circle of fifths also quickly shows us why the major scales that start on a black key on the piano are mostly written with flats instead of with sharps. Let me illustrate this with the Eb major scale, which has 3 flats.

Eb is enharmonic equivalent with D#, so let’s look how the D# major scale looks like. First of all, in the circle of fifths, from F# I will go on clockwise to C#, G# and then to D# (so every step a fifth up). You can see that D# major has 9 sharps (wow!).

circle of fifths D# major 9 sharps

Let’s, for fun, see how the D# major scale looks like (see also the lesson ‘How to form a major scale’):

From D#, a whole tone (W) up to E#

From E#, a whole tone (W) up to F## (or Fx)

From F##, a half tone (H) up to G#

From G#, a whole tone (W) up to A#

From A#, a whole tone (W) up to B#

From B#, a whole tone (W) up to C## (or Cx)

From C##, a half tone (H) up to D#

So the D# major scale is:

D#  E#  F##  G#  A#  B#  C##  D#

As you can see: a total of 9 sharps (don’t count the D# twice)!

Compare this with the Eb major scale:

Eb  F  G  Ab  Bb  C  D  Eb

Now, my question to you is: “Which scale do you prefer, the Eb major scale, or the D# major scale?” I think I know the answer… 🙂

 

Please tell us what you think of this lesson by leaving a comment below.

 

Characteristics of intervals – Inversions

Inversions

Let me start with the example of the perfect 5th interval from C to G, as indicated on the next keyboard:

perfect fifth C to G

You can make an inversion of this perfect 5th interval by either taking the highest note and move it an octave down, or by taking the lowest note and move it an octave up. In the keyboard below, you see the highest note that was moved an octave down. Whether you move the highest note an octave down, or the lowest note an octave up, the result is the same: the inversion of the perfect 5th interval from C to G is a perfect 4th interval from G to C.

perfect fourth G to C

So, a perfect 4th interval is the inversion of a perfect 5th interval. The reverse is also true: a perfect 5th interval is the inversion of a perfect 4th interval. Together they add up to an octave, because a perfect 5th (7 semitones) plus a perfect 4th (5 semitones) make together 12 semitones, an octave.

You can also see it the following way: when you want to go from C to G, you can either go up a 5th, or go down a 4th.

Inversions of other intervals

Now, this is not only true for the ‘perfect 5th-perfect 4th pair’. Other pairs of intervals exist that act the same way. In fact, every interval has its inversion. For example, the inversion of the major 3rd interval from –let’s say- E to G# is the minor 6th interval from G# to E. Also here, the intervals add up to an octave, because 4 semitones (major 3rd) plus 8 semitones (minor 6th) equals 12 semitones (an octave).

A special case is the tritone interval. The tritone doesn’t need a partner, it just needs itself! A tritone splits an octave exactly in two equal parts, so a tritone just needs another tritone to make an octave.

A tritone consists of 6 semitones, so: 6+6=12, an octave!

Here’s a list of intervals with their inversions:

Intervals with their inversion:
Perfect unison + perfect octave

Semitone (or minor second) + major seventh

Whole tone (or major second) + minor seventh

Minor third + major sixth

Major third + minor sixth

Perfect fourth + perfect fifth

Tritone + tritone

 

Notice that a perfect interval always goes together with another perfect interval and a minor interval always goes together with a major interval (and, of course, vice versa).

 

Please leave a comment below and tell us what you think of this lesson.

 

Note interval

When you play 2 different notes at the same time or one after the other, you will have a lower and a higher note. This means there is a distance (in pitch) between the 2 notes. This distance is called the interval between the 2 notes, the note interval, or simply interval.

You can measure this intervals between notes in number of semitones, and this takes us directly to our first interval: the semitone.

The semitone

The easiest way to explain semitones is to look at the piano keyboard. A semitone is the interval from a key on the keyboard to the first note at the left or the right. So, for example, the interval from C to C# (or Db) in the next figure is a semitone.

Semitone interval

Or, for example from G# (or Ab) to A:

Semitone interval 2

It’s also possible to have a semitone between 2 white keys; this is the case between E and F and between B and C:

semitone interval 3

Notice that it’s not possible to have an interval of a semitone between 2 black keys on the piano.

Other names for a semitone are: half tone or half step.

The whole tone

The whole tone, or also called whole step, is an interval that consists of 2 semitones. Here are some examples of a whole tone:

From C to D:

whole tone interval

From F# (or Gb) to G# (or Ab):

whole tone interval 2

From E to F# (or Gb):

whole tone interval 3

From Bb (or A#) to C:

whole tone interval 4

The minor third

The minor third is an interval of 3 semitones, or a whole tone and a half tone (semitone).

Some examples:

From C to Eb:

minor third interval

From A to C:

minor third interval 2

From F# to A:

minor third interval 3

From Bb to Db:

minor third interval 4

The major third

The major third is an interval of 4 semitones, or 2 whole tones.

Examples:

From C to E:

major third interval

From Eb to G:

major third interval 1

From A to C#:

major third interval 2

From F# to A#:

major third interval 3

The perfect fourth

The perfect fourth (very often simply called fourth) is an interval of 5 semitones (or 2 whole tones and a semitone).

Examples:

From C to F:

perfect fourth interval

From F to Bb:

perfect fourth interval 2

From Eb to Ab:

perfect fourth interval 3

From A# to D#:

perfect fourth interval 4

The tritone

The tritone is an interval of 6 semitones or 3 whole tones (that’s why it’s called tritone, since ‘tri’ means three).

Examples:

From C to F#:

tritone interval

From Ab to D:

tritone interval 2

The perfect fifth

The perfect fifth (very often simply called fifth) is an interval of 7 semitones (or 3 whole tones and a semitone).

Examples:

From C to G:

perfect fifth interval

From A to E:

perfect fifth interval 2

From Eb to Bb:

perfect fifth interval 3

From F# to C#:

perfect fifth interval 4

The minor sixth

The minor sixth interval consists of 8 semitones, or 4 whole tones.

Examples:

From C to Ab:

minor sixth interval

From F# to D:

minor sixth interval 2

The major sixth

The major sixth interval consists of 9 semitones, or 4 whole tones and a half tone.

Examples:

From C to A:

major sixth interval

From Eb to C:

major sixth interval 2

The minor seventh

The minor seventh is an interval of 10 semitones, or 5 whole tones.

Examples:

From C to Bb:

minor seventh interval

From F# to E:

minor seventh interval 2

The major seventh

The major 7th is an interval of 11 semitones, or 5 whole tones and a half tone.

Example:

From C to B:

major seventh interval

From Gb to F:

major seventh interval 2

The perfect octave

The perfect octave (mostly just simply called octave) is an interval of 12 semitones, or 6 whole tones.

Since there are 12 different notes in Western music, this means that when you go up an octave, you arrive at the same note. Well, it’s of course not exactly the same note, since it’s higher in pitch: an octave higher.

For example, from C to C:

perfect octave

Or, from Ab to Ab:

perfect octave 2

The perfect unison

We haven’t mentioned yet the simplest of all intervals: the perfect unison, mostly simply called unison.

The unison is the interval between a note and itself, so 0 semitones. Now, that sounds a bit strange and it’s actually not really an interval in the real sense of the word.

When, for example, a piano and a trumpet play the same note at the same time, you can say that they play in unison. I don’t think I have to give an example on the piano keyboard 🙂

To resume

It might seem like a terrible task to memorize all the intervals with their names, but perhaps the next scheme based on the scale of C major might help to have a better overview of the intervals. The names of the intervals indicated above the keys of the keyboard are the intervals from the low C (indicated with the red 1) to that note.  Compare the name of the interval with the number of the note in the C major scale (in red, under the keyboard):

intervals in C major scale

Below a complete overview of all the intervals with even other alternative names (source: Wikipedia):

table with all intervals

Note names in a scale

A note in a scale is often named after the interval it makes with the root note.

What I mean is, for example when we are in the key of C, that the E is called the major 3rd, the Eb the minor 3rd, the F the 4th, the G the 5th, the A the 6th, the B the major 7th and the Bb the minor 7th.

The 2nd note (D in the case of the key of C) however, is not called after its intervals with the root. You could call the 2nd note just the 2nd. The Db would then be the minor 2nd. There is however another name for the 2nd, I will talk about that in another lesson.

There are still some more notes: the Gb is the flattened 5th (or short: the b5). F#, which is the same note, would be the sharpened 4th (#4).

The Ab is a flattened 6 (b6). The same note, the G# is the sharpened (or augmented) 5th (#5).

You will often see even other notes like the 9th, the 11th etcetera. I will treat those in another lesson.

 

It’s very practical to be able to quickly recognize intervals. For that reason, I advice to do the exercises below.

Which interval is played on the piano (from C)?

Which interval is played on the piano (from any note)?

How to form a major scale

For piano players, the C major scale is the easiest major scale because it starts on C and consists of all the white notes up to the next C. So, the notes of the C major scale are: C  D  E  F  G  A  B  C  (this looks as if the scale has 8 notes, but since the C is played twice, the scale consists of 7 different notes).

Let’s now look at the intervals between its consisting notes:

  • From C to D: whole tone (W)
  • From D to E: whole tone (W)
  • From E to F: half tone (H)
  • From F to G: whole tone (W)
  • From G to A: whole tone (W)
  • From A to B: whole tone (W)
  • From B to C: half tone (H)

So the intervals between the consecutive notes of the C major scale are:

W W H W W W H  (see figure)

intervals in major scale

Since all major scales sound the same way, this structure is valid for all major scales. That means that the only difference between all major scales is their root (starting note). So we can use this structure to find out all the other major scales. Let me illustrate this with some examples:

The D major scale

Let’s apply our ‘formula’ (W W H W W W H) to find the scale of D major.

  • From D, a whole tone (W) up to E
  • From E, a whole tone (W) up to F#
  • From F#, a half tone (H) up to G
  • From G, a whole tone (W) up to A
  • From A, a whole tone(W) up to B
  • From B, a whole tone (W) up to C#
  • From C#, a half tone (H) up to D

So, the notes of the D major scale are: D  E  F#  G  A  B  C#  D

Now, why did I call the 3rd and 7th notes F# and C# and not Gb and Db? Well, this is because we have to apply one of the following 2 rules (you can choose which rule to apply, since one rule implies automatically the other):

  • Don’t use the same letter for 2 consecutive notes
  • Don’t leave a ‘gap’ between 2 consecutive notes

Let me explain those rules:

Don’t use the same letter for 2 consecutive notes: Imagine that in the D major scale, I would have used Gb instead of F#. The first 4 notes of the scale would then have been: D  E  Gb  G …

In this case, the letter G is used twice (even if the first has a flat sign), so this is against our first rule.

In the same way, you can show that you have to use C# instead of Db.

Don’t leave a gap between 2 consecutive notes: Again, imagine I would have used Gb instead of F# in the D major scale, so: D  E  Gb  G …

Now, between E and Gb, there’s a ‘gap’ because we miss the letter F. We have therefore to use the letters in the order as they appear on the white keys of the piano keyboard.

The F major scale

When we apply our formula to find the F major scale, we get:

  • From F, a whole tone up to G
  • From G, a whole tone up to A
  • From A, a half tone up to Bb
  • From Bb, a whole tone up to C
  • From C, a whole tone up to D
  • From D, a whole tone up to E
  • From E, a half tone up to F

Did you notice that the scale of F major has a flat note (the Bb), not a sharp? It cannot be an A# (just apply one of the rules mentioned above and you will see that the 3rd note in the scale of F major is a Bb, not an A#).

So, the scale of F major is:  F  G  A  Bb  C  D  E  F

The other major scales

With our formula (WWHWWWH), you can now find out yourself the other major scales. Since there are 12 different notes, that means that there are also 12 major scales.

When you do the scales in the order as listed below, you will see that each time you will get one more sharp in the scale. Starting from the C major scale (0 sharps), move on to the G major scale (1 sharp), then the D major scale (2 sharps, as you have already seen before), etcetera, till you reach the scale of F# (6 sharps). And don’t forget to apply one of the 2 rules (don’t repeat letters & don’t leave gaps). At the end of this lesson you will find the right solutions.

Order for the major scales with sharps:

C major (0 sharps)

G major (1 sharp)

D major (2 sharps)

A major (3 sharps)

E major (4 sharps)

B major (5 sharps)

F# major (6 sharps)

Notice that in the list above, we go up a 5th in every step. So, starting with C major, every time you go up a 5th, the major scale gets one more sharp.

When done, then go to the list of major scales with flats.

Starting with C, every time you go a 5th down, you will get one more flat in the scale. So the list for the major scales with flats is:

C major (0 flats)

F major (1 flat)

Bb major (2 flats)

Eb major (3 flats)

Ab major (4 flats)

Db major (5 flats)

Gb major (6 flats)

Btw, instead of saying a 5th down, I could also have said a 4th up, this is explained in the lesson characteristics of intervals.

You might have noticed that the two lists have together 14 items. That’s strange, because there are only 12 different notes, so also 12 different major scales. Well, as you can see, the C is repeated, so this eliminates already 1 item. When you look well at both lists, you can also see that the last item in list 1 is exactly the same as the last item in list 2: F# and Gb are enharmonic equivalent notes. So they are exactly the same note, only written differently. When you found the right notes for both major scales, you will see that they consist of exactly the same notes, but written as their enharmonic equivalents.

All the major scales (solutions)

It’s time to check if you found the right major scales, so first the table with the major scales with sharps:

Root

(first note)

Notes of the major scale
C C   D   E   F   G   A   B   C
G G   A   B   C   D   E   F#   G
D D   E   F#   G   A   B   C#   D
A A   B   C#   D   E   F#   G#   A
E E   F#   G#   A   B   C#   D#   E
B B   C#   D#   E   F#   G#   A#   B
F# F#   G#   A#   B   C#   D#   E#   F#

And now the table with the major scales with flats:

Root

(first note)

Notes of the major scale
C C   D   E   F   G   A   B   C
F F   G   A   Bb   C   D   E   F
Bb Bb   C   D   Eb   F   G   A   Bb
Eb Eb   F   G   Ab   Bb   C   D   Eb
Ab Ab   Bb   C   Db   Eb   F   G   Ab
Db Db   Eb   F   Gb   Ab   Bb   C   Db
Gb Gb   Ab   Bb   Cb   Db   Eb   F   Gb

 

Compare the F# major scale from the first table with the Gb major scale from the second table: both scales are exactly the same, the notes are only written differently.

Note also the E#, which is enharmonic equivalent with F, and the Cb, the enharmonic equivalent of B.

Other enharmonic equivalent scales

You might have asked yourself: “Why are the Gb and F# scales listed as enharmonic equivalent scales and not for example Db and C#, or Ab and G#? Why are only the ‘flat scales’ listed?”

You will understand this better with the circle of fifths, but the short answer is: “Of course, you can make the C# major scale, the G# major scale and so on, but they have so many sharps (even double sharp notes), that they become difficult to handle.” What would you prefer? The Ab major scale with 4 flats, or the G# major scale with 8 sharps? I think the choice is not so difficult…

 

It’s of very big importance to know well your major scales. It will help you with all the other music theory if you can quickly come up with the right scale in all the 12 different keys. For that purpose, it’s important to practice a lot. The exercise below is an excellent way to practice your major scales.

Place the notes of a major scale on the piano

 

I hope that you learned a lot in this lesson about major scales and that the exercise helped you to quickly master the scales in all 12 keys.

Please tell us what you think of this lesson and the exercise by leaving a comment below.