## 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:

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:

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!).

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.

4

## Inversions

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

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.

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.

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

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:

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:

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

From E to F# (or Gb):

From Bb (or A#) to C:

## 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:

From A to C:

From F# to A:

From Bb to Db:

## The major third

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

Examples:

From C to E:

From Eb to G:

From A to C#:

From F# to A#:

## 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:

From F to Bb:

From Eb to Ab:

From A# to D#:

## 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#:

From Ab to D:

## 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:

From A to E:

From Eb to Bb:

From F# to C#:

## The minor sixth

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

Examples:

From C to Ab:

From F# to D:

## The major sixth

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

Examples:

From C to A:

From Eb to C:

## The minor seventh

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

Examples:

From C to Bb:

From F# to E:

## 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:

From Gb to F:

## 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:

Or, from Ab to Ab:

## 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):

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

## 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)

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.

## What are scales? Major scale vs minor scales

What are scales? How can you hear the difference between a major scale and a minor scale?

## What are scales?

Let’s start with the first question: what are scales?

A scale is a set of notes (usually 7 different notes) that you can play in ascending order, descending order or in any other order.

You can define a certain scale by the intervals between its consisting notes.

As you will see later, the scale determines the mood of the music.

## The difference between a major scale and a minor scale

As I said before, a scale sets the mood of the music. Below, you can listen to the C major scale played in ascending order over a C major chord.

And now, here below, listen to the C (natural) minor scale played in ascending order over a C minor chord.

Did you hear the difference? The major sound is much happier, the minor sound is more sad, tragic or melancholic.

Notice that both scales start on a (low) C and end on a (high) C and consist of 7 different notes (you hear a sequence of 8 notes, but the C is played as the first and lowest note and as the last and highest note, so twice). So the only difference between both scales are the intervals between their consisting notes.

I hope you liked this mini-lesson about the difference between major and minor harmony. Please tell us what you think of this lesson by leaving a comment below.

## The note names and how to find the notes on a piano keyboard

What are the music note names used in Western music?

In Western music, we can distinguish 12 different notes. Every song or piece of music is made of only those 12 different notes.

The easiest way to show the 12 notes is on a piano keyboard. On the keyboard, you can see a repetitive pattern of white and black keys.

One such a pattern consists of 12 keys,

7 white keys:

and 5 black keys:

Those are exactly the 12 different notes in Western music we spoke of above.

## The note names of the white keys

This might sound funny, but to find the names of the white keys, look first at the black keys: they come in groups of 2 black keys and 3 black keys. Just at the left of a group of 2 black keys you can find the note C.

To find the names of the other white keys, just go up alphabetically to G as in the next figure.

Now, we have to name 2 more white keys. Notice that we’ve used the letters C to G in alphabetical order, but we haven’t used the 2 first letters of the alphabet yet. So, let’s use them for the 2 missing keys, as follows:

## The note names of the black keys

Do you remember that we had to look at the black keys first to find the names of the white keys? Well, let’s reverse the roles now: to find the names of the black keys, we have to look at the white key names first, since the names of the black keys are derived from the white key names.

As you can see, a black key is always situated between 2 white keys. The black key indicated by the arrow in the figure below is for example between the C and the D. As this note is higher than the C, but lower than the D (the pitch of the notes gets higher when you go from left to right), we call this note C sharp, or D flat. So, sharp means: the note just at the right, and flat means: the note just at the left. We write C sharp as C# and D flat as Db.

So the black keys actually have 2 names, the name of the white key at the left with a sharp (#) sign, or the name of the white key at the right with a flat (b) sign.

In the next figure, you can see all the names of the notes on a piano keyboard.

As you can see, this is a pattern of 12 different notes (represented on the piano by 7 white keys and 5 black keys) that repeats itself.

## Double sharps and double flats

Btw, notice that on the right side of the B and on the right side of the E, there is no black key. So you could call the C also B#, and the F an E#. Or, in the same way, you could call the B a Cb and the E an Fb. In music theory, this is sometimes needed (the 7th note in the F# major scale is an E#, not an F, even if it is exactly the same note). It is even possible to have double flats (bb) or double sharps (##). For example, a C## is raised 2 times, so this is equivalent to a D. A shorter writing for double sharp looks a bit like an x (see figure below), so Cx would be the same note as C## or just simply D.

## Enharmonic equivalent

Two notes that are written differently, but that are actually one and the same note, are called enharmonic equivalent notes.

C# and Db are for example enharmonic equivalent notes: they are written differently, but are the same note.

Other examples:

• A# and Bb
• E# and F
• F## (or Fx) and G
• Bbb and A
• etcetera

After this lesson, you should be able to recognize the keys of the piano and know the names of the corresponding notes. In the beginning, you will probably not remember every note and every key on the piano, so just practice 5 minutes a day and you will see: in no time you will master it.

The exercises that are accesible via the links below will certainly help you to practice the notes.

Which note is played on the piano?

Place the note on the right key of the piano

Did you already know the note names and/or the corresponding keys on the piano? Did this lesson help you to learn the notes and keys on the piano? If so, please leave a comment below.
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