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Grade Five Music Theory Lesson 7: Intervals

Intervals

Intervals

An “interval” is the distance between any two notes. Each interval has a number and a quality, which you have to know for Grade 5 Music Theory. “Melodic intervals” are read horizontally and are found in melodies, whereas “harmonic intervalsare read vertically, and are found in chords.

They are described in the same way.

B-D as a melodic (horizontal) interval:     B-D as a harmonic (vertical) interval:
Melodic intervals Harmonic interval

 

 Interval Numbers

To find the number of an interval, first find the note names of the two notes, (ignore any sharps and flats for now), and count the letter names, starting with the lower note on the stave, (it could be the first or second note along on the stave if it is a melodic interval). 

Some examples: 

Letter Names
(start with lower note)

No. of Notes

Interval Number

Example

F-G

2

a second

A second

B-D

3

a third

A third

B-D sharp

3

a third

a third

E-A

4

a fourth

a fourth

C sharp - G sharp

5

a fifth

a fifth

C-G sharp

5

a fifth

a fifth

D-B flat

6

a sixth

a sixth

A-G

7

a seventh

a seventh

 

If the letter name is the same, the interval will be either "unison" (the same note), or "octave" (the next one up or down).

A unison

G-G is a unison

 

An octave

G-G1 is an octave

 

 Starting on the Higher Note - a Very Common Mistake!

What happens if you try to calculate an interval by starting with the higher note on the stave? You will get the wrong answer! This is a common mistake, so let’s look at an example of what can go wrong. What is the following melodic interval?

What is this harmonic interval 

Smiley faceFirst, the correct way: starting on the lower note (C), we count letter names to the higher note, (G), C-D-E-F-G =5, which gives us a 5th. This is the right answer! 

Sad faceNow the wrong way. Starting on the first note (G), we count the letter names to the second note (C), G-A-B-C =4, which gives us a 4th. This is the wrong answer!

 

Interval Qualities

Each interval has quality name which goes before it, for example “major sixth”.

There are 5 quality names which are: perfect, major, minor, augmented and diminished.

We will look at each of these interval qualities in more detail. 

 

 Perfect Intervals

Think of the scales of G major and G minor. What’s the difference? Let’s look at the note names: (the differences are underlined).

G Major:

G

A

B

C

D

E

F sharp

G

G Minor Harmonic:

G

A

B flat

C

D

E flat

F sharp

G

G Minor Melodic up:

G

A

B flat

C

D

E

F sharp

G

G Minor Melodic down:

G

F natural

E flat

D

C

B flat

A

G

 

 Let’s start with two intervals all the scales have in common- G-C and G-D. These intervals exist in both major and minor scales, and we call them perfect.

Perfect fourth

G-C is a perfect fourth and

 

Perfect fifth

G-D is a perfect fifth.

 

If you turn the intervals upside down, you get a mirror image (called inversion). Here are the above intervals inverted (remember, we always start on the lowest note):

Perfect 5th

C-G is a perfect fifth and

 

Perfect fourth

D-G is a perfect fourth.

 

The intervals of a fourth and a fifth are perfect intervals, when the higher note exists in either the major or minor scale of the lower note. Exact unisons and octaves are also defined as perfect.

 

Major and Minor Thirds and Sixths

Now let’s look more closely at the differences in the scales. G major has G-B, but both G minor scales (harmonic and melodic) have G-B flat.

Major third

So, G-B is a major third but

 

Minor third

G-B flat is a minor third.

 

If you turn those intervals upside down (or invert them), you have a mirror image too, and you find the sixths. Notice that major becomes minor, and minor becomes major:

Minor sixth

B-G is a minor sixth but

 

Major sixth

B flat -G is a major sixth.

 

Watch out here! B natural occurs in G major, but B-G is a minor interval, and although B flat occurs in G minor, B flat-G is a major interval! You should always think of your lower note as a kind of key signature when calculating intervals. 

Think of B-G as an interval in the key of B. G only occurs in B minor, so B-G is a minor interval. Similarly, with B flat - G, think of the key of B flat. G occurs in B flat major, so B flat- G is a major interval. 

Tip! A major 3rd/6th is always a minor 6th/3rd if inverted!

 

 Major and Minor Seconds and Sevenths

A tone is a major second (think of A-B in G major) but a semitone is a minor second (think A-B flat in G minor).

Major second

Similarly, D-E is a major second (think of C major) but

 

Minor second

D-E flat is a minor second (think of C minor).

 

The phenomenon of mirror images (inversion) applies here too, so inverted seconds become sevenths:

Minor seventh

E-D is a minor seventh (D natural occurs in E minor melodic descending) but

 

Major seventh

E flat -D is a major seventh (D occurs in E flat major).

 

Tip! A major 2nd/7th is always a minor 7th/2nd if inverted!

 

More about Inversions

Double checking by inversions can be a quick and convenient way to check your answers to interval questions. 

All inversions add up to 9: an inverted 3rd is a 6th (and vice versa), 3+6=9. An inverted 5th is a 4th; 4+5=9. An inverted 2nd is a 7th; 2+7=9. 

All major intervals become minor intervals when inverted, and vice versa.

 

Summary of the Common Intervals:

Here’s a summary of the common technical interval names, in order of size, starting with the smallest, with an example of each:

Minor 2nd  Minor 2nd 
2 Major 2nd  Major 2nd
3 Minor 3rd  Minor 3rd
Major 3rd   Major 3rd
5 Perfect 4th Perfect 4th
6 Perfect 5th Perfect 5th
7 Minor 6th Minor 6th
8 Major 6th Major 6th
9 Minor 7th Minor 7th
10 Major 7th Major 7th

 

 

 Diminished and Augmented Fourths and Fifths

Diminished intervals are narrower than normal, and augmented intervals are wider than normal, by the difference of one semitone.

C-G is a perfect 5th

So, the interval C-G is a perfect 5th, but

 

C-G# is an augmented 5th

the interval C-G sharp is an augmented 5th, and

 

C-Gb is a diminished 5th

C-G flat is a diminished 5th.

 

C-F is a perfect 4th

Similarly, C-F is a perfect 4th, but

 

C-F sharp is an augmented 4th

C-F sharp is an augmented 4th.

 

Notice that although G flat and F sharp are the same note on the piano, they are not the same technically!

 

Diminished and Augmented Seconds and Sevenths

In the harmonic minor scale, you will remember that we have a step of 3 semitones (marked 3S below):

The harmonic scale - tones and semitones

Here, D flat to E natural is clearly an interval of a second, since we count D - E which is 2 notes - but what kind of second is it? 

If we had D flat to E flat, we would have a major 2nd. The E natural makes the interval wider, so the interval D flat to E natural is an augmented 2nd

Tip! Every minor harmonic scale contains an augmented second between the sixth and seventh notes.

 

Remember our laws of inversions? Well, an inverted diminished interval is an augmented interval, and vice versa. So, if D flat to E natural is an augmented second, what is E natural to D flat? Point your mouse at the image below to find out!

Augmented 2ndWhat's this interval

 

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Grade Five Music Theory Lesson 7: Intervals

Intervals

Intervals

An “interval” is the distance between any two notes. Each interval has a number and a quality, which you have to know for Grade 5 Music Theory. “Melodic intervals” are read horizontally and are found in melodies, whereas “harmonic intervalsare read vertically, and are found in chords.

They are described in the same way.

B-D as a melodic (horizontal) interval:     B-D as a harmonic (vertical) interval:
Melodic intervals Harmonic interval

 

 Interval Numbers

To find the number of an interval, first find the note names of the two notes, (ignore any sharps and flats for now), and count the letter names, starting with the lower note on the stave, (it could be the first or second note along on the stave if it is a melodic interval). 

Some examples: 

Letter Names
(start with lower note)

No. of Notes

Interval Number

Example

F-G

2

a second

A second

B-D

3

a third

A third

B-D sharp

3

a third

a third

E-A

4

a fourth

a fourth

C sharp - G sharp

5

a fifth

a fifth

C-G sharp

5

a fifth

a fifth

D-B flat

6

a sixth

a sixth

A-G

7

a seventh

a seventh

 

If the letter name is the same, the interval will be either "unison" (the same note), or "octave" (the next one up or down).

A unison

G-G is a unison

 

An octave

G-G1 is an octave

 

 Starting on the Higher Note - a Very Common Mistake!

What happens if you try to calculate an interval by starting with the higher note on the stave? You will get the wrong answer! This is a common mistake, so let’s look at an example of what can go wrong. What is the following melodic interval?

What is this harmonic interval 

Smiley faceFirst, the correct way: starting on the lower note (C), we count letter names to the higher note, (G), C-D-E-F-G =5, which gives us a 5th. This is the right answer! 

Sad faceNow the wrong way. Starting on the first note (G), we count the letter names to the second note (C), G-A-B-C =4, which gives us a 4th. This is the wrong answer!

 

Interval Qualities

Each interval has quality name which goes before it, for example “major sixth”.

There are 5 quality names which are: perfect, major, minor, augmented and diminished.

We will look at each of these interval qualities in more detail. 

 

 Perfect Intervals

Think of the scales of G major and G minor. What’s the difference? Let’s look at the note names: (the differences are underlined).

G Major:

G

A

B

C

D

E

F sharp

G

G Minor Harmonic:

G

A

B flat

C

D

E flat

F sharp

G

G Minor Melodic up:

G

A

B flat

C

D

E

F sharp

G

G Minor Melodic down:

G

F natural

E flat

D

C

B flat

A

G

 

 Let’s start with two intervals all the scales have in common- G-C and G-D. These intervals exist in both major and minor scales, and we call them perfect.

Perfect fourth

G-C is a perfect fourth and

 

Perfect fifth

G-D is a perfect fifth.

 

If you turn the intervals upside down, you get a mirror image (called inversion). Here are the above intervals inverted (remember, we always start on the lowest note):

Perfect 5th

C-G is a perfect fifth and

 

Perfect fourth

D-G is a perfect fourth.

 

The intervals of a fourth and a fifth are perfect intervals, when the higher note exists in either the major or minor scale of the lower note. Exact unisons and octaves are also defined as perfect.

 

Major and Minor Thirds and Sixths

Now let’s look more closely at the differences in the scales. G major has G-B, but both G minor scales (harmonic and melodic) have G-B flat.

Major third

So, G-B is a major third but

 

Minor third

G-B flat is a minor third.

 

If you turn those intervals upside down (or invert them), you have a mirror image too, and you find the sixths. Notice that major becomes minor, and minor becomes major:

Minor sixth

B-G is a minor sixth but

 

Major sixth

B flat -G is a major sixth.

 

Watch out here! B natural occurs in G major, but B-G is a minor interval, and although B flat occurs in G minor, B flat-G is a major interval! You should always think of your lower note as a kind of key signature when calculating intervals. 

Think of B-G as an interval in the key of B. G only occurs in B minor, so B-G is a minor interval. Similarly, with B flat - G, think of the key of B flat. G occurs in B flat major, so B flat- G is a major interval. 

Tip! A major 3rd/6th is always a minor 6th/3rd if inverted!

 

 Major and Minor Seconds and Sevenths

A tone is a major second (think of A-B in G major) but a semitone is a minor second (think A-B flat in G minor).

Major second

Similarly, D-E is a major second (think of C major) but

 

Minor second

D-E flat is a minor second (think of C minor).

 

The phenomenon of mirror images (inversion) applies here too, so inverted seconds become sevenths:

Minor seventh

E-D is a minor seventh (D natural occurs in E minor melodic descending) but

 

Major seventh

E flat -D is a major seventh (D occurs in E flat major).

 

Tip! A major 2nd/7th is always a minor 7th/2nd if inverted!

 

More about Inversions

Double checking by inversions can be a quick and convenient way to check your answers to interval questions. 

All inversions add up to 9: an inverted 3rd is a 6th (and vice versa), 3+6=9. An inverted 5th is a 4th; 4+5=9. An inverted 2nd is a 7th; 2+7=9. 

All major intervals become minor intervals when inverted, and vice versa.

 

Summary of the Common Intervals:

Here’s a summary of the common technical interval names, in order of size, starting with the smallest, with an example of each:

Minor 2nd  Minor 2nd 
2 Major 2nd  Major 2nd
3 Minor 3rd  Minor 3rd
Major 3rd   Major 3rd
5 Perfect 4th Perfect 4th
6 Perfect 5th Perfect 5th
7 Minor 6th Minor 6th
8 Major 6th Major 6th
9 Minor 7th Minor 7th
10 Major 7th Major 7th

 

 

 Diminished and Augmented Fourths and Fifths

Diminished intervals are narrower than normal, and augmented intervals are wider than normal, by the difference of one semitone.

C-G is a perfect 5th

So, the interval C-G is a perfect 5th, but

 

C-G# is an augmented 5th

the interval C-G sharp is an augmented 5th, and

 

C-Gb is a diminished 5th

C-G flat is a diminished 5th.

 

C-F is a perfect 4th

Similarly, C-F is a perfect 4th, but

 

C-F sharp is an augmented 4th

C-F sharp is an augmented 4th.

 

Notice that although G flat and F sharp are the same note on the piano, they are not the same technically!

 

Diminished and Augmented Seconds and Sevenths

In the harmonic minor scale, you will remember that we have a step of 3 semitones (marked 3S below):

The harmonic scale - tones and semitones

Here, D flat to E natural is clearly an interval of a second, since we count D - E which is 2 notes - but what kind of second is it? 

If we had D flat to E flat, we would have a major 2nd. The E natural makes the interval wider, so the interval D flat to E natural is an augmented 2nd

Tip! Every minor harmonic scale contains an augmented second between the sixth and seventh notes.

 

Remember our laws of inversions? Well, an inverted diminished interval is an augmented interval, and vice versa. So, if D flat to E natural is an augmented second, what is E natural to D flat? Point your mouse at the image below to find out!

Augmented 2ndWhat's this interval

 

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grade 5 music theoryDownload this Grade 5 Music Theory Course

Buy Grade 5 Theory Past Papers

Get some help!

Resources by Music Grade: Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |