Grade Five Music Theory Lesson 7: Intervals

B-D as a melodic (horizontal) interval:	B-D as a harmonic (vertical) 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
B-D	3	a third
B-D sharp	3	a third
E-A	4	a fourth
C sharp - G sharp	5	a fifth
C-G sharp	5	a fifth
D-B flat	6	a sixth
A-G	7	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).

G-G is a unison

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?

First, 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!

Now 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).

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.

G-C is a perfect fourth and

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):

C-G is a perfect fifth and

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.

So, G-B is a major third but

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:

B-G is a minor sixth but

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).

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

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:

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

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 and their Inversions:

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

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

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

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

C-G flat is a diminished 5th.

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

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):

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!