Welcome to Music Theory for the Songwriter!!

Theory lesson 3: Intervals

An interval is simply how far a note is from the tonic.
A tonic is what you call the first note in a scale
In the key of E, the first note is E.
The first note in the E Major scale is E.
E is the tonic note.

Also...the first note in a scale is the 1st degree.....the 2nd note in a scale is the 2nd degree...and so on.

Let's use the key of C...it's the easiest...no sharps or flats.

In a melody you might play a C and then a D. How far is the D from the C? Well, in counting an interval, you count the original note also. C plus D makes two notes so the interval is two notes in length...a 'second' (2nd).

So for the key of C the intervals are as follows:

C to D - 2nd 
C to E - 3rd 
C to F - 4th 
C to G - 5th 
C to A - 6th 
C to B - 7th 
C to C - 8ve 'Octave '

But it's not exactly that simple. These are just the interval "type's". There is also interval 'quality'.

There are 5 different interval Qualities:


In a Major key...each interval is either Perfect or Major.

The 1st, 4th, 5th and Octave intervals are always Perfect intervals. eg. (C to F...Perfect 4th...C to G...Perfect 5th)

The 2nd, 3rd, 6th and 7th are always major. eg. (C to D...Major 2nd...C to A...Major 6th)

To read the following ....P means Perfect interval.....M means Major interval:

The scale of C Major 
C     D      E     F     G     A     B      C 
P     M      M     P     P     M     M      P 
This means that a 
2nd....C to D...is a Major 2nd interval 
3rd....C to E...is a Major 3rd interval 
4th....C to F...is a Perfect 4th interval 
5th....C to G...is a Perfect 5th interval 

But what if you took a 3rd(C to E), and changed the E to an Eb? It's still a 3rd, because the letter name is still E, and C to E is a 3rd whether that E is flat, natural, or sharp.

So how can you tell which kind of 3rd is meant? You know that the interval C to E is a Major 3rd. So making the E flat, makes the interval shorter; it is decreased. Whenever you decrease a Major interval by one half step, it becomes minor. So then the interval C to Eb is a minor 3rd:

If you increase a Major interval by one half step, it becomes an Augmented.
If you decrease a Major interval by one half step, it becomes a minor.
If you decrease a Minor interval by one half step, it becomes a diminished.

If you increase a perfect by one half step, it becomes Augmented.
If you decrease a perfect by one half step, it becomes diminished.

Perfects can be lowered to become diminished
Perfects can be raised to become Augmented
The order according to size from smallest to largest is:
diminished -- Perfect -- Augmented

Majors can be lowered to become minor....then lowered again to become diminished.
Majors can be raised to become Augmented .
The order according to size from smallest to largest is:
diminished -- minor -- Major -- Augmented

Majors can never become Perfects...and Perfects can never become Majors.

Likewise, minors can never become Perfects, and Perfects can never become minors.

Here is a chart representing all the intervals a Half step at a time in one octave. It shows how many half steps are in each interval.

C to C#   -   1 Half step   -   minor 2nd 
C to D    -   2 Halfsteps   -   major 2nd 
C to D#   -   3 Halfsteps   -   minor 3rd 
C to E    -   4 Halfsteps   -   major 3rd 
C to F    -   5 Halfsteps   -   perfect 4th 
C to F#   -   6 Halfsteps   -   augmented 4th..or..diminished 5th 
C to G    -   7 Halfsteps   -   perfect 5th 
C to G#   -   8 Halfsteps   -   augmented 5th..or..minor 6th 
C to A    -   9 Halfsteps   -   major 6th 
C to A#   -  10 Halfsteps   -   minor 7th 
C to B    -  11 Halfsteps   -   major 7th 
C to C    -  12 Halfsteps   -   8th..or Octave 

You don't have to memorize the half steps, but you should memorize all twelve interval names in order. (minor 2nd, Major 2nd, minor 3rd, Major 3rd, etc)

We use a capital M to stand for Major and a small m to stand for minor. Diminished is a small d....Augmented is a capital A. Perfect is a P.

Do you see all the enharmonics in the chart above? Diminished 4th is the same as Major 3rd, the exact same interval.
If you take the higher note of the Perfect 4th and lower it by a half step, you make a diminished 4th.
P4th: C to F so C to E is a d4th. but C to E is also a M3rd.

Other enharmonics are:
A2nd, m3rd ... A3rd, P4th ... A4th, d5th ... A5th, m6th ... A6th, m7th ... and an A7th is an octave. (C to C)

To help you see the enharmonics more easily, here is one more list of the interval types and qualities with the enharmonics in brackets. The best enharmonic names to use in order to help memorize the interval order, in my opinion, would be the ones that are not in brackets.

m 2nd 
M 2nd 
m 3rd 
M 3rd (d4th) 
P 4th 
A 4th (d5th) 
P 5th 
A 5th (m6th) 
M 6th (d7th) 
m 7th (A 6th) 
M 7th 
P 8ve 

Interval Inversions

If you reverse the order of an interval....for example if the lower note is C and the higher note is G and you lower the G by an octave so that the lower note is G and the higher note is C....the reversed order changes both the quality and the type of interval.

When inverted, 2nds always become 7ths 
When inverted, 3rds always become 6ths 
When inverted, 4ths always become 5ths 
When inverted, 5ths always become 4ths 
When inverted, 6ths always become 3rds 
When inverted, 7ths always become 2nds 

For easier memorization: 
2nds become 7ths,  7ths become 2nds 
3rds become 6ths,  6ths become 3rds 
4ths become 5ths,  5ths become 4ths 

When inverted, Majors always become minors
When inverted, minors always become Majors
When inverted, Perfects always remain Perfects
When inverted, diminished always becomes Augmented
When inverted, Augmented always becomes diminished

For easier memorization:
Majors become minors, minors become Majors
diminished becomes Augmented, Augmented becomes diminished
Perfects remain Perfects

Here is a chart showing the inversion of both the type and the Quality of the intervals:

minor 2nd       becomes      Major 7th 
Major 2nd       becomes      minor 7th 

minor 3rd       becomes      Major 6th 
Major 3rd       becomes      minor 6th 

Perfect 4th     becomes      Perfect 5th 
Perfect 5th     becomes      Perfect 4th 

minor 6th       becomes      Major 3rd 
Major 6th       becomes      minor 3rd 

minor 7th       becomes      Major 2nd 
Major 7th       becomes      minor 2nd 

I didn't mention the first interval called a 'unison'. It is an interval of two exactly equal pitches. From C to C (but not next octave C...the same original C is played). Unisons are Perfect as well as Octaves. When inverted, unisons remain unisons, and octaves remain octaves. (perfects remain perfects)

Theory Lessons

Theory Lesson 1: Scales
Theory Lesson 2: Key Signatures
Theory Lesson 4: Chord Formation
Theory Lesson 5: Modes

Other Theory Links

Jason's Theory Page
(more to come)

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