Music theory > Pitch of sounds > Intervals

Intervals

An interval is the inclusive distance between two notes. An interval may be melodic or harmonic.

Each melodic or harmonic interval has a number and a quality, we will see this later.

Melodic interval

A melodic interval is an interval in a melody when notes are played one after the other:


Harmonic interval

An harmonic interval is an interval between two notes in the same chord, when notes are been playing at the same time:


Number of an interval

Each interval has a number that is the number of letter name it contains. For example, if you consider the interval starting from C and ending on G, you must count like this: C-D-E-F-G = 1-2-3-4-5, so this interval is a fifth (5th).

List of interval numbers


1 Unison
2 Second
3 Third
4 Fourth
5 Fifth
6 Sixth
7 Seventh
8 Octave
9 Ninth
10 Tenth
11 Eleventh
12 Twelfth
13 Thirteenth
.. ......
.. ......
and so on

Ascending and descending intervals

An interval may be ascending or descending:

Ascending and descending intervals

Interval quality

To identify intervals with precision, intervals have a quality identifier.

Qualities of intervals may be one of them:

- Perfect
- Major
- Minor
- Augmented
- Diminished
- Doubly diminished
- Doubly augmented

But all intervals can't be identified with some of all identifiers, here are all possibility:

MajorMinorPerfectAugmentedDiminishedDoubly augmentedDoubly diminished
Unisoninvalidinvalidvalidinvalidinvalidinvalidinvalid
Secondvalidvalidinvalidvalidvalidvalidvalid
Thirdvalidvalidinvalidvalidvalidvalidvalid
Fourthinvalidinvalidvalidvalidvalidvalidvalid
Fifthinvalidinvalidvalidvalidvalidvalidvalid
Sixthvalidvalidinvalidvalidvalidvalidvalid
Seventhvalidvalidinvalidvalidvalidvalidvalid
Octaveinvalidinvalidvalidinvalidinvalidinvalidinvalid

Below is the same table but classified to be more clear:

MajorMinorPerfectAugmentedDiminishedDoubly augmentedDoubly diminished
Unisoninvalidinvalidvalidinvalidinvalidinvalidinvalid
Octaveinvalidinvalidvalidinvalidinvalidinvalidinvalid
Fourthinvalidinvalidvalidvalidvalidvalidvalid
Fifthinvalidinvalidvalidvalidvalidvalidvalid
Secondvalidvalidinvalidvalidvalidvalidvalid
Thirdvalidvalidinvalidvalidvalidvalidvalid
Sixthvalidvalidinvalidvalidvalidvalidvalid
Seventhvalidvalidinvalidvalidvalidvalidvalid


Only unisons, fourths, fifths and octaves can be perfects but never major or minor.

Only seconds, thirds, sixths and sevenths can be major or minor but never perfects.

Intervals qualities in the C Major scale

Starting from the first note of the C Major scale, all intervals are only Majors or Perfects

C Major scale
C - CUnisonPerfect
C - DSecondMajor
C - EThirdMajor
C - FFourthPerfect
C - GFifthPerfect
C - ASixthMajor
C - BSeventhMajor
C - COctavePerfect

You should keep in mind that in all Major scales, from the first note of the Major scale, all intervals are only Majors or Perfects.

Augmented and diminished intervals


Augmented and diminished intervals

- When a half step united states of america (semitone united kingdom) is added to a major interval, it results in an augmented interval
- When a half step united states of america (semitone united kingdom) is removed to a major interval, it results in a diminished interval

- When a half step united states of america (semitone united kingdom) is added to a perfect interval, it results in an augmented interval
- When a half step united states of america (semitone united kingdom) is removed to a perfect interval, it results in a diminished interval

- When a half step united states of america (semitone united kingdom) is added to an augmented interval, it results in a doubly augmented interval
- When a half step united states of america (semitone united kingdom) is removed to a diminished interval, it results in a doubly diminished interval

Examples of augmented and diminished intervals


Examples of minors, majors, augmented and diminished intervals


How to find interval name and quality?

For example, let's consider the interval C - B♭ :

Interval C - B flat

C D E F G A B = 1 2 3 4 5 6 7 = Seventh

The name of the interval C - B♭ is Seventh.

Now we will find the quality of this interval:

We know that from the first note of the C Major scale, all intervals are only Majors or Perfects and that only seconds, thirds, sixths and sevenths can be major or minor but never perfects...

So the interval C - B natural is a seventh major, so the interval C - B♭ is a seventh minor!

Interval C - B flat

That's all! Easy no?

Enharmonic

Two notes are enharmonic when they are tuning the same pitch but spelled or named differently, examples:

Enharmonic notes

Inversion of intervals

An interval may be inverted by raising the lower pitch an octave or lowering the upper pitch an octave, example:

Inversion of intervals

inversion unison - octave

unison become octave

inversion second - seventh

second become seventh

inversion third - sixth

third become sixth

inversion fourth - fifth

fourth become fifth

inversion fifth - fourth

fifth become fourth

inversion sixth - third

sixth become third

inversion seventh - second

seventh become second

inversion octave - unison

octave become unison


During inversions, intervals qualities change like this:

- Diminished intervals become augmented
- Minors intervals become majors
- Majors intervals become minors
- Augmented intervals become diminished
- Perfects stay perfects

Compound intervals

A compound interval is an interval greater than one octave:

compound intervals

The quality of a compound interval is the same as the corresponding simple interval.


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