Intervals

An interval is the inclusive distance between two music notes. An interval can 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:


Melodic motions

Melodic motions can be conjunct or disjunct:

Conjunct melodic motion

When 2 notes follow each other, then it is a conjunct melodic motion:


(Conjunct melodic motions can be ascending or descending)

Disjunct melodic motions

When 2 notes do not follow each other, then it is a disjunct melodic motion:


(Disjunct melodic motions can be ascending or descending)

Number of an interval

Each interval has a number that is the number of letter name it contains.

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

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).

The unison is a null interval, that is to say that the 2 music notes of a unison intervall have the same sound.

Numbers and intervals

Ascending and descending intervals

An interval can be ascending or descending:

Ascending and descending intervals

Interval quality

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

Qualities of intervals can 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 possibilities:

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 is removed to a major interval, it results in a diminished interval
  • When a half step is added to a perfect interval, it results in an augmented interval
  • When a half step is removed to a perfect interval, it results in a diminished interval
  • When a half step is added to an augmented interval, it results in a doubly augmented interval
  • When a half step 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 majors or minors but never perfects...

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

Interval C - B flat

That's all! Easy no?

Numbers of whole steps (tones) in intervals

List of intervals according to the number of whole steps (tones):

MajorMinorPerfectAugmentedDiminishedDoubly augmentedDoubly diminished
Unison0
Second10.51.52
Third21.52.5130.5
Fourth2.5323.51.5
Fifth3.5434.52.5
Sixth4.5453.55.53
Seventh5.5564.56.54
Octave6

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 can 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 intervals 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.

Intervals in the chromatic scale

Each notes of the chromatic scale are separated by a harf step interval (semitone), which can be either diatonic or chromatic:

Here is the ascending chromatic scale played on the piano:

ascending chromatic scale

And the descending chromatic scale:

descending chromatic scale

Reminder :
- A half step is chromatic when the two notes have the same name (C / C♯)
- A half step is diatonic when the two notes do not have the same name (C / D♭)

Liste of intervals


External links to learn more about :

1 - https://www.dolmetsch.com/musictheory12.htm
2 - https://en.wikipedia.org/wiki/Interval_(music)


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