Music Intervals

Type - Quality - Number - Class - Inversions

Music Intervals are the difference in pitch between any 2 notes or tones.

Diatonic Intervals occur between the notes of a diatonic scale while chromatic intervals occur between the notes of a chromatic scale.

  • Diatonic Scales consist of tones and semitones
  • Chromatic Scales consist of semitones only

Intervals are named depending on their position in the scale.

Simple Intervals: Intervals that are shorter than or equal to an octave

Music Intervals
Compound Interval

Compound Intervals: Intervals which are beyond the range of an octave.

The Octave: The most fundamental interval as it determines the first and last note of the scale.

Unison: When you have 2 notes of the same pitch.

All other intervals are determined by their distance from the first note of the scale, also known as the Root or Tonic. These intervals are called seconds (2nds), thirds (3rds), fourths (4ths), fifths (5ths), sixths (6ths) and sevenths (7ths).

Further Definition: There is a system of names which further defines each interval. These are perfect, major, minor, augmented and diminished intervals.

  • The term Perfect applies to the Unison (1st), the 4th, the 5th and the Octave (8th).
  • The 2nd, 3rd, 6th and 7th intervals may be either Major or Minor.
  • The interval between the 4th and 5th in a Diatonic scale is called the Tritone.

The Tritone can be either an augmented 4th or a diminished 5th. This is because of enharmonic spellings. It is actually the same interval but with 2 different names.

Quality & Number of Interval

To name an interval, we need to determine the quality and number of the interval, e.g., a minor third (m3) is the name of the interval. The m (minor) describes the quality of the interval, while the third (3) describes the number of the interval.


Rules for Music Intervals:

  • Minor Interval - contains 1 semitone less than a major interval.
  • Major Interval - contains 1 semitone more than a minor interval.
  • Augmented Interval - contains 1 semitone more than a Perfect or Major Interval.
  • Diminished Interval - contains 1 semitone less than a Perfect or Minor Interval.
  • Perfect Interval - raised by one semitone becomes an Augmented Interval.
  • Perfect Interval - lowered by 1 semitone becomes a Diminished interval.
  • Intervals are always counted upwards unless stated to the contrary, with the lower note counted as 1.
  • The lower note of a music interval is always classed as the keynote or root of the interval in question, even when inverted.
  • A major third is equal to 4 half steps or 4 semitones ( 2 tones)
  • A minor third is equal to 3 half steps or 3 semitones (1+1/2 tones)
  • 1sts, 4ths, 5ths and 8ths can be made Perfect, Augmented and Diminished.
  • 2nds, 3rds, 6ths and 7ths can be made Major, Minor, Augmented and Diminished.

Classes of Intervals

Harmonic & Melodic Music Intervals

Music Intervals can be classed as Harmonic or Melodic.

  • Harmonic - are formed when 2 notes are played together
  • Melodic - are formed when 2 notes are played in succession....(one after the other)

They are divided into 2 classes. 1) Consonant 2) Dissonant

  1. Consonant Intervals - satisfactory to the ear and do not need resolution.
  2. Dissonant Intervals - unsatisfactory to the ear and generally require resolution

By resolution is meant passing from a dissonant interval to a consonant interval.

Consonant Intervals:

Divided into 2 classes: 1) Perfect and 2) Imperfect

  1. Perfect Intervals: 1sts, 4ths, 5ths & 8ths
  2. Imperfect Intervals: Major Thirds, Minor Thirds, Major Sixths and Minor Sixths.

Dissonant Intervals:

2nds, 7ths, 9ths and all Augmented and Diminished Intervals


Compound Intervals:

Intervals which are beyond the range of an octave.

  • When a 2nd is an octave higher, it is called a 9th.
  • When a 3rd is an octave higher, it is called a 10th.
  • When a 4th is an octave higher, it is called an 11th.
  • When a 5th is an octave higher, it is called an 12th.
  • When a 6th is an octave higher, it is called a 13th...

Interval Inversions

A simple interval can be inverted by raising the lower pitch an octave, or lowering the upper pitch an octave. To invert, place the lower note above the upper note or vice versa, e.g. the interval C - E upon inversion becomes E - C.

There are 2 rules to remember in determining the number and quality of any simple interval inversion...

1. Numerical value of an Inversion:
  • The number of the interval and the interval inversion always add up to 9... OR
  • Subtract the interval number from 9. The remainder is the numerical value of the Inversion.
In the example above C - E, this is a third interval. Upon inversion E - C becomes a sixth interval. If you add the 3rd interval and 6th interval, you reach 9. Alternatively, if you subtract the interval number (3rd) from 9, you get the interval inversion (6th). Now we need to calculate the quality of the interval, i.e. minor, major, diminished, augmented, perfect, etc.

2. Quality of an Inversion:

  • Major becomes a Minor: e.g. a major 3rd becomes a minor 6th (9 - 3 = 6) Example: C - E is a major 3rd. Upon inversion, E - C becomes a minor 6th.

  • Major becomes a Minor: e.g. a major 7th becomes a minor 2nd (9 - 7 = 2) Example: C - B is a major 7th. Upon inversion, B - C becomes a minor 2nd.

  • Minor becomes a Major: e.g. a minor 3rd becomes a major 6th (9 - 3 = 6) Example: C - E♭ is a minor 3rd. Upon inversion, E♭ - C becomes a major 6th.

  • Minor becomes a Major: e.g. a minor 7th becomes a major 2nd (9 - 7 = 2) Example: C - B♭ is a minor 7th. Upon inversion, B♭ - C becomes a major 2nd

  • Augmented becomes Diminished: e.g. an augmented 5th becomes a diminished 4th (9 - 5 = 4) Example: C - G# is an augmented 5th. Upon inversion, G# - C becomes a diminished 4th.

  • Diminished becomes Augmented: e.g. a diminished 7th becomes an augmented 2nd (9 - 7 = 2) Example: C - B♭♭ is a diminished 7th. Upon inversion, B♭♭ - C becomes an augmented 2nd

  • A Perfect Interval always remains Perfect because it is common to both keys. Let us look at this example. You know that a perfect interval is a 1st, 4th, 5th or 8th. If you subtract any of these from 9, you still get a 1st, 4th, 5th or 8th, which are all perfect intervals. e.g. a perfect 4th becomes a perfect 5th (9 - 4 = 5) Example: C - F is a perfect 4th. Upon inversion, F - C becomes a perfect 5th.

Let's Recap Music Intervals:
  • Diatonic Interval - occurs in an unaltered Diatonic Scale.
  • Chromatic Interval - occurs in an unaltered Chromatic Scale.
  • Harmonic Interval - sounds are heard simultaneously or together.
  • Melodic Interval - sounds are heard in succession or one after the other.
  • Simple Interval - contained within the range of an octave.
  • Compound Interval - beyond the range of an octave.

Tritones

A Tritone is a Music Interval which contains 3 full tones (diatonic) or 6 semitones(chromatic)

In a Major Key, there is one example of a tritone between the subdominant (4th degree of a scale) and the leading note (7th degree of the scale), e.g., in the C Major Scale C D E F G A B there are 3 full tones from F (4th degree) to B (7th degree)

In a Harmonic Minor Key there are 2 tritones:

  1. Between the subdominant (4th degree) and the leading note(7th degree)

    e.g. D Harmonic Minor: D - E - F - G - A - B - C# (3 whole tones between G and C#)

  2. Between the subdominant (6th degree) and the upper supertonic (2nd degree)

    e.g. D Harmonic Minor: D - E - F - G - A - B - C# - D - E (3 whole tones between Bb and E)

Music Intervals in a Chromatic Scale

The following table shows the common names used for intervals between the notes of a chromatic scale.

  • A semitone is any interval between two adjacent notes.
  • A whole tone is any interval spanning two semitones.
  • A tritone is any interval spanning three tones or six semitones.

Initials For Intervals: perfect (P), major (M), minor (m), augmented (A), and diminished (d).

Semitones Major / Minor / Perfect Initials Augmented / Diminished Initials Latin Initials
0 Perfect Unison P1 Diminished Second d2  
1 Minor second m2 Augmented Unison A1 Semitone S
2 Major Second M2 Diminished Third d3 Whole Tone T
3 Minor Third m3 Augmented Second A2  
4 Major Third M3 Diminished Fourth d4  
5 Perfect Fourth P4 Augmented Third A3  
6 Diminished Fifth A4 Diminished Fifth d5 Tritone TT
6 Augmented Fourth d5 Augmented Fourth A4 Tritone TT
7 Perfect Fifth P5 Diminished Sixth d6  
8 Minor Sixth m6 Augmented Fifth A5  
9 Major Sixth M6 Diminished Seventh d7  
10 Minor Seventh m7 Augmented Sixth A6  
11 Major Seventh M7 Diminished Octave d1  
12 Perfect Octave P8 Augmented Seventh A7  
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