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What’s An Inversion?
To invert an interval is to turn it upside down: to take the lower note and move it up an octave, or take the higher note and move it down an octave. The order of the notes is reversed.
Interval + Inversion = Octave
A Special Relationship
Octaves have the unique property of being musically interchangeable.
Going up or down by an octave is like going up or down a flight of steps in an apartment building. Each octave is a higher or lower version of the next.
This means that there is a strong musical relationship between an interval and it’s inversion.
Melody And Harmony
Take a melody and a harmony, for instance.
A typical close harmony more-or-less follows the melody, adjusting here or there to fit the key (and the chords, but more on that in a future post). Usually, the harmony is sung higher than the melody.
The above example is played at the pitch of a female or young child’s voice. Now imagine that the harmony is sung by a lower voice such as that of an adult male.
Typically, adult male voices are typically about an octave lower than female or children’s voices. This would put the harmony an octave lower: lower than the melody.
As you can hear, the notes fit together just as well as the original. Sure, you can tell that the harmony is lower than it was, but they fit together just as well – as they should, because the note names are still the same.
Inversions And Interval Names
Theory is meant to reflect reality. If there’s an audible relationship between an interval and its inversion then their interval names should reflect this relationship.
Fortunately, they do.
Semitones And Letters
An interval plus its inversion equals an octave.
Consider the following example:
The first interval, A-E, is 7 semitones. Its inversion, E-A, is 5 semitones. This adds up to 12. An octave is 12 semitones, so that’s what we expect.
It doesn’t matter which way round we view this. Just as E-A is the inversion of A-E, so, too, the other way: A-E is the inversion of E-A. They are inversions of each other.
Now let’s look at their interval names. A-E is a perfect 5th and E-A is a perfect 4th. 5+4=9, yet the total is an octave, which is 8 letters.
The simple reason for this is because when we count an octave as two intervals, we count the middle note twice; once as the upper note of the first interval and again as the lower note of its inversion.
- An interval plus its inversion equals 12 semitones
- Also, an interval plus its inversion equals 9 letters
Let’s look at a few more, this time on G:
From these, we can add another observation:
- The inversion of a major interval is a minor interval
- The inversion of a perfect interval is a perfect interval
- The inversion of an augmented interval is a diminished interval
Also: - The larger the interval, the smaller its inversion
NOTE: There is nothing inherent in determining which is the interval and which is the inversion. They are interchangeable. They are inversions of each other.
How To Invert An Interval Name
To invert an interval is easy: we reverse the pitch order of the two notes. We can name the new interval from scratch using an interval ruler as shown in B2. Intervals 2: Augmented And Diminished Intervals, but there is a quicker way.
If we know the name of the original interval we can invert the interval name by using our observations of how the names of interval and inversion are related.
In general, the names invert as follows:
For example:
G-A is a major 2nd. What is its inversion?
- The degrees add up to 9
- 9 – 2 = 7
- A-G is a 7th
- As for the quality, major goes with minor
A-G is a minor 7th
Eb-G# is an augmented 3rd. What is its inversion?
- The degrees add up to 9
- 9 – 3 = 6
- G#-Eb is a 6th
- As for the quality, augmented goes with diminished
G#-Eb is a diminished 6th
F#-C# is a Perfect 5th. What is its inversion?
- The degrees add up to 9
- 9 – 5 = 4
- C#-F# is a 4th
- As for the quality, perfect goes with perfect
C#-F# is a perfect 4th
Try These…
a) Name the following intervals
b) Invert the following intervals
c) Name the inversion by inverting the interval name
- G-Bb
- G-D
- D-B
- D-G#
- E-Db
- F-Gb
Example: C-E
a) C-E is a major 3rd
b) To invert an interval, reverse the pitch order of the notes. C-E becomes E-C
c) To invert the interval name, major becomes minor and 3rd becomes 6th. E-C is a minor 6th
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NEXT LESSON: B6. How To Name Intervals The Quick Way
PART 2 CONTENTS: Basic Music Theory Course Contents
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Answers To Try These…
a) G-Bb is a minor 3rd
b) Invert G-Bb to get Bb-G
c) The inversion of a minor 3rd is a major 6th
a) G-D is a perfect 5th
b) Invert G-D to get D-G
c) The inversion of a perfect 5th is a perfect 4th
a) D-B is a major 6th
b) Invert D-B to get B-D
c) The inversion of a major 6th is a minor 3rd
a) D-G# is an augmented 4th
b) Invert D-G# to get G#-D
c) The inversion of an augmented 4th is a diminished 5th
a) E-Db is a diminished 7th
b) Invert E-Db to get Db-E
c) The inversion of a diminished 7th is an augmented 2nd
a) F-Gb is a minor 2nd
b) Invert F-Gb to get Gb-F
c) The inversion of a minor 2nd is a major 7th