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Triads do not always appear with the root at the bottom. Let's learn about the other possibilities...
All of the triads we have met so far have been in root position: with the root of the triad at the bottom, the third above it, and the fifth above that.
However, it's easy to see that we could place the notes of a triad in any octave, and end up with any of the three notes at the bottom. Each of these variations is called an inversion.
There are three inversions in which a triad can appear. These are defined by the note that appears at the bottom of the triad: the bass note. We have already encountered the first type – root position – in which the bass note is also the root of the triad.
When a different note appears in the bass, the triad has been "inverted". The root appears higher up, and a different note appears in the bass. There are two kinds of inversion other than root position, and we conveniently call these first inversion and second inversion.
When the third is used as the lowest note of the triad, the triad is said to be in first inversion.
We add the letter "b" to the Roman numeral notation to show that a triad is in first inversion; therefore, triad
I in first inversion is called
Ia refers to the root position form, but a simple
I is usually sufficient to describe the root position form. The same notation is used for minor triad inversions:
ia (or just
The second type of triad inversion is called the second inversion. A triad in second inversion has the fifth degree in the bass and is described by a "c" in Roman numeral terms - for example,
Ic for a triad on the tonic in a major key, or
ic in a minor key.
Using the form of notation in which a chord of A major is A and a chord of A minor is Am, we do not use
c to indicate inversions.
Instead, it is often down to the player to choose the inversion, but if a specific inversion is required, the chord might be written as Am/C to call for a first inversion A minor chord, or G/D if a second inversion G major chord is needed.
Where is the 4th?
In root position, a triad is comprised of two 3rds stacked on eachother, but you can see that in the first and second inversions, there is always a 3rd and a 4th.
In first inversion, the 3rd is at the bottom and the 4th is on top; and in second inversion the 3rd is on top and the 4th is on the bottom.
Try to get used to these characteristic shapes, as this will help you quickly spot the correct inversion of a triad or a chord.
Chords in inversions
Remember that a chord is a general name for three or more notes sounding together, and that a triad is a special kind of chord. It is possible to have chords in inversions, just the same as triads.
Here is an example that you've seen before:
Not all of these C major chords are root position C major chords. The fourth from the left has an E in the bass, and is therefore in first inversion, and the 6th from left has a G in the bass, and is therefore in second inversion. All of the others have C in the bass, and are in root position.
Bass not root
It is important to distinguish between the bass of a chord or triad, and the root of a chord or triad.
Only in root position are they the same note!
In first and second inversions, the bass note is not the same as the root note.
Triads in other keys
Here are some tonic triads in some other keys that you might have encountered recently, in all inversions. Compare in particular the major and minor triads that have the same root, such as E major and E minor, and look for the major and minor 3rds between the 1st and 3rd degree.
Figured bass notation
There is another way of symbolically notating inversions which you will come across in music theory, which comes from the system of figured bass notation found in Baroque music.
An example of this notation is shown below:
In this example, the numbers "6", "4", "5" and "3" refer to the interval of each note above the bass note of the triad.
So, in root position, the numbers are "5" and "3" for a third and a fifth. In first inversion, the numbers are "6" and "3" because the notes in the triad are now a third and a 6th above the bass note. In second inversion, the notes are a 4th and a 6th above the bottom note.
When writing down triads using the shorthand Roman numeral method, you can use the figured bass notation instead of
c to indicate inversions, as shown in the example above. Either form is correct and you are likely to come across both.
Are you sure you've understood everything in this study guide? Why not try the following practice questions, just to be sure!