Check for Understanding
In the key of C, what notes does a V⁴₂ have in it and what is the bass note? The C major scale is shown on a piano below.
Seventh chords can be inverted just like the basic chords. In this section, we will discuss the notation used to denote the different inversions of seventh chords and show how they are used in popular music. Recall from Hooktheory I that the basic chords each have three notes and two inversions. First and second inversions are a result of playing one of the other notes that make up the chord in the bass.
As a reminder, the following diagram shows the intervals between the notes in each inversion of a basic I chord and the longhand superscripts/subscripts of each inversion. The shorthand notation for inversions that we use in practice is shown below. The superscripts and subscripts used to label first and second inversions come from the spacing between the notes relative to the bass when written in this form. \n\nh4Labeling conventions for inversions of basic chords
The notation for inverted seventh chords works the same way, but since seventh chords have four notes, they have three inversions (one more than the basic chords). The following example shows scale degrees 1, 3, 5, and 7 of a I⁷ chord arranged with each note in the bass to create each inversion of I⁷. As in the inversions of the basic chords, the superscripts and subscripts used to label the first, second, and third inversions come from the spacing between the notes relative to the bass when written in this form.
The following table summarizes the superscript / subscript conventions for basic and seventh chords and their inversions.
| Superscript/subscript | Description |
|---|---|
| None | Basic chord in root position. |
| ⁶ | Basic chord in first inversion. |
| ⁶₄ | Basic chord in second inversion. |
| ⁷ | Seventh chord in root position. |
| ⁶₅ | Seventh chord in first inversion. |
| sup4sub3 | Seventh chord in second inversion. |
| ⁴₂ | Seventh chord in third inversion. |
To give a concrete example of a seventh chord and its inversions, a Cmaj7 chord (made up of C, E, G, and B – scale degrees 1, 3, 5, and 7 of the C major scale) is in root position if the lowest note being played is a C. It’s in first inversion if the lowest note being played is an E (Cmaj7/E). It’s in second inversion if the lowest note being played is a G (Cmaj7/G). It’s in its third inversion if the lowest note being played is a B (iCmaj7/B). Below you can listen to the Cmaj7 chord along with its three inversions:
Practice getting familiar with the naming conventions with the following challenge questions.
Check for Understanding
In the key of C, what notes does a V⁴₂ have in it and what is the bass note? The C major scale is shown on a piano below.
Check for Understanding
In the key of C, what notes does a ivi⁶₅ have in it and what is the bass note? The C major scale is shown on a piano below.
One of the most common uses of inverted chords that we learned about in Hooktheory I is in connecting bass lines. We learned, for instance, that if you want to get to a IV chord from a iii chord, using a I⁶ (I in first inversion) with its scale degree 3 in the bass is a great way to create a nice ascending melodic feel. Inversions of seventh chords are also frequently used in this way. Let’s look at some common examples in popular music.
One inverted seventh chord that often gets used as a bass connector is vi⁴₂ (vi⁷ in third inversion) to connect vi with IV (6 → 5 → 4 in the bass). “Can’t Help Falling in Love” by Elvis Presley uses the vi⁴₂ in this way. Listen as it continues with the descending bass pattern by proceeding by step to I⁶ then again to a Vsup4sub3 chord (a V⁷ chord in second inversion):
If you find yourself struggling to remember which scale degree is in the bass, use the colors to guide your eye. Anytime you see neighboring chords with colors that are next to each other in the rainbow, you’ll know the songwriter is connecting the notes in the bass.
“Can You Feel the Love Tonight” by Elton John is another great use of vi → vi⁴₂ → IV. After this pattern, you can see another great use of an inverted seventh to create an ascending pattern, as it goes ii → I⁶ → ii⁶₅ → V (2 → 3 → 4 → 5 in the bass):
“Octopus’s Garden” by The Beatles also uses vi⁴₂ to connect vi with IV. Also, don’t miss the I⁴₂ (I⁷ in third inversion) to connect I with vi. This creates a nice bass line of 1 → 7 → 6:
The above ivi⁴₂ examples showcase instances in which a seventh chord in third inversion is used to connect the bass lines of two neighboring chords. One of the reasons using a seventh chord in third inversion like this is so common is that it’s so natural to play on an instrument. You start by playing the basic root position chord and then you just keep playing the same chord but drop the bass by one note. For example, if a song started on a C major chord, the bass player can easily drop down to a B while the rest of the players continue playing exactly what they were before. Adding the B makes the C chord a Cmaj7 in third inversion (Cmaj7/B). Similarly, if the bass note is being played by a guitarist or a pianist, this technique can be achieved by moving a finger down one note/fret.
Another common inversion that often shows up in more complex pieces is the V⁴₂ (V⁷ in third inversion). The interesting thing about this chord is that while root position V⁷ has a very strong pull to I, V⁴₂ does not. The scale degree in the bass is 4 (V⁷ is made up of scale degrees 5, 7, 2, and 4), and many songs instead use it to effectively move to chords that have 3 in the bass such as I⁶ (I in first inversion) or iii.
“Fellow Travellers” by Procol Harum is good example of a V⁴₂ resolving down to a I⁶ chord.
Basic V chords (regardless of the inversion) usually do not go to iii, making this an interesting change in functionality resulting from the fact that scale degree 4 is now in the bass.
Japanese composer Nobuo Uematsu uses V⁴₂ → iii in the score for the video game Final Fantasy IV:
In “I’ll Make Love To You” by Boyz II Men, a slight variation of this idea is used:
Instead of going directly to iii (actually iii⁷), the songwriter briefly touches on the IV first. The bass is already playing the right scale degree, and this note is not replayed. The 4 in the bass is allowed to continue resonating as the rhythm section played by the synth strings slides easily to IV followed by iii⁷.
Check for Understanding
A passing chord is a short chord used to bridge two neighboring chords by connecting their bass line. Name at least three examples of passing chords that connect the vi and IV chords below:
Hint: We’ve learned one of these chords in this section.
Check for Understanding
Use the following three chords and their inversions to create a progression that has a stepwise bass line from scale degree 6 to scale degree 1 (i.e., the first chord has 6 in its bass, the second chord has 5 in its bass, etc.). Optional challenge: Use each chord and one inversion of each chord exactly once.
