An inversion can refer to several different aspects of music and music theory. In this article, we're focusing on notation conventions for inversions in the context of triadic chords and their inversions. This means we'll be looking at ways to properly notate a chord's root position and its own two inversions, giving us the following three elements:
- Root position
- First inversion
- Second inversion
In music theory, there are two different ways to understand this concept:
- Roman numeral notation (scale degrees)
- Figured bass notation
The more common of the two is the Roman numeral approach, where notes and chords within a scale are given a Roman numeral notation to indicate their position within that scale. For example, in the C major scale you have the following notes:
C, D, E, F, G, A, B
In the C major scale, an E chord would be the third scale degree and would be given the following Roman numeral indicator: iii
You can match the other scale degrees with their respective notes in the C major scale using the following diagram, which can be applied to any major scale:
For most, this is the more familiar method of notating triads and inversions. Before we get into the method of using figured bass notation, which has its advantages in certain contexts, we should cover the practice of using the Roman numeral method with some more concrete examples.
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Understanding Roman Numeral Notation
Roman numeral notation allows us to understand all of the notes within a scale or chord in relation to the root of those notes. Thus, when dealing with a triadic chord you have the following three components:
- The Root
To illustrate this, let's use a basic C major triad. Not only do we want to notate the three notes properly, but we also need to identify the root, third and fifth of each chord. Keep in mind, inverting a chord in root position means that the bass or lowest note is no longer the root of the chord. However, this does not mean that the actual notes change.
They simply shift positions.
All the notes included in the chord are still the same, but the bass note is changing its order in the chord. For the first and second inversions, it's not the lowest-positioned note. In other words, it's no longer the bass of the chord.
Thus a triadic root position chord could be written, in Roman numeral notation, as the following: I, iii, V
This would be a valid form of notation for any major triad, regardless of its root. The Roman numerals allow us to arrange notes, based on their scale of origin in relation to the root note. It's extremely helpful for understanding chord inversions and lead segments, where the key might be subject to change.
Roman numeral notation will differ slightly, depending on the mode and whether the scale is minor or major.
The Ionian mode is the most typical arrangement of scale degrees, since it matches the common C major scale.
Let's look at one more simple example using the Roman numeral method.
Triad in the key of E Major with Both Inversions
Let's say you want to build and notate a triad in the key of E major. In the context of the guitar, we'd start with a basic tab sheet, tabbing out our root E along with the third and fifth of that E note, since everything is understood in relation to a chord's root.
We'd start with just the root position:
Now we add the standard notation above the tab.
Make sure you identify the root, third and fifth, at least making a mental note of each.
Now we can add the notation for both inversions, making note of the root, third and fifth for each one.
Assuming the E major scale, you could write out the Roman numeral notation for each chord like this:
- Root position: I, iii, V (E, G♯, B)
- First inversion: iii, V, I (G♯, B, E)
- Second inversion: V, I, iii (B, E, G♯)
I've highlighted the root in each arrangement to show that this method of notation allows us to easily identify the root note, even if it's not in the bass of each chord.
While there are other ways to use Roman numerals (you can even use them in conjunction with figured bass notation), this is the simplest way to understand the chord and its inversions in relation to the root. This notational method is also commonly used to illustrate chord progressions within a given key. For example, in the key of C major, the I, IV and V chord progression would translate to C, F and G, which is a common arrangement derived from that scale.
Now we'll look at using figured bass notation instead of the Roman numeral method.
Understanding Figured Bass Notation
Figured bass notation is a shorthand method that relates everything to the bass note of a given chord or pattern. It's implemented by adding numbers beneath a chord to indicate the intervals of each succeeding note from the bass note of the chord. Thus, figured bass notation deals exclusively with intervals, without necessarily making reference to the root of the chord it's describing.
As you can see from the following diagram, everything references the bass note for the triad and both of its inversions. As we did with the Roman numeral method, let's use the C major triad and its subsequent inversions for our first example.
The value of this method is that it allows us to describe triadic structures in abstract terms. Moreover, it's a somewhat simpler (structural) way to look at the chord.
First, we should label our notes starting with the bass note of each chord, along with the two subsequent intervals.
Now that we've identified the intervals above the bass note of each chord, we can add our actual figured bass notation underneath the root position chord - which is in the first bar - and its two inversions that follow.
In this notational method the bass note is assumed to be the lowest in the chord, while the two numbers given represent the interval spacing between that bass note and the other two notes in the chord.
Thus, in the root position example - in the first bar - the three and five represent the third and fifth interval in relation to the bass note which, in this case, happens to be a C.
With the two inversions that follow, it can be a little trickier to visualize the concept without defaulting back to the Roman numeral mentality. Just remember, the bass note is the same, and is now our anchor for the chord. This means that in the second bar, the six and three represent the sixth and third interval above the bass note of the first inversion of the C major triad. That's a mouthful, so let's summarize and repeat.
In the second bar, the six and three represent the sixth and third interval above the bass note of the first inversion of the C major triad.
Let's look at another example, this time using an F major triad positioned at the eighth fret.
Using Figured Bass Notation with an F Major Triad and Inversions
The F major triad and its two inversions can be plotted with the root F starting at the eighth fret, giving us the following:
I've positioned the low F on the eighth fret and built my root form triad out from that spot. Just as before, our intervals will provide the figured bass notation, which will be the same since we're still in a major key.
Abbreviating Figured Bass Notation
To make figured bass notation less cluttered and easier to read, the three number combinations can be reduced to the following abbreviations:
- Nothing: Simply omitting the five and three assumes a root position triad.
- 6: Indicates a first-inversion triad.
- 6/4: Indicates a second-inversion triad, using both numbers to distinguish it from a first-inversion triad.
This means that the above graphic could have been displayed in figured bass notation like this:
Keep in mind that figured bass notation is not giving us any information about the quality of the triad. Major, minor, augmented and diminished triads will all use the same figured bass notation, while accidentals will be indicated by sharp, flat and natural symbols.
Handling Altered Pitch and Accidentals
The topic of handling accidentals (sharps and flats), in relation to figured bass notation, is something I would consider a step above this material in terms of difficulty. Take a look at this diagram developed by Robert Kelley:
That's a lot of information to digest, so let's break it down into the simpler aspects that apply to our entry-level understanding of figured bass. First, there are essentially two different ways in which accidentals will show up with figured bass notation:
- Taken alone
- Accompanying a figure
Taken alone refers to an accidental being displayed beneath a chord without any number. In this case, the accidental will apply to the third interval above the bass note.
If the accidental accompanies a figure (a number) it simply means to apply the action to that particular note.
As you can see, this process gives you the ability to alter pitch and make semitone-level changes to your chords while using the figured bass method. It's a bit tricky to see initially, but just make sure you remember the distinction between accidentals displayed alone and accidentals displayed with an accompanying interval number.
For more info on using accidentals with figured bass notation check the further reading section below.
Using figured bass notation is more of an academic discipline, though it can be a valuable bit of knowledge for rhythm guitar players in particular, who might be dealing with triadic chords and their inverted patterns on a regular basis. In any situation where you need to reference those chords in relation to their bass-most note, the figured bass method is going to be your most optimal approach.
Knowing it in conjunction with the Roman numeral method gives you a more complete understanding of notational disciplines and a more comprehensive way of analyzing and writing your chord progressions.
Check the further reading section below for some of the materials I referenced while writing this content. There's plenty of good info on both the Roman numeral and figured bass notational methods.
Further Reading and Works Cited
- Crist, Timothy. “Introduction to Figured Bass.” clt.astate.edu/tcrist/figuredbassintro.pdf.
- Vigil, R. “Figured-Bass Notation.” www.colby.edu/academics_cs/courses/MU182A/upload/Figured-Bass-Notation.pdf.
- Kelley, Robert. “How to Realize a Figured Bass -.” Robert Kelley, Ph.D., robertkelleyphd.com/home/figured-bass/.
- Kelley, Robert. Robert Kelley's Music Website, www.robertkelleyphd.com/scaledegrharm.htm.
- “Theory and Practice of the Basso Continuo.” Theory of Music, 14 Sept. 2008, theoryofmusic.wordpress.com/2007/11/23/theory-and-practice-of-the-basso-continuo/.
- Flickr Commons image courtesy of Kmeron