All the notes of a chord can be rearranged so that the order from bottom to top may be different. The most important note is the bass note. When the root of the chord appears in the bass, we consider this to be in root position. If a different chord member appears in the bass, we have was is called a chord inversion. Take a look!
Example: Chords in Ab Major
We can see above that when the third of the chord is in the bass, the chord is considered to be in 1st inversion. When the fifth is in the bass, the chord is considered to be in 2nd inversion. During the Common Practice Period (CPP), chord inversions were labeled using Arabic numerals (the numbers you and I normally know and use: 1, 2, 3, etc.) to denote the intervals seen above the bass note. We call this figured bass.
No, not that type of bass 🙄, but keep reading!
When we are looking at a composition through a harmonic lens, these Arabic numerals are used to signify the corresponding inversions to each chord.
What do these figured bass numbers mean?
They indicate the exact interval between the bottom note and the top note when an inversion is in a closed position. In 1st inversion, the interval between the bottom note and the top note in the closed position is a 6th. There is sometimes indicated that it is a 6/3, but almost all the time the 3 is omitted. The number below (such as when we use it in the 2nd inversion) refers to the distance between the bottom note and the next note up, in a closed position. In the case of the 2nd inversion, the outer interval is a 6th, and the distance between the bass note and the next interval up is a 4th. Hence, 6/4.
When we also analyze the harmonies of a composition through Roman numerals, we can attach the Arabic numerals to the side of Roman numerals to provide information about the inversion (Arabic) of the chord in the key (Roman). It would look a little something like this:
In figured bass, a figure with a slash (/) or a plus sign ➕ indicates the pitch denoted by that figure is to be raised a half step.
An accidental appearing alone, (without an Arabic numeral) indicates that the third above the bass should be altered according to the accidental.
Another system of labeling chords takes the root and uses a capital letter-name (such as G) and attaches the quality of the chord (Major, minor, etc.) with its abbreviation. For example a G-Major chord would look like: GM. A minor chord would have a lowercase m, such as the chord Dm. You might see E+ for an augmented E chord, or F#° for an F-sharp diminished chord.
You can find this system of labeling chords in lead sheets, and in genres ranging from jazz, to rock, to musical theater.
🦜 Polly wants a progress tracker: For a 2nd-inversion subdominant chord in the key of F, what would its figured bass symbols be? How do you spell that chord?