As we learned in the previous music theory lesson, we use figured bass symbols to label chord inversions. I’m going to begin this lesson in the simplest possible manner, giving you only the information you need to label chord inversions. Then, I’ll provide a more detailed explanation of why we use the labels.
- No number under a bass note means the harmony is a root position triad; the bass note is the root of the chord.
- A 6 under a bass note means the harmony is a first inversion triad; the bass note is the third of the chord.
- A 6/4 under a bass note means the harmony is a second inversion triad; the bass note is the fifth of the chord.
C Major Chords
- A 7 under a bass note means the harmony is a root position seventh chord; the bass note is the root of the seventh chord.
- A 6/5 under a bass note means the harmony is a first inversion seventh chord; the bass note is the third of the seventh chord.
- A 4/3 under a bass note means the harmony is a second inversion seventh chord; the bass note is the fifth of the seventh chord.
- A 4/2 under the bass notes means the harmony is a third inversion seventh chord; the bass note is the seventh of the chord.
All you need to do is memorize the points above, and you will know most of what you need to know about figured bass for music theory. The seventh chord figures are easy to memorize: the sequence of numbers from root position to third inversion is 7, 6-5, 4-3, 4-2. And in some cases only a 2 is used for a third inversion seventh chord, in which case the sequence would be 7, 6-5, 4-3, 2. Some have suggested to memorize the sequence as a phone number: 765-4342.
Now let’s find out what these numbers mean.
Interval Structure of Inverted Triads
Remember, figured bass indicates the intervals above the bass. A root position triad has a 5th and a 3rd above the bass. In practice, these intervals were so common, composers stopped using them and expected the performer to know that if a bass note had no symbol, a 3rd and a 5th were to be played, in modern terms, a root position triad.
A first inversion triad has a 6th and a 3rd above the bass. Again, the third was so common that composers only used the 6, assuming the third; so today, the abbreviated version (6) is the common indication for a first inversion triad.
It doesn’t matter how the chord is voiced. In the example above, the 6th above is actually a 6th plus an octave (technically a 13th). The 6th and the 3rd can be in any octave above the bass, and in any order. In other words, the 3rd can be higher than the 6th.
A second inversion triad has a 6th and a 4th above the bass. There is no third, and there is no way to abbreviate the figured bass any further. The 6 and the 4 both have to be there to indicate a second inversion triad.
In the example above, the 4th is actually higher than the sixth, once again demonstrating that voicing doesn’t matter. The only requirement is that there is a 6th and a 4th somewhere above the bass.
Finally, the quality of the interval (M3, m3, M6, m6, etc.) depends on the key signature. Any accidentals are indicated with special symbols. See this figured bass chart for a complete explanation.
Now, let’s say you have a bass note with a “6″ underneath it, and you are asked to spell the chord. You know it’s a first inversion triad, and the bass note is the third of that triad. The best way to spell an inverted chord given the bass note is to stack the notes in thirds. The slideshow below shows you the thought process to spell a first inversion chord, given the bass note. The notes in red are showing the process when you are first learning to spell. I usually have my students sketch these notes on a separate piece of manuscript paper. With a little practice, you’ll be able to recognize and spell triads quickly without going through this process. Click anywhere on the slideshow to pause it.
(If you are used to reading chord symbols, don’t confuse the D6 with an added six chord. Eventually we will be using roman numerals for the chords instead of the letter name.)
This slideshow demonstrates the process for spelling a second inversion triad, given the bass note:
Interval Structure of Inverted 7th Chords
A root position 7th chord is nothing more than a 7th added to a triad. So the abbreviated symbol (7) is all that is needed to indicate a 7th chord.
A 7th chord in first inversion has a 6th, a 5th, and a 3rd above the bass. As with triads, the 3rd is implied, so we use the abbreviated symbol 6/5. Remember, the arrangement of the intervals above the bass doesn’t matter:
The following chart summarizes the structure, figured bass symbols and abbreviations for triads and seventh chords. You may also download this music theory pdf version of the chart which also includes figured bass alterations and additional symbols.
Next Lesson: Why You Need to Learn Traditional Harmony