Addendum to: An Intro to Figured Bass

In my previous post An Intro to Figured Bass, I said that I'd send the post to my Theory professor to see if he had any feedback. Well, I did & he did! Here's what he said:

I think it works really well and I like very much the little charts, they make a lot of sense. There's only one problem spot:

Once you have figured out which of your 3 notes is the root, etc., you then look to see which one is in the bass. In our example above, we'll say that D is in the bass. Since Chart One told us that D is the third of our chord, we know that the figure we will need to use is "6".

Inevitably, someone will ask, "Why '6'?" Or why any of the numbers indicating inversions, for that matter. Of course, explaining where "6" came from is difficult: over the years I've had to go over and over the reasons for those numbers, because it takes a while to sink in for students. They're so used to root position chords that inversions is another universe for them. I'll try and see if I can think of something simple by way of explanation that you might be able to use.

Of course he's right. My "intro" assumed that the student already understands inversions.

But let's take a look at where those numbers come from anyway, shall we?

I have three different Theory books here at home. I have the Benward/Saker; I have the Kostka/Payne. But I think the best explanation of inversions appears in the Introduction to Music Theory Through Literature, Volume I by John Baur of the University of Memphis. The book has this to say about triads:

If two intervals are sounded together, the result is a triad. Although any three pitches results in a triad, there are four standard triads constructed from major and minor thirds: Major, minor, augmented, and diminished.

A major triad contains two intervals, a major third and a perfect fifth.



A minor triad contains a minor third and a perfect fifth.



A diminished triad contains a minor third and a diminished fifth.



An augmented triad contains a major third and an augmented fifth.



Any of these four triads can be constructed above any given pitch. The lowest note is called the root, the second note is the third, and the top note is the fifth.

If the root is on the bottom, the triad is said to be in root position.



If the third is on the bottom, the triad is in first inversion.



If the fifth is on the bottom, it is in second inversion.



The intervals above the lowest note are different in each case.



Even though the quality of the interval may change because of the quality of triad, the basic intervals for each inversion remain the same - 53 for root position, 63 for first inversion, and 64 for second inversion.

When doing figured bass or inversions, we just need to remember that the 53 is not written (since it's the "default" - root position) and that the 63 leaves the 3 off (again, because it's just "understood").

The same logic holds true for the figures used in 7th chord inversions.

NEXT TIME: a discussion of solfege! Specifically: the pros & cons of Moveable Do vs Fixed Do and Do-based minor vs La-based minor. Fun stuff!

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