the many flavors of 7th chords

Seventh chords are triads that have had a third added to their uppermost member, the 5th (a triad contains some form of 1, 3 and 5). The third will 'skip' a note if you're thinking alphabetically, meaning that it skips a scale degree -- there the 6th -- and so we end up with a tone that is a 7th above the root of the original triad.

OK, my apologies for such a convoluted definition. Since a picture is worth a thousand words here's a C major seventh (the gray notes are not part of the chord):


Looking at this it's clear that a seventh chord can also be seen as a triad with the interval of a 7th added to the root of that triad. Regarding this approach the first thing to keep in mind is that there are two main intervals of a 7th: major and minor. (There's actually another one that comes into play and we'll talk about it in a minute.) So if we recall that there are 4 basic triads we should be able to produce (4 triads x 2 types of sevenths =) 8 types of 7th chords.

So the major triad gives us a major 7th and a dominant 7th.

The minor triad: a minor/major 7th and a minor 7th.

The augmented: a major 7th +5 and a dominant 7th +5

The diminished...well, let's talk about this one for a second. Here we really need to look at the first way (of stacking thirds) of constructing sevenths to see how these come about. We could slap a major 7th interval onto the root of a diminished triad but in practice this doesn't happen: it's enharmonically equivalent to a B major triad with a b9. But the real reason that it doesn't "happen" is that seventh chords developed historically from voice leading and from functional harmonic concerns. The diminished triad is a chord that came about as a VII chord, and in neither the major nor the minor modes will we get a VII chord that is diminished and has a major seventh.

So what chords do we get? If we add a minor seventh to the triad we get a (classically appelled) half-diminished chord. On modern charts you're most likely to see this called a minor 7 b5.

Then there is a fully diminished seventh chord: it results from stacking minor thirds up from the root. In the key of C we could start on B and get:
b, d, f, a-flat.
And if we added another minor 3rd we'd be back to b. (If we examine the sort of 7th here we don't have a major or a minor variety: in this case it's a diminished 7th.)

This chord is unique because any of it's tones could be the root (and because of this in 19th century music it was used a pivot chord in modulations). Mo' on dat in a later post...

There is one more seventh that is not a basic triad with an added third. It kind of results from whole tone harmony, or it can be seen as an analogue of the dominant 7th +5:
the dominant 7th b5:

You won't really see a C-E-Gb chord floating around out there all on it's own, but this seventh chord is not uncommon at all (and not just in jazz: it comes up in Granados' Valses Poeticos if memory serves).

Play the sevenths, use them, they're beautiful...