Half and Whole Diminished
It's a bit confusing — why is one diminished chord half diminished and another whole diminished? Well, for starters, part of this is simply a name. But there's more to it than that. The diminished triad is a symmetric chord in that it uses all minor third intervals. When you spell a diminished seventh chord, you actually use all minor thirds again (B–D–F–Ab). It is called “fully” diminished because it follows the pattern of all minor thirds and becomes perfectly symmetrical at that point. A half diminished chord (B–D–F–A) has a major third between the fifth and the seventh and isn't fully diminished because it loses the pattern of all minor thirds. That's where the difference comes from. In music, when you see diminished chords with sevenths, 90 percent of the time, they are fully diminished seventh chords. You do see half diminished chords, mostly in jazz but sometimes in classical and popular music as well.
Since the diminished chord comes in two flavors — half and full diminished — modern musicians, especially jazz musicians, help to differentiate these two chords. One way that they differentiate them is simply by not callinga half diminished chord a half diminished! If you look at a half diminished chord, you could look at it as a minor seventh chord with a b5. To avoid confusion, most modern music uses min7b5 instead of the half diminished symbol (Ø) to avoid confusion. This way, when you see a diminished symbol (º), you can infer that it's a fully diminished chord.
Augmented triads are weird chords to begin with. They have a particular sound that simply isn't used very much. Nonetheless, modern music, especially jazz, makes use of augmented seventh chords, which come in two varieties.
Start with FIGURE 9.9.
Start with the G augmented triad of (G–B–D#) and add an F#. The interval from G to F# is a major seventh, so this chord would be called an augmented major seventh. For short, you see the symbol G+(maj7) or Gaug(maj7).
If you wanted to derive a formula for this chord, it would look like this:1, 3, #5, 7 (if you derive this from the degrees of a major scale).
This chord does not occur in natural major or minor scales, but you can find it on the third degree (submedi-an) of the harmonized harmonic and melodic minor scales. It's a very strong musical sound and it's used in modern jazz quite a bit as well as late romantic and twentieth-century music.
The other augmented chord is shown in FIGURE 9.10.
We start again with the G augmented triad and add the note F. The interval from G to F is a minor seventh, so the full name for this chord would be an augmented minor seventh. Typically, you'll see this shortened to G+7, Gaug7, or G7#5 — all are synonymous. The G+7 chord is closely related to a G7 chord. The augmented nature of the raised fifth is simply seen as an alteration. Typically, when you see this chord, it functions much the same way that a dominant V chord does. More in the next chapters on usage.
If you wanted to see the formula for this chord, it would look like this:1, 3, #5, b7 (if you derive the formula from major scale degrees).
Well, as far as seventh chords go, that's all you have! As you will see from the music looked at later in the book, out of the eight chords, you typically see four or five of these chords in everyday usage, but if you want to understand everything there is to know about chords and how they are formed, then you'll want to at least understand how to form them from their intervallic relationships.