Section 2 - Seventh Chords
Let's take a C major triad and stack another 3rd on top of it (review "stacking thirds" from part 2).
The highest note of the triad is G, the 5th note. If we add a minor third to that, we get Bb, which is the b7 of C. Add Bb to a C major triad and you get a "C dominant 7 chord" or simply "C7." If we added a major 3rd to the G instead we would have B, and the chord would be "Cmajor7." So C-E-G-Bb is C7 and C-E-G-B is C major 7. Here are the formulas for 7th chords:
1-3-#5-7 Augmented Major7
1-b3-5-7 Minor/Major7 or minor-major7 or minor(major7)
1-b3-b5-bb7(or 6) Diminished7 or "fully-diminished" 7
Now let's figure out how 7th chords work in diatonic harmony. Recall that diatonic harmony involves using only the notes available in a given diatonic scale. So let's harmonize the G major scale into 7th chords:
So we end up with this formula for 7th chords in major scales:
(Usually to notate a half-diminished7 you'll see a little o in the upper right corner with a / through it, since I can't type that on my keyboard I used the notation you see above)
So the I and IV chords are major7ths, the ii, iii, and vi are minor7ths, the V is a dominant7, and the vii is a half-diminished7.
Section 3 -Extensions
By stacking more thirds you get 9th chords, 11th chords, and then 13 chords, but usually we don't use "block voicing" in real music. A block voicing is an 11th or 13th chord that includes every note (So a 13th chord that includes the 9th and 11th note for example). Usually notes are "omitted." Let's use a Cmajor13 chord
The important note is the 13, so we keep it or it isn't a 13th chord. The 11th and 9th are extensions we can get rid of easily. The 7th depends on your taste - Some jazz players consider the 7th to always be an essential note, while some classical composers consider it an extension just like 9, 11, or 13. The 5th can also be omitted because, unless it's a b5 or #5, 5s don't really change the sound of the chord, they only make it sound thicker. A great way to handle extensions is "add harmony" which is when you add the extension of your choice to the triad, not concerning yourself with tertian (stacking 3rd) harmony much at all.
9ths, 11s, and 13s can each be flattened or sharped, just like any other note, for a different sound. They are often used to emphasize melodic notes. For example, if the chord progression is C, F, G, and the melody is C-G-A, F-A-C, G-D-E, you might want to include the 13ths in the C major and G major (A and E) because they are in the melody.
Next week I'll talk about modulations and borrowed chords.