To recap from last time: We have triads built from the major scale. Following the exact same procedure as what was described before, you could also construct the triads coming from the minor scale. A note about this: if you construct the dominant triad in a minor scale, you will end up with a minor triad. Most music (and therefore most theory) mandates that, actually, the dominant triad of a minor scale is a major triad; therefore, the triad of G major is both V in the key of C major and V in C minor.
So, in our harmonic story so far, we have melodies and we have chords. Melodies are played over chords, to make the melodies sound better. Last time, I mentioned that chords are not only the notes they’re made out of, but how they function in common practice music. By that, I mean what sequences of chords sound good played in a row. A sequence of chords played in a row is called a chord progression.
Here are a few really common examples:
I-V-I. This is, in a certain manner, the most basic progression—it can be characterized as having a consonant beginning, a tension, and then a resolution. This fundamental narrative is to some degree representative of all common practice music. The minor equivalent, i – V – i, is even more pronounced, since the V has a pitch that is not in the minor scale—this comes from mandating as above that the V in a minor scale is a major triad. The “V-I” part is called a cadence, and the “I-V” part (as well as any other chord moving to V) is called a half-cadence.
I – IV – V – I. The IV here is a preparation for the V chord. Because this progression is so ubiquitous, we say that IV has predominant function, or is a predominant chord. Other predominant function chords are ii (in a major key) and iio (in a minor key), as well as other chords we haven’t learned yet.
IV-I. Note that this contradicts what I said above, that IV is predominant. In music, there are not rules as much as there are tendencies and good suggestions. This progression is called a plagal cadence; in the end of hymns and other sacred music, it is often set to “Amen.” You can hear a lot of them in The Beatles’ “Yesterday”.
V-vi. This is called a deceptive cadence. It’s really close to a V-I cadence, except the second chord has one note changed. If we’re in C major, vi is A minor; the C major triad is made of C,E,G, while the A minor triad is made of A, C, E. Because vi (and iii) are so close to I, often vi and iii are treated in chord progressions as if they are I. This gives us vi-V-I, iii-IV-V-I, and so on.
So, now we have triads situated in keys, and we have ways to put these triads together to make some nice sounding progressions. I haven’t yet said anything about how to play these chords yet, though. While we constructed these chords based on counting up from scale degrees, this construction does not dictate where to place the notes in terms of higher and lower pitch. Remember from last time that in a G major triad, the note G is called the root, the note B is called the third, and the note D is called the fifth, and similarly for other triads. When the triad is played with the root lowest, the triad is said to be in root position. When the third is lowest, the triad is said to be in first inversion, and when the fifth is lowest, the triad is said to be in second inversion. Another way to denote this is to call first inversion chords “six” chords, and second inversion chords “six-four” chords. These names come from the intervallic relation between the lowest note and the next notes up.
Choosing what note to play lowest changes the theory a small amount; tacitly, the above chord progressions were assumed to all be in root position. Chords in root and first inversion are treated exactly the same, and six-four chords are different. The reason for this is that if the fifth is in the bass, the chord sounds less like what the chord actually is, and more like the triad that is based on that lowest note. For example, a C major triad in second inversion, written lowest to highest, is G, C, E, which sounds similar to a G major triad in first inversion, lowest to highest being G, B, D. This connection is the point of my next progression:
I (six-four) – V – I. Because the I (six-four) flows so nicely to the V, and we would never end a piece with the tonic triad in second inversion, we actually say that the I (six-four) triad is a predominant function chord.
Triads themselves, though, can be a little boring for classical music. There’s no dissonance in a triad. Think back to last article about how we constructed these triads; we took a sequence of three scale degrees from the major scale, picking out every other one. What if, instead, we picked out four? Then we get seventh chords! Let’s list them, using bold numbers for scale degrees again: 1357, 2461, 3572, 4613, 5724, 6135, 7246. They’re called seventh chords because the interval between the root and the last note is a seventh (if the root is lower than the last note). Just as when we constructed the triads, we had multiple qualities (major, minor, diminished), we’re going to have different kinds of seventh chords. For this categorization, we’re again in C major, so we can connect scale degrees to notes.
1357 and 4613 are called major 7th chords, since the interval from 1 to 7 (C to B), and from 4 to 3 (F to E) is a major 7th (+11). This chord is also constructed by taking a major triad, and putting a major third on top of the fifth (G to B, and C to E). This chord is rarely used in common practice classical music, but is incredibly common in jazz, where it ends up taking the place of the I triad often. When written in jazz, it often is written as CM7, or FM7, and so on.
2461, 3572, and 6135 are called minor 7th chords, since the interval from 2 to 1 is a minor seventh (when 2 is on the bottom). They are also constructed by taking a minor chord (here, ii, iii, or vi) and putting a minor third on top. These are written in roman numerals as just ii7, iii7, vi7, and so on.
7246 is called a half-diminished 7th chord, and is made from placing a major third on top of a diminished triad. The reason it’s called half-diminished will be explained later. Half diminished chords are written iiø7 (the slash through the circle means that it is half diminished).
5724 is called a dominant 7th chord, since it is constructed on the dominant (5). It is constructed by playing a minor third on top of a major triad. It is written V7, and functions similarly, if not identically, to how V functions. So, V7 – I is a perfectly valid progression, and often is seen more than its purely triadic counterpart.
This last one, the dominant 7th chord, is the most special of them all; in fact, whenever you see a dominant 7th chord (major triad with a minor third on top), you can expect to hear a V-I progression somehow.
If you’re still following, you actually now know a bunch of music theory! (Minus the notation, that is.) You are now perfectly equipped to apply this knowledge to analyze a whole ton of classical music—Mozart, Vivaldi, and so on. If anyone reading this feels like applying this knowledge to some real pieces of classical music (after learning how to read music notation), feel free to email me at gancherj@reed.edu.
Next time: Secondary dominants, and modulations, and maybe some analysis.