Triads

(entry for 9/6/2024)

The study of music is traditionally broken up into three parts: melody, harmony, and rhythm. The first and last are easy. Melody is the study of how pitches in a single line go through time, and rhythm is the study of how that time is organized. Harmony is a bit harder. Harmony is the study of how different pitches affect each other when played or sung together at the same time. Another way of saying this is that melody is pitch arranged horizontally and harmony is pitch arranged vertically.

Mostly, harmony is about ‘chords,’ which are made up of intervals. Having talked about Intervals two posts ago, and Transpositions, last post, it is now time to talk about Chords. But to be safe, let’s define the word before we begin using it.

A chord is three or more different pitches sounding simultaneously. (That is, ‘in accord.’ Get it?)

I hear you ask, ‘Why not two pitches?’ The answer is that, technically, two simultaneous different pitches go by the name ‘duad’ (pronounced ‘DEW-add’) rather than ‘chord.’ However, you’ll see a lot of written musical information that refers to ‘two-note chords,’ so to avoid being unnecessarily nit-picking, we’ll allow the incorrect term to stand, though I’ll try not to use it that way myself. (For most purposes, a duad and an interval are the same thing. We’re just thinking about them differently when we use the two different names.)

When we talked about intervals, we stressed that (except in ear training) intervals are named not by how they sound but by how they are spelled. That is, by what note-names are given to the pitches. The same thing is true for chords.  A chord spelled C, E, and G-sharp is not given the same name as a chord spelled C, E, and A-flat, even though they sound the same.(We’ll get to the different names for those a bit later.)

Three-note chords are called ‘triads’ (TRY-adds), provided the three notes have different pitch names.Even in four-part harmony, where one of the pitches has to be ‘doubled’ in order to have four parts, a chord with three different pitches is still called a triad. Which brings us to some more definitions! A triad is in ‘root position’ when the name note of the chord is also the bottom note of that chord. For example, the root position of a D major triad is when the D is at the bottom, regardless of how the other notes are arranged above that. (As we’ve said before, almost everything in music is ‘bottoms up.’) A triad is also said to be in ‘closed position’ when there are no gaps in it, whereas it’s said to be in ‘open positon’ where there is at least one gap. For example, a C-major triad spelled, from bottom to top, C – G – E, is open position, because you could take the E off the top, and put it in the middle.

So to be precise in naming a triad we need to say both whether it is in root position or not and whether it is in closed position or not. (The root-position triad at the top of this post is in open position, pretty obviously. It has two huge gaps.)

An F-major chord, when spelled, F – A – C (assuming no octave jumps), is in closed root position. When spelled F – C – A, it is open root position. Both are considered root position, because the F is the bottom note. But the second one is considered open position, because there’s a gap: you could put the A between the F and C, whereas there are no gaps in the first one.

Triad names are mostly the same as interval names. There is one exception. There are perfect intervals, but there is no such thing as a perfect triad. The four other names are the same. There are diminished, minor, major, and augmented triads, just as there are intervals with those four names. 

The other thing you need to know about triads is that, in general, they are built of thirds and fourths stacked up, though there are fifths and sixths involved in the finished product as well. Two thirds, stacked one above of each other, create a fifth from the bottom note to the top one. Two fourths stacked on top of each other, create a seventh, not an octave. (Remember? Music is not math.) A third and a fourth merged create a sixth.

We mentioned in the post about intervals that some intervals are considered ‘dissonant.’ Both major and minor seconds, for example, are considered dissonant. (‘Sonant’ means ‘having to do with sound.’ ‘Dis-’ is of course the prefix of disagreeable. A dissonance is therefore a disagreeable sound. It needs to be ‘resolved’ in order for our ears to be happy.) The fact that seconds are dissonant is why most triads are built of thirds and fourths, but not of seconds.

If you put a minor third on top of a major third, the result is called a ‘major triad,’ because the major sound of the lower third predominates over the minor sound of the higher third. Likewise, if you put a major third on top of a minor third, the result is a ‘minor triad.’ For example, the minor third from A to C surmounted by a major third from C to E is called an A-minor triad, because the minor third is at the bottom. Likewise, a major third from F to A, with a minor third from A to C on top of that, is called an F-major triad. (And, if it matters, both of these triads are in closed root position.)

Which brings up a question: Is C – E – C a triad? Answer: No. To have a triad, you must have three different pitch names. Even though the two Cs in that example are different pitches, they are the same pitch name. So they don’t form a triad. (They are a chord, but not a triad.)

A diminished triad consists of two minor thirds, stacked. An augmented triad consists of two major thirds, one above the other. Both are considered dissonances and must be resolved. (Unless your name is Debussy or Ravel, in the case of the augmented, but that’s another story.)

Major and minor triads are both considered consonances or assonances, which do not need resolution.

But what if the triad does not have the chord name at the bottom? What if there is a fourth on top of a third, instead of two thirds. (Or underneath it, for that matter.)

A triad with a fourth on top of a third is said to be in ‘first inversion.’ If you have an E, and then the G above that, and then the C above that, you have a first inversion C major triad. (It’s a closed position first inversion, because there are no gaps.) The reason it’s called C-major rather than E something, is that the pitch names are exactly the same as if the chord was in closed root position: C – E – G, but you’ve taken the C off the bottom and put it on top. In other words, you’ve rolled the chord upward without changing its basic nature. When a triad consists of intervals other than two thirds of some sort, it is not in root position.

Let’s say you have a G, with a C just above that, and then an E top of that. That is in second inversion. (You’ve rolled it again. And if you were to roll it up one more time, you’d be back in root position again.)

Notice: a triad with a fourth on top of a third is in first inversion. A triad with a fourth underneath a third is in second inversion. Thirds being major and minor don’t matter in this case. What matters in determining inversions is where the fourths and thirds are in relation to each other. And most importantly of all, a root position closed triad has no fourths! Both of its intervals are thirds.

By the way, it's easy to see where the fourths and thirds are in the triads. For a third, the notes are either both line notes or both space notes. For a fourth, there's one of each.

I promised you earlier that we would eventually explain why C – E – G-sharp is not the same triad as C – E – A-flat. Think about it. Where are the thirds? Where are the fourths, if any? The first triad has only thirds, no fourths. It’s in closed root position. It’s a C-augmented triad. The second triad has a major third, with a diminished fourth on top of that. (From E to A-flat has to be a fourth, because there are four names involved: E F G A.) Therefore it is an A-flat augmented triad in first inversion, because the fourth is above the third. (I know, I know. This is mind-boggling at first. I promise you, it will all become clear eventually!)

That’s probably more than enough to chew on for this post. We’ll save four-note chords for next time!

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