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Basic Chords (triads)

1 Unless you learned Classical guitar, but even then you do chords, you just don't call them that.

If you play guitar, even a little, probably the first thing you learned was a handful of 'chords.'1 They were a challenge, but maybe you made it all the way to 'F' before you gave up. Technically, any time you have more than one note sounding at the same time, you have a chord. Some of them sound better than others. Some groups of notes, when they sound together, sound nice. We say that such combinations are consonant (lit. 'sounding together'). When they don't sound so nice, we call that dissonant ('sounding apart'). What 'sounds nice' is often different for different people. Some of that is culturally shaped, or acquired later, but there are probably natural consonances and dissonances formed by the (dis)similarity of the waves themselves. See the discussion in Waveforms and Harmony.

In this chapter we will be discussing the core notes that make up most of the chords that you will hear, and how they combine.

Triads

At this point we are going to pull up that piano keyboard we have been using from time to time. Later I will show how this connects to the guitar and other stringed instruments, but it is much better to understand what is going on before moving on to how it is implemented on various instruments.

2 By "at the core," I don't mean to imply that there won't be variations, but they are usually understood in terms of their relationship to the standard.
The C chord highlighted (in green) on the keyboard C chord on the keyboard
The C chord on the staff C chord on the staff
If the audio button is screwed up, try the MIDI

This is a basic C chord (green notes). To the right, we have the same chord written on the staff. You can see that there are three notes, and within the C scale they fall every other one, in this case the scale steps are 1, 3, & 5. Simple as it may seem, this configuration is at the core of every chord you are going to learn.2 It is called a triad.

The most consistent parts, those that vary least from type to type, are the root and the fifth. The third determines whether the chord will be major or minor. If, in the example above, the e were an e♭ it would be a Cm chord. Notice the interval layout. The interval between the c and the e above it is a major third (and between the e and the g it is a minor third). If the e became e♭ the first interval would become a minor third, and the second a major third. [By the way, you may have noticed I am using lower case for notes and upper case for chords and scales.]

3 This convention is violated, normally, only when the location a chord's notes within a key is of particular importance.
The Am chord highlighted (in orange) on the keyboard Am chord on the keyboard
The Am chord on the staff Am chord on the staff
If the audio button is screwed up, try the MIDI

This interval relationship is consistent across all major and minor chords. Have a look at this A minor chord. As you can see the relationship between the notes is the same as with the C chord above, except for the intervals between the first and third, and the third and fifth respectively. You may also have noticed that the 1, 3, & 5 of both chords correspond to the 1, 3, & 5 of the scales with the same name (C major and Am respectively). This is conventional when talking about chords, even though in any given key there are fully six core triads that are not built on the 1, 3, & 5 of the key.3

Having said that, let's look at some of the other triads in a major key. If you think about it, any note in any key (major, minor, or modal) can have this kind of every other note relationship built on top of it. c-e-g is the chord build on the root note in the key of C major, but we can move up one step and do the same thing on the second step (D). The resulting chord is d-f-a. Because it is built on the second note, that is called the '2' chord (Note that I do not use italics for chords as I do for scale steps. This is to visually distinguish them when possible). Can you tell whether it would be major or minor?

Hopefully, you said 'minor' because of size of the intervals between d & f and f & a (you have to look at both, for reasons that will become clear in a moment). You can do this with any note in the scale (although the b is a little different). We have already looked at the a (the sixth in the C scale), but try it with e, f, & g (3, 4, & 5). Which are major, and which minor?

The D chord highlighted (in green) on the keyboard D chord on the keyboard
The D chord on the staff D chord on the staff
If the audio button is screwed up, try the MIDI

We have been looking at the key of C major, because the all white key format makes it easy to see, but it works the same way with all keys. If we were in the key of D, with two sharps, the root chord would look like this pair of pictures. The 2 chord would be a minor chord built on e, the third on f♯, and so forth. What would be the 4 chord in D? Would it be minor or major? What about the 6 chord?

The chord highlighted (in green) on the keyboard B° chord on the keyboard
The chord on the staff B° chord on the staff
If the audio button is screwed up, try the MIDI

OK, now back in the key of C, do the same thing with the b. What is different? Rather than having one major third and one minor third, you have two minor thirds. This also means you don't get a perfect fifth, but rather a diminished one, which is why it called a diminished chord. It is generally indicated with a little circle (like a degree sign); this one is B. In major keys, like C, this type of chord always falls on the seventh step. With minor keys (like Am), it is always on the second. With the modes it will be in different places depending on which mode you are using, but it will always be in there somewhere.

Augmented chords

4 I emphasized 'natural' because the augmented chord is what you get if build a triad on the third of a harmonic or melodic minor scale.
Augmented chords (on the staff) augmented chords
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The one other kind of chord I will mention here is not actually part of any natural scale.4 I am talking about it now simply because it completes the set of standard triads. Logically similar to the diminished chords that are made up of two minor thirds, creating a diminished fifth, these are made up of two major thirds, which results in an augmented fifth. Hence, these are called augmented chords. They are indicated with a slightly elevated '' after the chord name. You can build them off of any note on the keyboard, of course, but taking enharmonic equivalencies into consideration, there are actually only four distinct augmented triads. In the musical score fragment above, the ones shown are the firsts in the groupings (C, E♭, D, & E♭). The others listed will sound the same, but be represented differently (see below).

Chords format

We will return to diminished and augmented chords, and what they are good for, in another chapter, but for now, notice that—diminished, augmented, major, or minor—the pattern is always the same: three notes with an every other one format, all of them (except the augmented) within the scale for that key. In each case they receive their names from the lowest note in this layout, accompanied by 'm' if it is minor, a '' if it is diminished, or a '' if it is augmented. Major chords are usually just represented by the letter by itself.

5 I bet you were thinking you would never see, or need, a double sharp () for anything, right? Actually, you are unlikely to see many A♯ chords in real life if the writer understood how these things work (which means, of course, that you will probably see them all the time on those on-line chord charts). Obviously, you can play one, but it isn't actually part of any key on the circle of fifths (although . A♯m is on there). If you think you need one, chances are what you actually wanted was a B♭. We will talk about rare exceptions, other than augmented chords, (much) later.

Observe that the letters of the note names are all skip-one format as well. This is always true, even if it gets you into some interesting notes. All A chords, for example, are a-c-e, in some way or another: A♭ is a♭-c-e♭; A♭m = a♭-c♭-e♭; A♯ = a♯-c-e♯. Of course, normally we think of c♭ as b, and c as d, but nevertheless, the a-c-e rule needs to be adhered to.5 This is a natural outgrowth of the same rule we saw a couple of chapters ago, that all scales have one note for each of the letters ag.

A side implication of this is that you should be able to memorize these three note combinations pretty easily (there are only seven), and, in fact, that is exactly what you should do. This will save you from making common mistakes like D/g♭; you will know that all D triads are d-f-a, so that must be D/f♯.

Here is the full B major scale (5s) with chords and scale steps labeled:

B scale in chords B scale in chords
If the audio button is screwed up, try the MIDI

When you are building augmented chords on what ever note of your choosing, remember that they still have to conform to the every-other note rule for triads. If you insist on building one on b, for example, you will end up with a F, but the same chord could just as easily be a first inversion implementation of G(if that works in your key), which only has one sharp (d).

6 I am not convinced by the analogy, but the observation is certainly true.

You doubtless saw that the 1, 4, & 5 chords are major, while the 2, 3, & 6 are minor, with the 7 being the lone diminished chord in a natural scale. If it were a minor scale 1, 4, & 5 would be minor, and the diminished would fall on 2, with the other three being major (see the G♭ minor scale in the next illustration). The major 1, 4, & 5 are called primary chords; the others are secondary. Some people see a connection between this observation and the fact that the 1, 4, & 5 intervals are considered perfect, while with the others you have to specify major or minor.6 It is certainly true that in any given key, these chords are the ones that are used most frequently.

7 It 'contributes,' but is not essential. Even natural minor dominant chords lead the listener back to the tonic, just not with quite as much urgency.

You remember from the last chapter that the note at the five of the scale is called the dominant. This is also true for the five chord; the other chords also derive their names from the note names. The dominant (both note and chord) is so named because, other than the tonic, it is the most important. In the major key, the dominant chord contains the leading tone (and in minor keys it is often added, as you will remember); this contributes7 to the fact that the chord, and even the note, create an instability that the hearer wants to return to the tonic. We will return to this in the next section, and when we talk about chord movement.

The first monkey-wrench: inversions

So far we have been looking at the chords in what is called root position. What that means is that each of them have had the note bearing the name of the chord in the lowest sounding position. It is the notes, however, and not the order, that make them what they are. It is easier to visualize them in this order than in any other, but they can just as easily be written with the notes jumbled around, and while the chords remain the same, the sound changes slightly depending on what note is in the bass.

8 If the numerical representation at the bottom looks a little strange to you, fret not; I will talk about that stuff in a minute after we finish with inversions.

If we flip these such that the third is in the bass, as with the Gm scale in the next image, we get what is called first inversion.8

Gm scale first inversion Gm scale first inversion
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So in this case, as you can see, the thirds are in the bass (the roots happen to be the high notes). If you play this you will hear that it has a slightly different sound. Until you get used to hearing this, your ear might get fooled into hearing a different chord. The Gm, for example, in first inversion sounds a lot like a B♭ major. If fact, if you look carefully you can see that there is only one note difference between Gm and B♭ anyway, so putting the b♭ in the bass increases this aural similarity. These chords have a less stable sound, so you wouldn't usually want to end on one, but on other occasions, one of these is likely to be exactly what you are looking for.

It should come as no surprise that if there is a first inversion, there is probably a second inversion as well. I suspect that you can guess what it looks like, too. Where first inversion puts the third in the bass, second inversion puts the fifth there. Here is an A scale in second inversion.

9 Oddly, if you are strumming a chord on an instrument like a guitar, second inversion sounds more stable than first. Go figure.

10 If the bass line is moving from one place to another, second inversion is a perfectly good stop along the way, as long as it doesn't hang around too long.
A scale second inversion A scale second inversion
If the audio button is screwed up, try the MIDI

If first inversion sounded slightly unstable, second inversion is downright tottering.9 It is that instability that is its primary attraction to composers. It usually creates a tension that wants to resolve to the chord of the bass note. In the case of the A chord above, the note in the bass of a second inversion chord is, as you can see, e. So this triad tends to wants to be followed by an E chord. That doesn't mean that it always happens that way,10 but it is what your ear has come to expect, and many writers are happy to oblige. The most common form, as you can imagine, is the 4 chord with the 1 in the bass wanting to resolve to the root chord for the key.

Numeric notation

The method I am using for numeric representation of chords within a key is not the one you will usually see in theory manuals. It is a combination of that method with a technique called Nashville Notation, although people who are familiar with N.N. will complain that is not that either. I will discuss the latter method fully on a later page, and point out the ways that it differs from this. In this section I will explain the system I am using, and show how it differs from the alternative version usually used in theory texts. They are, in any case, not that different. What they have in common is that they both assign numbers to the scale step upon which any given chord is based, and then go on to assign the same number to the chord built from it. For any given key there will be seven numbers associated with the seven scale steps. The octave is simply shown as a return to the beginning.

11 If you analyze this carefully, you will note a number of non-chord notes present. These are called 'passing tones.' We will talk about such things in the section on melody, but for now, you can just ignore them.

12 So, too, should the '' and '' for diminished and augmented, although they are not in this passage.

13 Without the slash it has a different meaning, as will become clear in the next section. I usually try to indicate these relative scale steps with a slightly smaller and vertically lower number than that used for the main chord indicator, although, as you have probably noticed, some software (such as what I use for score entry) does not allow me to do that. In other contexts where scale steps rather than chords are intended, I prefer italics, although with the same software caveat.

This much, illustrated in the next passage, should look pretty familiar to you,11 as should the 'm's for minor chords.12 The numbers after the slashes might be new. Rather than telling you straight-up what the inversion is, my approach lets you know what scale step (relative to the chord) is being used for the note in the bass (if it is not the same as the chord). Using this method, 5/3 means this is the chord based on the fifth, or dominant, note of the scale, with the third of that chord in the bass.13 I do not tell you whether that is a major or minor third as long as it is within the major or natural minor scale of the piece. You should be able to determine that from whether the chord itself is major, minor, augmented, or diminished.

Two numeric notation styles Numeric notation styles
If the audio button is screwed up, try the MIDI

What, then, do most theory texts texts do? The main difference, visible in the passage above, is that they prefer to use roman numerals for chords. This allows them to differentiate major and minor chords with upper or lower case respectively. Regular scale steps are indicated with Arabic numbers, sometimes with a caret (^) over top. Some folks like this better, but I, and many others, prefer the Arabic numbers for chords as well because they are easier to read quickly.

14 That last date, however, simply coincides with the death of J.S. Bach. Most composers, including Bach's own sons, were well into the age of Rococo by then.

The other thing that standard texts do, and which I am absolutely not going to do, is to distinguish inversions with a system called 'figured bass.' This approach hails back to keyboard improvisation styles in the Baroque period (~1600-175014). It is historically interesting, but not of much use for this kind of study. I do plan to have a page on it, to satisfy the interest of the merely curious, and those on an insatiable quest for knowledge, however obscure. But we need to cover some more material, before you will be ready for that link.

Jazz musicians and studios have their own preferred notation approaches which are designed for quick reading and writing, rather than analysis. I talk about them in Alternate Notations.

Chords and string instruments (like guitar)

Unless you play balalaika, you probably have more than three strings. So how do these triads translate to the chords you learned for your guitar, mandolin, or whatever? The obvious answer is that you can repeat notes. Unlike certain brands of potato chips, it's OK to have more than one of each. Let's look at a couple of standard chords. On the guitar, the C chord looks like this:

C chord on the guitar C chord on the guitar
C guitar chord on the staff C guitar chord on the staff
If the audio button is screwed up, try the MIDI

The hollow circle on the low E string means that is an optional fingering, so the chord can be played either with that fretted, or with that string left open.

If we translate that into staff notes, it looks like this (the optional note is in fuchsia):

As you can see, all the notes, including the optional one, are either c, e, or g—in other words, the C major chord. However, you may have noticed that if you play it with the bottom note open, it is in first inversion, and if you use the optional g instead, it is in second inversion. For strumming chords, the g is a little stronger, but the strongest form will come from not playing the bottom note at all.

D chord on the mandolin D chord on the mandolin
D mandolin chord on the staff D mandolin chord on the staff
If the audio button is screwed up, try the MIDI

Let's try a different chord, this time on a mandolin. The mandolin is tuned, lowest to highest, g, d, a, & e. We are going to figure out how to play a D chord. If you play mandolin, you already know this, but humor me for a moment and pretend you don't. For the D chord we will need the notes d, f♯, & a. We look at the open strings and see that d & a are conveniently provided on open strings 3 & 2, respectively. But we don't want the low g, so we start counting notes up from there (one fret per half-step). Two frets up from the low g we arrive at an a. We say, "Alright..., I guess." We already have an a, but we know that with four strings, looking for three notes, we are going to get two of something, so we move on to the other problem string, e. One fret up is f, which we don't need (it would be right if were making a Dm), so we keep on going. The second fret is f♯, which we do need. Now we have at least one of each of the notes in the triad, so we have a fingering for a D chord. The 'at least one of each note' point is important though. You need all of them. If you have to end up with a harder chord to play in order to make this happen, well, that is what you have to do.15

15 There are exceptions to this rule, though, which we will talk about in the next section.

The violin is tuned the same way. Can you simply use the same chord(s)? Well, yes and no. The way the violin is set up, you can really only chord two notes at any given moment (called a double-stop). If you wanted to do this triad, you would have to sort of arpeggiate across the strings to get it, but it would work.

Obviously, you wouldn't go through all this for a D chord that you can easily look up in a book or on-line. But sometime, you are going to have some weird chord that isn't in the book, and you need to figure out how to do it. Now you know.

Musicianship

In this category, we have talked about sight singing/playing and developing the ability to recognize the intervals and rhythms that you hear (ear training). Applying that to chords works much the same way. The idea is to be able to hear a chord progression and identify it, relatively, of course. This includes being able to distinguish the inversions. Part of that is being able to separate out the bass part in your head, as well as the melody.

It is much harder to hear 'inside voices' specifically. These are the notes other than the treble and bass, or those exposed by clearly different tonality (the trumpet part in a folk song). For example, it is difficult to tell the difference between {d, f♯, a, d} and {d, a, f♯, d}. Only a few musicians, even professionals, can pull that off. You can hear texture, though, so you can learn to tell if something is major or minor, or has other non-triadic parts. You put that together with what you already know about music, and you can figure out the other notes, even if not the order.

Country songs are a good place to start learning to hear chord progressions, mostly because they only occasionally wander away from 1, 4, and 5 in the major key. The rare exceptions should be easy to locate and identify, but remember that first inversion major chords often sound like minor chords, so listen carefully. Folk tunes are a good next step. You will probably want to hold off on Stravinsky for now.

I could say to check your listening skills against on-line chord charts, but they are so often wrong, that they are likely to get you more confused than anything else. Published scores are usually right, although they may not be in the same key. The relative relationships, though, should be the same.

Moving on

In the next section we will continue with chord structure, moving beyond triads to expanded chords (like D9, etc.)

© 2013 Alan Humm