Triads may be thought of as generated by stacking two thirds atop one another. For example:

U

13

C HORDS

Thus far, we’ve discussed individual pitches (in Units 3, 5, and 6), and pairs of pitches and the intervals they form (in Unit 7). This unit will examine combinations of three or more pitches as they form chords.

Chords

Two pitches can combine to form an interval, as we learned in Unit 7. Three or more pitches can combine to form what musicians call a CHORD. Some musicians feel that only certain three- and four-note groups constitute chords.

Others feel that some chords can be formed even by five or more pitches. We’ll investigate three- and four-note chords in this unit, and touch on the idea of extending chords with more pitches.

In Western tonal music, not every combination of three or more pitches forms a chord. In fact, what we consider to be a chord is based on some narrow restrictions, stemming from acoustic principles and cultural practices. We’ll begin by investigating the simplest of chords — triads.

Triads as Stacks of Thirds

Triads may be thought of as generated by stacking two thirds atop one another.

For example:

The Members of a Triad: Root, Third, and Fifth

When triads are viewed as a stack of thirds, the lowest pitch is the ROOT. The pitch a third above the root is called the THIRD, and the pitch a fifth above the root is called the FIFTH:

Triad Qualities

To begin with, let’s build triads by using only the pitches in a single major key.

We can build a triad on each scale degree in a major scale, using only the pitches from the key of that scale:

Let’s now investigate the structure of these triads by examining the thirds they comprise. The first consists of a major third surmounted by a minor third:

But the second has a minor third surmounted by a major one:

fifth

third

root

m _

M3

M3

m _

If you examine the remaining triads, you’ll notice that they are all either major or minor triads, except for one:

This triad consists of two minor thirds. We call this a DIMINISHED TRIAD.

And there is one more type of triad, which can’t be constructed from the diatonic pitches in a single key, but which is nonetheless important to know. If we stack two major triads atop one another, the result is an AUGMENTED TRIAD.

To determine the quality of a triad, identify the qualities of its two component thirds (from root to third, and from third to fifth), and compare to the triad- quality definitions above. For example, consider the following triad:

The interval from root to third (Fs to A) is a m_

3. The interval from third to fifth (A to Cs) is a M3. Therefore, this is a minor triad.

A MAJOR TRIAD can be constructed by stacking two thirds: a major

third with a minor third above it.

A MINOR TRIAD can be constructed by stacking two thirds: a minor

third with a major third above it.

A DIMINISHED TRIAD can be constructed by stacking two thirds: a minor

third with a minor third above it.

An AUGMENTED

TRIAD can be constructed by stacking two thirds: a major

third with a major third above

it.

m _

m _

M3

M3

Naming Triads

We name triads by their roots. There are two common ways to do this: one uses the letter name of the root; the other uses a Roman numeral to label the scale degree of the root within a key.

Naming Triads with Letter Names

We can name a triad by stating the letter name of its root, followed by the quality of the triad. Here’s an example:

Bf major

The root of that triad is Bf. And because it consists of a major third surmounted by a minor third, the quality of that triad is major. Therefore, we may call it a Bf major triad.

Some musicians use symbols to represent each triad’s quality. This kind of system is used widely among jazz, rock, and pop musicians, but the symbols vary quite widely. Here are the four types of triads, each built on C, and some of the more common pop/jazz chord symbols used to represent them:

triad type example symbol(s)

major triad

Cmaj, C

minor triad

Cmin, c, Cm, C-

diminished triad

Cdim, C

augmented triad

Caug, C+

Naming Triads with Roman Numerals

We can also name a triad by using a Roman numeral to represent the scale degree of its root. For example, look at the chord formed by the pitches in m. 5 of the following folk song:

Those pitches (Af – C – Ef) form a major triad with a root of Af — the 4^th scale degree in the key of Ef major. Therefore, we use the Roman numeral

›

Ef: ›

This kind of labeling requires the context of a prevailing key. You must be sure to identify the tonic of the surrounding music and write that down before any Roman numerals you write. You should write the tonic once, followed by a colon, at the beginning of a passage before you write any Roman numerals to identify chords. For example:

B: ⁄ › fi ⁄

We can use upper-case and lower-case Roman numerals to distinguish between major and minor chords.

F: ⁄ ™

We represent diminished triads by adding a superscript circle to the right of a lower-case Roman numeral. We represent augmented triads by adding a superscript plus sign to the right of an upper-case Roman numeral.

c: ¶ o fi+

Inverting Triads

In most Western music, the lowest pitch in a chord is especially important because it supports and governs the pitches above it. We refer to that lowest pitch as “the bass,” and we say that a pitch or member of the chord is “in the bass.” For example, in referring to the very first triad we examined at the beginning of this chapter, we could say “the bass is C” or “C is in the bass.” We could also say that the root of the chord is in the bass.

Triads don’t always appear with their roots in bass. In fact, many times the third of a triad will show up in the bass. Thus, we might find the same C-major triad not with C (the root) in the bass, but with E (the third) in the bass:

That chord is still made up of the pitches of the C-major triad, but those pitches have been rearranged so that a different member of the chord is in the bass. When this happens, we say that the triad has been INVERTED.

If the root of a chord is in the bass, we say the chord is in ROOT POSITION.

If the third of a chord is in the bass, we say the chord is in FIRST INVERSION.

If the fifth of a chord is in the bass, we say the chord is in SECOND INVERSION.

It’s important to note the intervals above the bass (not the root) formed by each inversion. In root position triads, the other two chord members form a fifth and third above the bass. (These might appear in higher octaves, but we still refer to the intervals they form as fifths and thirds.) We say that this triad is in ⁵₃ (“five- three”) position.

In a first-inversion triad, the other two chord members form a sixth and third above the bass, and we can also say that the triad is in ⁶₃ (“six-three”) position.

And in second inversion, the other two chord members form a sixth and fourth above the bass, and we can also say that the triad is in ⁶4 (“six-four”) position.

A chord is INVERTED when a member other than the root

appears in the bass.

A FIRST INVERSION chord has its third

in the bass.

A ROOT POSITION chord

has its root in the bass.

A SECOND INVERSION chord has its fifth

in the bass.

5

3

6

3

These numbers represent intervals above the

bass

These numbers represent intervals above the

bass (not the same as root, third,

or fifth)

In Western music, most triads appear frequently in root position or first inversion. Second inversion triads — because of the prominence of the dissonant fourth above the bass — are usually reserved for special uses.¹

In classical music theory, we combine a Roman numeral that represents the root (not the bass) of a triad with Arabic numerals, called FIGURED BASS, to indicate the intervals above the bass in inverted chords.² If a triad is in root position (with a fifth and third above the bass), we write only the Roman numeral. A Roman numeral without figured bass represents a root-position chord:

D: fi

For triads in first inversion, we write “6” (as shorthand for ⁶3):

D: fi ^

And for triads in second inversion, we write “⁶₄.”

1 Those special uses are nearly always restricted to cadential, passing, neighboring (or pedal), and arpeggiated six-four chords. Although any discussion of these uses is beyond the scope of this manual, you should keep in mind that six-four chords are not equivalent in sound or affect to root-position and first-inversion triads and may not be freely substituted for them.

6

4

These numbers represent intervals above the

bass (not the same as root, third,

or fifth)

D: fi ¢^

Pop, rock, and jazz musicians represent inverted chords by drawing a line under the chord symbol, then writing the letter name of the pitch in the bass. For example:

Amaj C#

Constructing Triads

You may be given certain sets of criteria on which you must construct triads. In general, you’ll be given a root, a quality, and an inversion. This might come it one of several forms. For example:

Write a B-major triad in first inversion:

Write a mediant chord in root position in the key of F major:

F: £

Write the following chord:

Write the following chord:

Seventh Chords

Since triads are built by stacking thirds, it seems logical that more complex chords can be constructed by stacking more thirds above the three pitches of a triad. For example:

G G& G

(

Four-note chords generated by stacking thirds are quite common in Western music, so we will investigate them in greater depth here. Chords built from stacking more thirds (chords with 9ths, 11ths, etc.) and chords with added or altered tones (+6, f9, for example) are beyond the scope of this manual.³

F# min C#

e: ™ o^

Four-note chords are often referred to as “seventh chords” because — when such chords are in root position — there is a seventh above the root.

There are several different qualities of seventh chords used in Western tonal music. Each has a distinct sound based on the intervals between its pitches.

Particularly important are the quality of the triad formed by the root, third, and fifth, and the quality of the interval formed by the root and seventh.

The following table shows the most common types of seventh chords, written in root position with the third, fifth, and seventh printed directly above each root as a stack of thirds. To the left of each stack of thirds are printed the qualities of the successive thirds. To the right of each stack are printed the quality of the triad and the quality of the seventh above the root. In parentheses below each chord name are alternative chord names with which you should also become familiar.

Below the chart are some common symbols for these chords (each written — for the sake of example — with D as the root):

Major-major (Major)

Major-minor (“Dominant 7^th”)

Minor-minor (Minor)

Half-diminished Fully- diminished (Diminished)

w w w w w

w w w w w

w w w w w

w w w w w

Dmaj &

Dma &

DM &

DΔ &

D & Dmin &

Dmi &

Dm &

D- &

D O ^&

Dm &

% D- &

%

D o&

Ddim &

And here are examples of those seventh chords with Roman-numeral and figured-bass symbols:

http://www.tsmp.org/keyboard/lias/lias_survival_kit_beginning_jazz.html and M7

Major triad

M3 m3 M3

m7

Major triad

M3 m3 m3

m7

Minor triad

m3 M3 m3

m7

Dim.

triad

m3 m3 M3

d7

Dim.

triad

m3 m3 m3

C: ⁄ & fi & ™ & ¶ O& ¶ o&

Like triads, seventh chords may be inverted. Here are the figured-bass symbols used to represent seventh chords in root position and their three inversions (here appended to a fi chord:

G: fi & fi ∞^ fi £$ fi ™$

Chord Spacing & Doubling

Thus far, we’ve been looking at only the simplest incarnations of triads — three pitches spaced closely together. However, triads appear in all kinds of spacing (also called “voicing”). For example, the pitches in a triad need not be spaced closely together:

And it is possible to double members of a triad at various octaves as well:

Different doublings and spacings change the texture (see Unit 15) of a chord (and hence some of its affect), but they do not alter its root, quality, and inversion. For example, the following are all E major triads in first-inversion:

In assessing the root, quality, and inversion of a chord, we ignore the spacing and any doublings.

Here are some musical excerpts that exhibit an assortment of spacings and doublings. Identify the root, quality, and inversion of each chord, ignoring spacing and doubling:

Non-chord Tones

Because music is made up of various strands of activity, some parts may move temporarily to pitches that are not part of the prevailing chord. You can usually use your eye (and ear) to determine the prevailing chord despite these non-chord tones.

Here are some excerpts that contain non-chord tones (each of which is circled):

We’ll learn more about non-chord tones in Unit 14.

Figuration

Instruments don’t always strike all the pitches of a chord together. Instead, they often produce those pitches in succession — either each one separately, or some mixture of separate notes and combinations of notes. It’s important to be able to recognize for how long one chord is in effect, noting the various figurations, until it’s replaced by another chord (with its own figurations), and so on.

Here are some excerpts that use various kinds of figuration (each chord is enclosed in a rectangle):

Melodic Expression of Chords

Although certain instruments (such as the piano and guitar) are particularly adept at sounding chords by producing multiple pitches simultaneously (and groups of instruments together can create the same effect), even instruments and voices producing one pitch at a time can render chords by ARPEGGIATING through some or all of the pitches of each chord in succession.

Here are some examples of this effect:

E major triad____________________________

G: ⁄_____________________________________ fi____________________________________ ( ^⁄ )

D: ⁄_______________ ›____________ ⁄_______________

Ef major__ D diminished__________ Ef major_____

ARPEGGIATION is the process of

horizontally unfolding the pitches of a chord.