Triads and Inversions

Do you know how to play a G chord in first inversion? How about a D chord in 2nd inversion?

Knowing all the inversions can allow you to create more interesting bass lines for those standard

chord progressions as well as give you countless voicing possiblities on new chord progressions.

This a "concept" lesson that doesn't deal with any specific song yet contains important fundamental

voicings every guitarist should know. Work thru these voicings and maybe they'll be a catalyst for

the creation of the next great three chord song.

First a quick review on the basic triads:

Major triad (Ma3 plus a mi3, i.e. C E G),

Minor triad (mi3 plus a Ma3, i.e. C Eb G),

Diminished triad (mi3 plus a mi3, i.e. C Eb Gb),

Augmented Triad (Ma3 plus a Ma3, i.e. C E G#)

These days two additional three note structures are commonly used:

sus2 (or 2) triad (ma2 plus a P4, i.e. C D G) U2 and the Police used this alot.

sus4 triad (P4 plus a Ma2, i.e. C F G) in classical harmony this chord always resolves to a

more "stable" chord, in contemporary usage this chord doesn't need to resolve (unless, of

course, you want it to resolve)

So a triad has just three note names, but many triads are six string chords (like the basic E or G

chords). If you haven't already figured it out, notice there are only three different letter names used

on those chords. For instance the G chord is voiced (from string 6 to 1) G,B,D,G,B,G. Only G

(root), B (3rd) and D (5th) letter names are used but there are two 3rds (B) and three roots (G) in

addition to the one 5th (D).

The extra roots and 3rd are referred to as "doubling" chord tones. All basic major

and minor chords contain only 3 different letter names, the doubling of chord tones accounts for the

extra string(s) used for these chords.

For this lesson we will use simple three note versions of the triads, no doubling is used. In addition,

we will voice the triads in close position (the chord tones are as close together as possible, as

opposed to "open position" examined in a later lesson). First we start with root position triads then

work toward the inversions.

Four root position triads of each quality, with roots on strings 6 thru 3

Root position major triads

Root position minor triads

Root position diminished triads

Root position augmented triads

Root position sus2 triads

Root position sus4 triads

Four 1st inversion triads of each quality, with roots on strings 4 thru 1

First inversion major triads

First inversion minor triads

First inversion diminished triads

First inversion augmented triads

First inversion sus2 triads

This inversion results in a structure of Perfect 4ths, sometimes referred to as Quartal

Harmony. These would referred to as root position Quartal triads. Sorry,it sometimes gets

confusing.

First inversion sus4 triads

Notice how these voicings look like root position Sus2 chords (except the root is on a

different string). The structure of the Sus2 and Sus4 triads turn out to be inversions of one

another and are also related to Quartal Harmony.

Four 2nd inversion triads of each quality, with roots on strings 5 thru 2

Second inversion major triads

Second inversion minor triads

Second inversion diminished triads

Second inversion augmented triads

Second inversion sus2 triads

look familiar?

Second inversion sus4 triads

Hmm, didn't I see these before?

Let's examine the simple progression I-IV-V-I. This is referred to a "diatonic" chord progression,

one that uses notes from a single diatonic scale. In this lesson the examples use the major scale and

the harmonic minor scale to create these basic diatonic progressions in major and minor

respectively.

First the progression in major. In a major key the I, IV and V triads are all major in quality and

there are many way to connect the chords of this progression with regard to voiceleading.

We'll start by examining a limited set that uses a common tone voiceleading principle taught in

traditional harmony courses.

notation file

The common tone voicing shown at the above right (after the double bar line) is based on a

minimum motion prinicple that produces smooth voiceleading. The root position I chord moves to a

2nd inversion IV chord then a 1st inversion V chord and back to a root positon I chord.

The root of the I chord is a common tone with the IV chord (it is the 5th of the IV chord) and can be

kept in the lowest voice as the other two notes of the I chord move up one scale degree to become

the correct notes for the IV chord. (The 3rd and 5th of the I chord move up to become the root and

3rd respectively of the IV chord. It sounds more complicated than it really is!)

The movement from the IV chord to the V chord could have been simply up one whole step in

parallel motion however I've decided to go a different direction for three reasons:

1. Since there are no common tones between the IV and V chords (or between any triads of adjacient scale degrees i.e. I chord and II chord) there are no tones that direct the

voiceleading one way are another. Although it might seem most obvious to move in the

direction of the root movement of the progression (in the case, up from IV to V), by forcing

the voicing downward you create another relatively smooth voiceleading link to add to your

basic repertoire of chord connecting skills.

2. This sets up the V to I connection that I want, in other words I'm in control and recognize that the most obvious voiceleading from IV to V (up) is not the best for my specific goals

(to end on the same chord inversion that I started)

3. Tradition. Although the dreaded "parallel 5ths" (I jest) are not an issue in this example, if you continue this voiceleading idea and begin with a 1st inversion I chord the IV and V

chords are in root position. (are you bored yet?) The "obvious" up voiceleading movement

from IV to V will result in parallel 5ths!!! (sometime a few hundred years ago in some

learned music people got a bug up their butt and decided that parallel 5ths were a bad thing,

I've never understood that notion, however traditional music education has sort of hung on

to this rule. I suppose they still teach vacuum tube theory in electronic courses also.). The

way to avoid parallel 5ths (for those who care) is to "force" the voicing down. In other

words, don't move in parallel motion (in this case up) with the root movement of the two

chords. Instead, go the other direction (in this case, down) and you'll never have parallel

5ths, even if/when you add low roots to all the chord voicings (as in a basic four-part writing

assignment).

Who cares? (If you're still reading, maybe you care.) Welllll, I think its nice to know what

the traditions are so you can break them with a certain knowing smugness (but then I may

need profession help). Are parallel 5ths a bad thing? Really? Of course they aren't, and to

most people they sound fine (even good). So where am I going with this nitpicky nonsense?

Well, I have a confession to make.

I'm almost ashamed to admit it but I am guilty of marking students papers with red for the

meager offense of parallel 5ths. My respect for tradition produces a mild insanity that

prevents me from being ashamed. Sorry.

Anyway, regardless of your voiceleading politics, these common tone voicings are an essential

building block towards learning the fingerboard. And they sound nice too.

A set on strings 6,5,and 4

A set on strings 5, 4 and 3

A set on strings 4, 3 and 2

A set on strings 3, 2 and 1

for Mac:

11kHz aiff file of I-IV-V-I in major (350K)

5.5kHz aiff file of I-IV-V-I in major (180K)

for PC:

11kHz wav file of I-IV-V-I in major (350K)

5.5kHz wav file of I-IV-V-I in major (180K)

Now in a Minor Key, using the harmonic form, the I and IV chords are minor, while the V chord is

major.

A set on strings 6,5,and 4

A set on strings 5, 4 and 3

A set on strings 4, 3 and 2

A set on strings 3, 2 and 1

for Mac:

11kHz aiff file of I-IV-V-I in minor (400K)

5.5kHz aiff file of I-IV-V-I in minor (200K)

for PC:

11kHz wav file of I-IV-V-I in minor (400K)

5.5kHz wav file of I-IV-V-I in minor (200K)

Summary of diatonic common tone voiceleading principles

The principles illustrated this lesson are summarized below:

1. Diatonic chord progressions that have a root movement up a 4th (i.e. (I to IV) or (V to I) contain one common tone. The other two tones of the first chord move up one scale degree

to create the second chord. Try it, it works.

(conversely, progressions whose root movement move down a 4th i.e. plagal cadences: IV

to I, have one common tone and two tones moving down to the next chord. Test it out

yourself.) Get used to pivoting around the common tone of the two chords of these types of

progressions. They are the most common type of harmonic progressions.

By the way, many books refer to these progressions as root movement of a 5th. The

progression up a 4th will land on the same letter name as a progression down a 5th (they will

be one octave apart). Likewise a progression down a 4th will land on the same letter name as

a progression up a 5th. For theorical purposes they are considered equivalent and either the

4th or 5th will be used depending on the contextual needs.

Just remember this simple music math. (up a P4) = (down a P5) P = Perfect

The other direction also equates. (down a P4) = (up a P5).

The value of this knowledge is that when adding a bass (doubling the root) to the above

mentioned 3 note chord voicings, you know that when using the 4th interval you will be

moving in the same direction as other 2 moving voices (remember there is one common

tone) and when using the 5th interval instead you will be moving in contrary motion with

the other 2 moving voices.

2. Diatonic chord progressions that have a root movement of a 2nd (up or down) have no common tones. Going in the direction of the root movement produces a smooth parallel

voicing that is easy to find. Going in the opposite direction of the root movement can

produce relatively smooth voiceleading as well. The Old Masters often liked moving the

voices in the opposite direction as root movement's especially when the chord was in root

position. This method has been taught as the more "sophisticated" method and is one

guideline for following the common practice period rules. While, of course, no composer

ever feels any obligation to write within the common practice period rules, it does makes for

conversation, albeit boring.

3. Diatonic chord progressions that have root movement of a 3rd (no examples in this lesson, but here are the facts anyway) have two common tones*. The other chord tone moves one

scale degree to create the new chord. BTW, the non-common tone always moves in the

opposite direction as the root movement, i.e. C to Am (root movement down a 3rd), the

non-common tone 'g' (fifth of the C chord) moves up to 'a' (root of the Am chord) the other

notes (c and e) are common to both chord and don't move. Another example: C to Em (root

movement up a 3rd), the non-common tone is 'c' and it moves down to 'b'. The other chord

tones (e and g) are common to both chords.

* When shifting between different forms of minor, as is often done, there might be only one

common tone between the two chords. example key of Am: the VII chord from natural

minor G major (g,b,d) and the V chord from harmonic minor E major (e, g#, b).

Its really easy once you know these common tone voiceleading principles. Feel free to use some

totally different voicings as the need arises, but if you need some smooth voicings try these.

One final word: Don't cop a "I-already-know-this-simple-stuff" attitude! Completely master these

simple voicings! Memorize their shapes and their sounds!! It takes a little time but it is time well

spent. They are more useful than you may realize at first.