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Triads and Inversions

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

• 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)
  
  

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.

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.

• 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)
  

• 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

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).

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.

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