This document is for strictly personal use only. No public use may be made, including in the course of teaching, without the prior consent of the author.
Three-note chords (triads)
A chord is a set of at least 3 sounds played simultaneously.
Definition
A chord is a set of at least 3 sounds played simultaneously. A three-note chord is formed by 3 different notes.
Piano
Audio of Figure 1
chordis used when 2 notes are played simultaneously, although it is not an actual chord but a harmonic interval.
The term triad
is also used to designate a 3-note chord.
Root position and inversions
The same chord can be written in many different ways. A 3-note chord has three states.
Root position
The root position is the basic layout of the chord. In the root position, a chord is always constituted by a stack of thirds.
A 3-note chord will therefore consist of two harmonic thirds superimposed.
Piano
Audio of Figure 2
In the root position, the root note is at the bottom of the chord, which is the lowest note. The root note gives its name to the chord.
For example, in the root position, the C Major perfect chord has a C on the bass.
First inversion
As for intervals, chords can be reversed. For that, you just have to put the bass of the root position to the upper octave.
To get the first inversion of the C Major perfect chord, you have to put the C an octave above.
Piano
Audio of Figure 4
The E becomes the bass of the first inversion, but the root note remains the C. Note also that between G and C, we get a fourth: the stack of thirds has disappeared.
Second inversion
To get the second inversion, you have to put the bass of the first inversion one octave higher.
Piano
Audio of Figure 5
The bass (E in orange) of the first inversion becomes the highest note of the second inversion. The root note (C in turquoise) remains in place. The C Major perfect chord in its second inversion therefore has G for bass.
Piano
Audio of figure 6
Nature of the 3-note chords
Since a chord, in its root position, is always a stack of thirds and a third can be either major or minor, there are a total of 4 three-note chord possibilities.
Perfect chords
Two thirds stacked form a fifth. A 3-note chord is perfect when its extreme notes form a perfect fifth.
Major perfect chord
A Major perfect chord is formed by a major third between the root note and the intermediate note and a perfect fifth between the root note and the upper note.
If we consider the two thirds, the first is major and the second is minor.
Minor perfect chord
A minor perfect chord is formed by a minor third between the root note and the intermediate note and a perfect fifth between the root note and the upper note.
Piano
Audio of Figure 9
If we consider the two thirds, the first is minor and the second is major.
Diminished chord
When the two stacked thirds are minor, the fifth obtained between the root note and the upper note is diminished. The chord will therefore be qualified as diminished
Piano
Audio of Figure 11
Augmented chord
When the two stacked thirds are major, the fifth obtained between the root note and the upper note is augmented. The chord will therefore be qualified as augmented.
Piano
Audio of Figure 13
Piano
Audio of Figure 15
Open and closed positions
So far, we have studied chords in closed position, that is, with a minimum distance between each note. However, it is possible to "burst" the layout of the notes. These positions are called open positions. There is an infinity of open positions.
Being in an open position does not alter the state or the nature of the chord. When a chord is in an open position, it is necessary to put it back in the closed position in order to analyze it more easily.
In the following figure, the E of the chord in the closed position is octaviated to obtain an open position. The bass (C in dark green) remains in place.
Piano
Audio of Figure 16
Doubling
Each note of a chord can be doubled, that is, added to a different octave. Like the type of position, the presence of one or more doublings does not alter the inversion or the nature of the chord. Although the chord has more than 3 notes, it is still considered a 3-note chord.
It is therefore necessary to eliminate the doublings before being able to analyze a chord.
Piano
Audio of Figure 17 (without arpegios)
In the first example, there is a doubling of the C: the C is maintained on the bass and a doubling is added to the octave.
Piano - Audio of figure 17
First example
In the second example, there are two doublings: C and G. The C is not maintained at the same height, but it remains at the bass of the chord: the state of the chord is thus not modified. A doubling of C is added at the top of the chord. The G is held in place and a doubling is added on the bass clef.
Piano - Audio of figure 17
Second example
In the last example, there are three doublings: two doublings of C and a doubling of G. There too, the bass, although in the lower octave, remains a C: the nature and the state of the chord are therefore not modified.
Piano - Audio of figure 17
Third example
Chord analysis
In the previous paragraphs, we have studied in detail all the characteristics of a three-note chord. For the sake of clarity, we have confined ourselves to the study of chords with C as a root note. We will now deepen the process of chord analysis, explain the different steps and illustrate it with many examples.
Analysis steps
Here are the steps for analyzing a chord:
- Eliminate doublings
- Put in closed position
- Put back in root position
- Determine the nature and the inversion
This step allows you to delete unnecessary notes and thus verify that this is a 3-note chord.
This step reduces the extent of the chord so that all intervals are smaller than the octave.
To return the chord in its root position, the note layout must be modified in order to result in a stack of thirds.
Once in root position, the chord can be analyzed.
Detailed examples
Here are several illustrations of chord analysis following the steps described in the previous paragraph.
Piano
Audio of Figure 18
- Eliminate doublings
- Put in closed position
- Put back in root position
- Determine the nature and the inversion
The E (first note from the bottom) is doubled three times, once in bass clef and twice in treble clef. We remove these three doublings. The other two notes (A and C) are not doubled, so we keep them.
To simplify the reading, we move the E being in bass clef on the treble clef staff. Note that it would have been quite possible to move the other two notes in bass clef, the essential thing is to obtain a closed position at the end of this step.
To get the chord back to its root position, the note layout must be modified in order to result in a stack of thirds. We put the E an octave higher to get this stack of thirds. Again, it would have been quite right to move the other two notes to the lower octave.
The chord is now in its root position and can be analyzed. Between the extreme notes (A and E), there is a perfect fifth, so it's a perfect chord. Between A and C, there is a minor third. It's a minor perfect chord. As the root note is A, it is the A minor perfect chord. And since initially we had a E as bass, it's a A minor perfect chord in its second inversion.
Piano
Audio of Figure 19
- Eliminate doublings
- Put in closed position
- Put back in root position
- Determine the nature and the inversion
The D (on bass) is not doubled, we keep it. On the other hand, F and B are doubled once each, at the top of the chord. We therefore delete the two upper notes.
We move the F from treble to bass clef. (Here, we did the opposite of the previous example by writing the closed position on the bass clef.)
There is a fourth between F and B: the chord is not in root position. To put it back to its root position, we write the B an octave lower, to obtain a stack of thirds.
The chord is now in its root position and can be analyzed. Between the extreme notes (B and F ), there is a perfect fifth, so it's a perfect chord. Between B and D, there is a minor third. It's a minor perfect chord. Since the root note is B, it is the perfect chord of B minor. And since initially we had a D as bass, it's a B minor perfect chord in its first inversion.
Piano
Audio of Figure 20
- Eliminate doublings
- Put in closed position
- Put back in root position
- Determine the nature and the inversion
The E (on the bass) is doubled twice, once in bass clef and once in treble clef: we remove these doublings. The B (bass clef) is also doubled in treble clef: we delete it. Finally, G is present only once: we keep it.
We move the two notes (E and B) from bass to treble clef. At this point, notice that we find a part of the original chord. The closed position was therefore included in the starting chord. So we could have gone directly from the starting chord to the closed position without going through the previous step. With training, you will learn to locate this kind of shortcut to speed up the reading of a chord.
This is a stack of thirds. The chord is already in root position.
Between the extreme notes (E and B), there is a perfect fifth, so it's a perfect chord. Between E and G , there is a major third. It is a major perfect chord. Since the root note is the E, it is the E Major perfect chord in its root position.
Piano
Audio of Figure 21
- Eliminate doublings
- Put in closed position
- Put back in root position
- Determine the nature and the inversion
All the notes present in treble clef are already present in bass clef. We thus remove the notes in treble clef.
The chord obtained is already in closed position, so there is nothing to do.
In order to obtain a stack of thirds, we move the D to the lower octave.
Between the extreme notes (D and A ), there is a diminished fifth. Between D and F, there is a minor third. It's therefore a diminished chord. Since the root note is D, it is a D diminished chord. In the original chord, the bass note is F, so this is the first inversion of D diminished.