- G
- F
- C
There are two ways to think about building triads. One is based on intervals, and the other is based on scales. I will use both in the following discussion, so first I will cover each separately.
The interval approach looks at the relationships between the three notes in the triad. Here are the four triad types by interval:
| Triad Name | Component Intervals | Overall Interval |
|---|---|---|
| Major | M3+m3 | P5 |
| minor | m3+M3 | P5 |
| Augmented | M3+M3 | A5 |
| diminished | m3+m3 | d5 |
Some examples:
- G
- F
- C
The major and minor triads get their names from their bottom intervals, M3 and m3, respectively. Because major and minor triads both span a P5, they differ by only their middle note. In the C major and C minor examples above, the C and G are the same; the only thing that varies is the E, which is natural in the major and flat in the minor. The augmented and diminished triads do not span a P5. Their augmented and diminished fifths give the augmented and diminished triads their names.
For the scales approach, let's start with a major scale. In this approach, we build triads with the notes in the scale. Let's recall the major scale's interval relationships:
1 2 3 4 5 6 7 8 \ / \ / \ / \ / \ / \ / \ / M2 M2 m2 M2 M2 M2 m2Recall also that a M3 can be thought of as being composed of M2+M2, and a m3 M2+m2 (or m2+M2). We can build a triad on each scale degree. For example, the triad starting on the first degree will be the major triad 1 -3- 5 (which is why the notes are called the "root," "third," and "fifth," respectively). Remember that stuff about how modes were classified as major or minor? Saying that the triad on 1 is major or minor is almost the same as saying that the scale is major or minor.
By convention, scale triads are numbered with Roman numerals, as follows:
(or the
"dim" abbreviation)
Here are the naturally-occurring triads in major and minor scales (note that the scale degree names are also names of the triads built on them):
| Scale Degree |
Degree & Triad Name |
Degrees in the Triad |
Major Scale Triad Type & Symbol |
Minor Scale Triad Type & Symbol |
|---|---|---|---|---|
| 1 | tonic | 1 - 3 - 5 | Major, I | minor, i |
| 2 | supertonic | 2- 4- 6 | minor, ii | diminished, ii |
| 3 | mediant | 3 - 5 - 7 | minor, iii | major, III |
| 4 | subdominant | 4 - 6 - 1 | major, IV | minor, iv |
| 5 | dominant | 5 - 7 - 2 | major, V | minor, v |
| 6 | submediant | 6 - 1 - 3 | minor, vi | major, VI |
| 7 | leading tone (major scale)* subtonic (minor scale) |
7 - 2 - 4 | diminished, vii |
major, VII |
*recall that the seventh degree is called the "leading tone" if it is a m2 below the tonic, and is called the "subtonic" if it is a M2 below the tonic.
You can similarly derive the triads from any other scale, such as the church modes, whole tone scale (all of whose triads are augmented), etc. All the naturally occurring triads in a scale are called diatonic.
In minor keys (and in modes with a minor dominant), the dominant chord is often altered from the diatonic minor to a major. To do so, its middle note is raised a half-step. The middle note in the dominant triad (5 - 7 - 2) is the seventh degree. Raising it a half-step makes it into a leading tone. Why is this done? Many composers found the sound of the dominant chord to be more satisfying as a major triad than as a minor. One of the most common chord progressions used to end a musical passage (or a whole piece) is to move from a dominant chord to a tonic chord. Most classical composers usually preferred using a major dominant to a minor in minor keys; the sound of the leading tone moving to tonic was felt to be stronger than from subtonic to tonic. Try playing around with it and see what you think.
All other chords - seventh chords, ninths, thirteenths, etc. - are built with triads and stacked thirds. If you add another third on top of a triad, you get four notes that span the interval of a seventh. That's a seventh chord. If you add another third on top of that, you get five notes that span the interval of a ninth (an octave + a second). That's a ninth chord. A thirteenth chord is as high as it goes (in scale terms, 13 = 6, and the next third above 6 is 1 again).
In actual practice, all the notes are often not always included in the "larger" chords, and there are some fairly standard conventions about which notes you can omit and still have the chord you want. Here are the notes in the "extended" chords (the notes in parentheses can be omitted):
You may notice that the 5 is often omitted, but not the 1 or 3. The 1 - 3 relationship defines the basis of the chord (major or minor, what the root of the chord is, etc.), so those two notes are usually considered essential. Also, the seventh is usually not omitted; ninth, eleventh, and thirteenth chords are sometimes considered to be variants on the seventh chord.
As with triads, the various combinations of M3's and m3's make for different versions of seventh, ninth, eleventh, and thirteenth chords. With so many different combinations possible, it can get a little complicated. I cover the basic variants of the seventh chord below. For more info on all these kinds of chords, consult a jazz theory book.
The most commonly used seventh chords are these: dominant seventh (also just called "seventh"), major seventh, minor seventh, diminished seventh, and half-diminished seventh. The interval relationships of these chords are as follows:
| 7th Chord Type | Component Intervals | Overall Interval |
|---|---|---|
| Dominant 7th | M3+m3+m3 | m7 |
| Major 7th | M3+m3+M3 | M7 |
| Minor 7th | m3+M3+m3 | m7 |
| Diminished 7th | m3+m3+m3 | d7 |
| Half-Diminished 7th | m3+m3+M3 | m7 |
The names tell you something about these chords. If you build a seventh chord on the dominant of a major scale, you get a dominant 7th chord. If you build a seventh chord on the tonic of a major scale, you get a major 7th chord. If you build a seventh chord on the tonic of a minor scale, you get a minor 7th chord. The diminished 7th (aka "fully-diminished 7th") is what you get by stacking m3's only, and it spans the interval of a diminished seventh. The half-diminished 7th chord occurs as the seventh chord built on the leading tone of a major scale; the "half-diminished" name both distinguishes it from its fully-diminished cousin and tells you that its overall interval is not diminished.
There are two common exceptions to the "stacked third" approach to building chords, though both are still considered variants of the basic triad. Think of a triad as being 1 - 3 - 5 of a scale. You can make chords using this triad and 4 or 6. A triad with 4 is called a suspended fourth. A "sus 4" chord is one where you play 1 - 4 - 5 instead of 1 - 3 - 5. It is a very "unstable" sound that resolves to the 1 - 3 - 5 (that is, it sounds good if you play a sus 4 followed by the "normal" triad). The idea is that the 1 - 4 - 5 is really the 1 - 3 - 5 with an errant note that wants to get back in line. Try playing this to hear how it sounds.
The sixth chord is the same 1 - 3 - 5 triad with the sixth degree added (1 - 3 - 5 - 6), though the 5 is often omitted (1 - 3 - 6). Sixth chords are used a lot in classical music for certain types of modulations (modulation = changing key).
As with intervals, chords can be inverted. In practical terms (at least for keyboard and guitar players), learning chord inversions is one of the most useful things you can do. If you have inversions of most basic chords at your disposal, reading music, improvising chords (called comping in jazz), and pretty much everything else is much, much easier. As a guitarist, I find that knowing all the basic triad inversions all over the guitar neck not only makes it a snap to generate whatever chord I need, wherever I need it, but also greatly facilitates both reading music and playing leads.
For triads, there are three inversions possible. These are called the root, first inversion, and second inversion. Triad inversions involve playing the same notes, but varying which note is where.
Example: I triad
The 1 in the first inversion is the tonic above the 3; in the second inversion, both the 1 and 3 are the notes in the octave above the 5. Note also that the first inversion is not the first form - that's the root. Sometimes people get confused by this numbering (kinda like when the first floor of a building is called the lobby and the second floor is called the first floor).
When chords are written with Roman numerals, the first inversion is indicated with a superscript 6. The 6 indicates that the interval spanned by the triad is a sixth. In our example above, that would be 3 up to 1, which is a sixth. The second inversion is indicated with a superscript 6 and 4, indicating that, as with the first inversion, the interval spanned by the triad is a sixth, but unlike the first inversion, the interval between the bottom two notes in the triad is now a fourth. In our example, that would be 5 up to 3, which is a sixth, and 5 up to 1, which is a fourth.
For chords with more than three notes, there are as many inversions as there are notes in the chord. For example, in a seventh chord, there are four possible inversions (root, first, second, and third), because there are four notes. Depending on the inversion, a dominant 7th chord will have either a d5 or an A4. A lot of attention is paid in some areas of music theory to how these tritones are resolved.
A topic related to inversion is that of voicing. Voicing refers to how you arrange a chord (as on a piano keyboard or guitar fretboard, or among various instruments in an orchestra, jazz ensemble, rock band, etc.). A full discussion of voicing would take a lot of space. I just want to introduce the concept. The idea is that if you have ten fingers or six strings or four singers or a dozen instruments or whatever, you have to decide which notes of the chord to repeat and which to omit and how to arrange the chord for who/what is playing it. I highly recommend experimenting with different chord voicings. Unusual voicings can add interest to your music (for both players and listeners), and different instruments sound very different in different registers (a register is a general area of sound pitches). There are lots of practical considerations here, but the bottom line is how it sounds. So instead of giving you a lot of ideas about what other people think sounds good, I suggest you play with voicings and see what you like. Creative use of voicings is a great way to personalize your music.
There are whole other ways to construct chords besides what I've outlined above. The stacked-third approach, while certainly the most common in western music, is only one way. Since it is based on thirds, it is also sometimes called tertian harmony. If you build chords by stacking other intervals, you get other kinds of harmony, whose names reflect the intervals used. Chords built with stacked seconds create secondal harmony; if you use fourths, it's called quartal harmony; if you use fifths, it's called quintal harmony. These are largely 20th century innovations, similar to the whole tone or octatonic scales. There's not a lot of music that is fully non-tertian; I mention these options both to provide some context for the preceding materials and to suggest alternatives you may wish to explore. In music, nothing is set in stone: follow your ears!
Introduction | Steps | Intervals | Scales | Chords | Keys
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