A chord, simply, is any combination of three or more notes. While two notes is technically harmony, they are not considered chords. Theoretically, any combination of notes is a chord, however, when used in a certain combination, some notes complement each other better than others. These notes are played together the most often, and make up the most popular chords. Because of the broad nature of this definition, types of chords have been developed that "sound good", in the western philosophy of music.
Types of Triads
The following chords can be played in any key. To understand them, one should have the basic knowledge of a scale first. When considering what quality a chord is (major, minor, etc.), all that matters are the names of the 3 notes; it does not matter whether some notes are doubled or played in different octaves. For example, a C major triad must have a C, an E and a G, but it doesn't matter which is on bottom, nor does it matter if there are 2 E's or 2 G's.
The major triad is often symbolized with a capital letter (C). It is three notes: the first, third, and fifth note of a scale. Alternatively, you can figure this chord out by adding a note a major third (4 half-steps) up from the root note and then a minor third (3 half-steps) up from that. If you add the half-steps of a major and minor third you will notice the third note is 7 half-steps up from the root making a perfect fifth. This interval will remain the same in major and minor chords. All primary triads are created by stacking intervals of a third. It is a very whole sounding chord, and is found within most, if not all popular songs.
C Major triads, C - E - G: File:CMajor.png
The minor triad is often symbolized with a lower case letter, or 'min', or just an 'm' (c | Cmin | Cm). It is composed of three notes: the first, flat-third, and fifth. The lowered third represents the third note of a minor scale. Alternatively, you can figure this chord out by adding a note a minor third (3 half-steps) up from the root note and then a major third (4 half-steps) up from that. The quality of this chord is not as full as the major chord, and has a darker complexion. It also is found in a majority of popular music.
C Minor triads, C - Eb - G: File:CMinor.png
The diminished triad can be symbolized with either a '°' or with the abbreviation "dim" (C° | Cdim). Its components include: the first, flat-third, and flat-fifth. Alternatively, you can figure this chord out by adding a note a minor third (3 half-steps) up from the root note and then another minor third (3 half-steps) up from that. If you add the half-steps of two minor thirds together you will notice the third note is 6 half-steps up from the root making a diminished fifth, giving the chord its name. Having 2 lowered notes, a diminished chord does not have great euphony. It sounds slightly out of place, but adds a certain musical flavor.
C Diminished triads, C - Eb - Gb: File:CDim2.png
The augmented triad is usually symbolized with a '+' or 'aug'(C+ | Caug). It is rarely seen in music, but considered one of the main chord structures. It combines: the first, third, and an raised fifth. Alternatively, you can figure this chord out by adding a note a major third (4 half-steps) up from the root note and then another major third (4 half-steps) up from that. If you add the half-steps of two major thirds together you will notice the third note is 8 half-steps up from the root making an augmented fifth, giving the chord its name. An augmented fifth sounds the same as a minor sixth but is notated differently and consequently will sound different in context. It has a very unique sound.
C Augmented triads, C - E - G#: File:CAug.png
Dominant Seventh Chord
A seventh chord is attached to any other chord by the addition of the number '7' (Bb7). It can be attached to pretty much any chord, not just the major chord: (Bb7 | dim Bb7). Opposed to the logical addition of the seventh note of the scale, a flat-seventh note is added. When the seventh note is flat it is known as a "minor" 7. This chord became a dominant due to confusion if you were to say Bb minor7. That may lead somebody to believe it is a Bbminor with a 7th. Instead it is just a Bb7.
Bb - D - F - Ab
Major Seventh Chord
Like a dominant seventh chord, a note is added to a triad to create a major seventh chord. While a '7' represents the dominant seventh chord, the letters "maj" and a '7' represent a major seventh chord (Bb maj7). The note added to this chord is the seventh note of the root's major scale.
Bb - D - F - A
The suspended chord, also called sustained chord, is symbolized with "sus" or "sus4" (Bbsus | Bbsus4).
It is called suspended because the "third" of the chord is replaced by a fourth. Traditionally the fourth would resolve to the third of the chord. For example, a Csus chord would be composed of the notes:
C, F, G instead of C, E, G (the normal triad)
After a while the F, would move down to the E to form the normal triad. Now days, the sus4 chord can stand on its own and doesn't always resolve to a normal triad.
In the normal triad on C, the note E is the "third" because is it an interval of a third above C.
Another version of this chord is symbolized with "sus2" (Bbsus2).
A sus2 with C as its root would be:
C, D, G
Other examples, with Bb as the root:
Bb - Eb - F (Sus4)
Bb - C - F (Sus2)
This chord is just like a suspended chord in that it uses the second and fourth note. The difference is that, whereas in a suspended chord the third note is omitted, in an "Add2/Add4" chord, the third is kept.
Bb - D - Eb - F (add4)
Bb - C - D - F (add2)
The fifth chord or "power chord" is unusual because it only has two notes. The fifth chord is only the first and fifth scale degree of the root note and is represented with a 5 (Bb5). It is also called a "power chord" because it produces a very powerful sound. Many musicians use it when they wish the chord to have neither a major nor a minor effect.
The sound produced by a so called "power chord" sometimes has an ancient quality to it because it was used in early music. For example, it was used in Gregorian chant and was called parallel organum when a series of such chords were used. The fifth chord was a favorite of Hindemith, nearly all of his compositions end with this chord.
Bb - F
The sixth chord is a four note chord, adding the sixth note of the root's major scale to a triad. All triads can become sixths, represented by the addition of a '6' (e.g. Bbm6).
Bb - Db - F - G
All of these symbols and chords can be combined to form all other chords. For example, one could create a minor major seventh chord (Bbmmaj7).
Bb - Db - F - A
Technically, any combination of notes can be termed with the combination of these previous basic chord types.