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Chords

Chords are simply combinations of three or more notes. Thus, the simplest type of chord is the triad, which is a three-note combination. Chords are built on a root, which is the bottom note when the chord is in root position. For now, all you need to know is that the root position is the “original” position of a chord. It can then be inverted, as described later on in this lesson.

Triads

Other than having a root, a triad has a third, which is the middle note, and a fifth, which is the top note. Triads are built so that the root, third, and fifth are on consecutive lines or spaces.

There are four kinds of triads, similar to the four kinds of intervals. These are major, minor, augmented, and diminished. Remember that all triads have the same generic form of being on three consecutive lines or spaces when in root position. The only differences that are made with the four different qualities should be made with accidentals (to maintain correct spelling).

Major triads consist of the root, the note a major third up from the root, and the note a perfect fifth up from the root. For example, the C major triad consists of C, E, and G.

Minor triads consist of the root, the note a minor third up from the root, and the note a perfect fifth up from the root. For example, the A minor triad consists of A, C, and E.

You may have noticed that the general rule for major and minor triads is that you use the first, third, and fifth degrees of the major/minor scale (major for the major triad, minor for the minor triad).
To create a diminished triad, however, we use the root, the minor third above the root, and the diminished fifth above the root. For example, the E diminished triad consists of E, G, and Bb.

Augmented triads are created with the root, the major third above the root, and the augmented fifth above the root. For example, the D augmented triad consists of D, F#, and A#.

Triad Notation

Triads have a special set of symbols that are useful as shorthand.
Major triads are notated in uppercase. For example, the G major triad may simply be referred to as G.
Minor triads are notated in lowercase (A minor becomes a) or are uppercase followed by a lowercase m (A minor could be Am).
Diminished triads are uppercase followed by a ° (C# diminished becomes C#° ).
Augmented triads are uppercase followed by a + (Gb augmented becomes Gb+).

Inversion

So far, we have seen chords (specifically triads) in their root positions. There are two other positions: first inversion and second inversion.
First Inversion is when the root is moved from the bottom of the triad to the top (up an octave) so that the chord starts on the third degree. Thus, a C major triad in first inversion is E, G, and C.

Second Inversion is when the fifth is “moved” from the top to the bottom of the triad so that the chord starts on the fifth degree. Thus, a G minor triad in second inversion is D, G, and Bb.

Inversion Notation

The most popular way to notate inverted chords is the figured bass (or thoroughbass) method.
MAKE NUMBERS VERTICAL
Triad Notation (with G as the example triad)
Root Position G or G53
First Inversion G6 or G63
Second Inversion G64

The top number refers to the interval between the bottom note and the top note. The bottom number refers to the interval between the bottom note and the second note.
Insert cute diagram here
Seventh Chord Notation will be covered in the Seventh Chord section.
http://en.wikipedia.org/wiki/Figured_bass

Diatonic Chords

Diatonic chords are created by making generic triads out of every scale degree of the scale. For example, C major would look like this.

We then analyze each triad and determine what kind of triad it is. We use the Roman numeral notation a major triad is notated with capitals (ex. if the triad with the tonic is a major triad, it is notated as I), a minor triad is notated with lowercases (ex. a minor triad on the fourth degree would be iv), a diminished triad is notated with lowercases and a ° (a diminished triad on the seventh degree would be viiº), and an augmented triad is notated with capitals and a + (an augmented third degree would be III+).
The tonality of the triads will depend on the tonality of the key. If the key is major then:

I ii iii IV V vi viiº I

A natural minor:

i iiº III iv v VI VII i

A minor with a leading tone (raised 7th) or a harmonic minor:

I iiº III+ iv V VI viiº i

A melodic minor:

i ii III+ IV V vi viiº i

Seventh Chords

These are created, essentially, by taking a triad and adding in the seventh degree. Of course with all the different combinations of triads (major, minor, diminished, and augmented) and all the different types of seventh degrees (maj., min., dim., aug.) we can create numerous types of seventh chords.

Dominant seventh chords (Mm7)	major triad	minor seventh
Major seventh chords (MM7)	major triad	major seventh
Minor seventh chords (mm7)	minor triad	minor seventh
Minor Major seventh chords (mM7)	minor triad	major seventh
Major Minor seventh chords (Mm7)	major triad	Minor seventh
Fully Diminished seventh chords (dd7)	diminished triad	diminished seventh
Half Diminished (minor seventh flat five, Tristan Chord)	seventh chords (dm7)	diminished triad	minor seventh
Half Augmented seventh chords (AM7)	augmented triad	major seventh
Fully Augmented seventh chords (AA7)	augmented triad	augmented seventh

The dominant seventh chord is one of the most important chords in musical composition. The reason for this is that its major chord helps it make a strong sound of finality. Composers use it often as a concluding chord.

A note on notation: it is common to write a seventh chord with the letter of the root of the triad and a 7, i.e. C7, would be a Dominant 7th with a C major triad.

CMa7 would be a Major Seventh with a C major triad
Cmi7 would be a Minor seventh
Cº7 would be a fully diminished seventh
Cmi7(flat5) would be a half diminished seventh

Voice Leading

Learning the process of voice leading is a good way to learn chord progressions, as it is harmonic progression. Chord progressions are present in all compositions, even if the composer is unaware of their existence. In music theory, we study voice leading to gain a better grasp of different styles and forms of music.

For voice leading we need to create a range for the four voices, for the purposes of this site we will use these constraints:

Soprano	C4 (middle C) to G5 (Two G’s above middle C)
Alto	G3 (G below middle C) to D5 (Two D’s above middle C)
Tenor	C3 (C below middle C) to G4 (G above middle C)
Bass	C2 (Two C’s below middle C) to C4 (middle C)

There are certain rules that one must follow with voice leading and harmonies:

One cannot have more than an octave between the soprano and alto or between the alto and tenor.
Parallel unisons, perfect 5th, and octaves are not allowed
Voices must not cross or overlap each other (i.e. soprano stays above the alto)
No melodic augmented or diminished intervals (one voice moving into a diminished or augmented interval)

Closed and Open Structures

There are two different structures of chords that are applicable to voice leading.
Closed: the soprano, alto, and tenor are as close as they can get. In other words, there are no other notes within the chord in between the upper three voices that are not being used.
Open: there is a gap between two of the three upper voices. In other words, there is a note between the three voices that is in the chord, but is not being used.

Voice Leading: Harmonic progressions

for now we will be repeating the root in the chords for the four voices (four voices + three notes in a triad = a note needs to be repeated) unless noted

Moving from I to IV and V and back to I:
For now, the bass will always move to the new root
Keep the common tone in its current voice (for IàV that would be SO, for IàIV that would be DO)
Move the other two voices in step (if you did everything correctly the last two voices should only have to move one step to get to the correct notes)

*A note: in minor, always use a major V chord with a leading tone so that TI can go to DO

Moving in thirds (i.e. IàIII, IVàVI, etc)
Move the bass to the new root
Keep TWO common tones in their current voices (if two chords are thirds apart there should be two tones in common, always)
Move the last voice by step

Move the bass to the new root
Move TI to DO (deceptive cadence)
Move all other voices in contrary motion
Repeat the third degree instead of the root in VI chord