Harmony/Triads & Seventh Chords

Chords
Chords are combinations of three or more notes (although in reality two notes or even one can imply a chord just fine). Chords come in an almost endless variety, but they are limited in common practice music. The members of the first class of chords we will look at are called triads.

Triads
Triads are built by stacking two thirds on top of a root note. Only major and minor thirds are used because diminished and augmented thirds are enharmonically equivalent to seconds and fourths. This results in triads having a root, third, and fifth.

Seventh Chords
Sevenths are built like a primary triad, but with another third on top. This gives a root, third, fifth, and seventh. In common practice, the fifth is left out.

Open 5th
A chord with just the tonic and the dominant in it. It is so-called because, without the 3rd, it sounds 'open'.

Triads
Triads are three-note chords. Common-practice music theory recognizes four different types of triads:
 * Augmented
 * Major
 * Minor
 * Diminished

All of these triads are created by stacking two thirds above a root note. The thirds are limited to major and minor since other thirds become seconds and fourths enharmonically.

Types of Triad
We often think of triads as being built on top of the scale of a particular key. As there are 7 notes in the standard major or minor scale, there are also 7 corresponding chords. There is a whole language of chord names to be familiar with (in Roman numerals).

Primary Triads
I, IV, and V are considered the primary triads. Often, they are denoted with capital letters to show that they are primary. These are strongest because, in terms of fractions, chord V is a multiple of 3/2 of chord I, and chord IV is a multiple of 2/3 of chord I - these fractions (in terms of the sound waves' frequency) are very strong.

Secondary Triads
ii, iii, vi, and vii are considered the secondary triads. Often, they are denoted with lowercase letters to show that they are secondary.

Sevenths
Seventh chords have 4 notes in them.

Further Work
For general use, and if you ever study harmonisation of melodies, it is useful to have a chord table detailing the triads of every major and minor key.