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Triads are three notes played at the same time. The notes come from arpeggios of the various scales found in music. They can be built on any degree of the scale. Below, the examples are based on major and minor scales because these are more common. Triads can also be built on other forms of scales.

Triads in the major key
The primary triads in a major key are called and built on the tonic, subdominant and dominant. Secondary triads are from the supertonic, mediant and submediant. In a major key, each of the primary triads will be major and the secondary triads will be minor. The triad built on the leading note will be diminished.

Triads in the minor key
This is a little more complicated because there are two (harmonic and melodic) minor scales. The natural minor scale is the same as the descending melodic minor scale (eg. no raised sixth or seventh notes).

Harmonic: There are two minor triads in the harmonic minor scale. They are built on the tonic and subdominant. The dominant and submediant are both major triads. The supertonic and leading note are both diminished triads. Finally the mediant is an augmented triad.

Melodic: Because the sixth and seventh degrees of the ascending scale are different to the descending scale, each degree of the scale except the tonic has two possible triads. The tonic is minor, Supertonic diminished and minor, Mediant major and augmented, Subdominant and Dominant are both minor and major, Submediant major and diminished and finally the leading note can be major or diminished

Terms and inversions
Because a triad consists of three notes, there are three possible versions of the same triad. Changing the order of notes in the triad creates these inversions. To understand fully, compare the examples of the C Major triad.

Root Position
The tonic C is at the bottom with E and G above.
First Inversion
The third E is at the bottom with G and C above.
Second Inversion
The fifth G is at the bottom with C and E above.

These triads can be described in many ways.

Figured bass is a common way where a number (or numbers when used to describe chords) is placed under a note to work out what other notes to add e.g. number 1 is not needed since the note written is the first note. Root position can be described as a five three chord, First inversion a six three chord and Second inversion a six four chord.

Another way of describing triads could be using numbers or Roman numerals and letters e.g. a, b and c where a is root position, b is first inversion and c is second inversion. For example, IVb in the key of C major would be a 1st inversion triad on F. (=a,c,f).

If the notes of a triad are written so they spread beyond an octave then the triad is in open position. Triads within an octave are in close position.