Tertian harmony

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Tertian harmony is a technique that employs thirds as the building blocks of harmony. It was the essential harmonic system for much of the western common-practice period.

Chords created with tertian harmony

The triad

Main article: Triad
The basic unit constructed using tertian harmony is the triad, which can be defined as the vertical superposition of two thirds. Below, an Eb Major triad is shown.

<music> \meterOff <ees g bes>1 </music>

Other types of triads can be used and constructed, using different sequences of major and minor thirds above a root. Below, a diminished triad on F# :

<music> \meterOff <fis a c>1 </music>

The seventh chord

Adding a third to a triad produces another common chord belonging to tertian harmony. Many possibilities exist as to the construction of seventh chords. Some common examples are shown below:
A minor seventh chord on G (superposition of a minor third, major third and minor third above the root):

<music> \meterOff <g' bes d f>1 </music>

A major seventh chord on E (superposition of a major third, minor third and major third above the root):

<music> \meterOff <e gis b dis>1 </music>

A dominant seventh chord on C (superposition of a major third, minor third and minor third above the root):

<music> \meterOff <c e g bes>1 </music>

A diminished seventh chord on D# (superposition of three minor thirds above a root):

<music> \meterOff <dis fis a c>1 </music>

Extended chords

Chords that add another third to the seventh chord (accordingly termed ninth chords, eleventh chords and thirteenth chords) are termed extended chords. They are used primarily in jazz and in later romantic works. Examples of such chords include the (although extended, quite common even in the classical period) dominant major ninth chord, comprising a major third, minor third, (optional) minor third, and major third above a root. Below, a dominant major ninth chord on D:

<music> \meterOff <d fis a c e>1 </music>

The ninth may also be minor. In this case it is termed a dominant minor ninth chord. Below, a minor dominant ninth chord on D:

<music> \meterOff <d fis a c ees>1 </music>

Other tertian chords often found in more modern pieces of music include the eleventh chord, and thirteenth chord. Below, a major eleventh chord on Eb, followed by a major thirteenth chord on the same root:

<music> <ees g bes d f a>1 <ees g bes d f a c>1 </music>

The seventh is sometimes omitted in ninth chords and the seventh and ninth in eleventh chords. However, eliminating the seventh, ninth and eleventh in thirteenth chords is problematic, as the chord may be reinterpreted (the thirteenth being equivalent to a third below the root). Below is an example of a thirteenth chord on F being reinterpreted as a minor seventh chord on D:

<music> <f a c d'>1 <d f a c>1 </music>

More remote products of tertian harmony

Harmonies that are not directly built using thirds, using augmented or diminished intervals, but whose existence still originates from the use of tertian harmony during the common-practice period, may be of concern when discussing it. Such harmonies that are of common usage include the three augmented sixth chords. The italian sixth, notated in root position, is built from a diminished third and major third:

<music> \meterOff <f a dis>1 <dis f a>1 </music>

The German sixth, notated in root position, is built from a diminished third, major third and minor third:

<music> \meterOff <d fis a bis>1 <bis d fis a>1 </music>

The French Sixth, notated in root position, is built from a major third, diminished third and major third:

<music> \meterOff <g' b cis eis>1 <cis eis g b>1 </music>

However, as previously stated, these chords originate more from common-practice principles of voice-leading than from pure stacking of thirds.