Also referred to as quartal or quintal harmony when the chords are built by stacking fourths or fifths, respectively. These chords don’t need to have these intervals exclusively, as long as fourths or fifths predominate, they are still considered as such. The possibilities for building three-note fourth chords are:
These chord formations (in fourths or fifths) may be imposed by the notes involved in the scale you are using or as required by voice-leading purposes.
The term quartal is the most used one in detriment of quintal because the 5th can be considered as an inversion or a complement of the 4th. In the example below, this can be easily understood when a fifth chord is arranged into a sus2 chord and then inverting it, we will get a chord arranged in fourths:
It is true that the inverse could be accomplished by turning a chord by fourths into a chord by fifths using the available inversions. In effect, and theoretical questions aside, using chords whose intervallic structure is arranged in such a way that there is a prevalence of fourths or fifths in it, is a choice that will be influenced by your personal tastes and sensibilities – i.e. some composers feel that chords in fourths have an inherent “minor quality”, while chords in fifths sound close to the “major quality”, thus sound more uplifting.
Using inversions in quartal harmony is a way of preventing harmonic monotony caused by the fixed interval position of stacked fourths or fifths.
There are more than three note chords in quartal harmony and adding a fourth note to the chord creates a consonant interval that resonates with the root (a 10th interval):
When we start to play around with these inversions, you will notice the similarity with chords by thirds and this means that you can actually think of tertian harmony and arrange it in such a way that the fourth or fifth interval predominates:
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