Let's have a closer look to overtones before adding notes to chords. A single pitch generates a series of overtones that can be used whithin a chord on the same root.
Tonal harmony usually has thirds as building blocks, so in addition besides the 7, also 9, 11 and 13 can be added. Since the dominant chord often gets the most added notes, this chord is most used in the examples below.
Taken from Olivier Messiaens Technique de mon langage musical: a dominant chord with added 6 and 9, in the second example a major triad with added 6 and #11.
Scriabins 'mystic chord' with added 6, 9 and #11.
Chord notes can be easely shifted up and down, creating more added notes. In the first two examples a 3 alternates with a 4 and 9, in the last example a 6 becomes a b6.
Added notes can also derive from a previous chord, creating 'appogiaturas' in the new chord before finding a solution in a chord note.
An appogiatura is not necessarily prepared, it can also be an unintroduced non-chordal note.
An upper structure is an extra chord on top of another chord. This harmonization technique allows a pianist to explore tonality while incorporating influences from impressionism and jazz, both 20th century musical styles.
It is a more advanced technique of added notes, and using this technique has the advantage of creating several tensions at once, rather than adding tension notes one at a time.
Usually, an upper structure is a triad built on a chord note of the lower chord, but many more combinations can be made.
The following examples are limited to the more commonly used.
Minor triad on the third of a tonic chord, major triad on the fifth of a tonic chord.
Minor triad on the b9 of a dominant chord, major triad on the #11 of a dominant chord.
Upper structure example with an ‘octave rule’ in the right hand, while the left hand repeats a I-VI-II-V structure.
Many combinations are possible, as for example the first chord structure of Dances of the Young Girls from The Rite of Spring by Igor Stravinsky. This example shows a minor triad on the b9 of a dominant chord, but the structure is reversed, the upper structure is used as a 'lower structure'.
A chord can be developed into a cluster sound by using ‘inner structures’.
In the following example from Technique de mon langage musical (1944), Olivier Messiaen shows a dominant chord containing all the notes of the major scale, followed by the solutions of the tensions.
Inner structures can lead to clusters that no longer have harmonic functional significance, but rather create a sound effect like in the following fragment of Phasma (2002) by Beat Furrer.