harmonizations II: alterations and added notes
In his publication The Material Used In Musical Composition (1889), Percy Goetschius defines altered chords in the following way on p.116:
Altered and mixed chords contain one or more tones written with accidentals (♯, ♭, or ♮) and therefore foreign to the scale in which they appear, but which nevertheless, from their connections and their effect, obviously belong to the principal key, and not to that key which the chromatic (foreign) tone seems to indicate.
The object of such foreign tones is: To enlarge and enrich the scale; to confirm, or to modify, the melodic tendencies of the scale-steps; and to afiliate the keys by increasing the number of common tones (for instance, by raising the 4th step of C to/#, the scales of C and G major are afiliated).
Goetschius provides examples and exercises to be played at the piano.
Goetschius’ theory is build upon the common 19th-century idea that the original key cannot be ‘disturbed’ too much: 'The most important condition is, that the following chord shall unmistakably indicate and confirm the original key.'
In 20th-century harmony, altered chords are used less strictly and can in many ways contain combinations of altered notes. In jazz theory for example, a dominant chord could contain the 'guide tones' (root, 3rd, and ♭7), and all the available tensions (♭9, ♯9, ♯11, and ♭13) can be added. This way the ‘altered scale’ comes to life, including all possible tensions for a G7 chord:
Some options for altered dominant G7 chords:
To understand more about the history of added notes like 9, 11 and 13 and the use of the appogiatura, read chapter XXI from Harmony (1959) by Walter Piston (1894-1876).
For further reading: The Jazz Piano Book (1989) and The Jazz Theory Book (1995) by Mark Levine (1938-2022).
Alterations come from the overtone series. A single pitch generates a series of overtones that can be used within a chord on the same root.
The following example shows Messiaen’s ‘chord of resonance' taken from Technique de mon language musical (1944) (chapter XIV, p. 70), with the following description: Nearly all the notes perceptible, to an extremely fine ear, in the resonance of a low C, figure, tempered, in this chord.
Another interesting example is Scriabin's 'mystic chord' with added 6, 9 and #11. The 5 is not present in this chord.