Vincent Persichetti

Basic harmonic materials may be traced to the overtone series, but only general facts concerning chordal structure and resonances are indicated by the partials. A triad is formed by partials 1-3-5 (root, fifth, and third), a seventh chord by 1-3-5-7, a ninth chord by 1-3-5-7-9, the whole-tone chords by 7 to 11, chords by fourths by 6-8-9, and the augmented fourth chord by 6-8-11. However, deduction concerning harmonic implications of partials beyond the 6th is not wholly practicable because the tempered scale does not coincide in pitch with the 7th, 11th, 13th, and 14th partials. It is quite possible to relate multi-note chords by thirds to the series but the overtones produce limited resonance. The major triad (partials 1-3-5) is clearly in tune. But the seventh partial is slightly less than a minor third from the sixth, and if considered as the seventh (in chords by thirds) misinterprets the natural phenomenon. Our tempered aural thinking can include tones up to the sixth partial but beyond that point the aural perception is merely rational. The acoustician's observations are useful to the composer only if blended with artistic intuition.

The fifth (partial 3) is lower partial than the third' (partial 5) and consequently is more powerful; this is an important factor in understanding relationships of tones, chords, and tonalities. Resonant harmony is not formed by seeking higher and higher overtones but by using overtones of overtones. For example, in a C-E-G-B chord, the seventh (B) is the fifth above the third (E). In this sense both C and E are accompanied by their fifths and therefore have strong relationships with these other tones. If we wish to add an additional resonant tone, we should add not a higher, weaker overtone of C (such as F#) but a lower and stronger overtone of an overtone (such as G# which is partial No. 5 of E). [Persichetti, Vincent, Twentieth-Century Harmony, Creative Aspects and Practice, W. W. Norton & Company, Inc. New York, 1961, p24]