The Augmented-Fifteenth Chord:
IF WE WERE TO SUPERIMPOSE a major third over the top of the thirteenth chord, we would realize that such a third would correspond to the 17th overtone (C#) of the natural harmonic series.
But, if in keeping with the established norm, we were to classify this major
third in a tertian chordal order, we would then denominate it as the
augmented-fifteenth degree of the chord root, an interval consisting of a
high double octave (fifteen notes) plus one chromatic semitone.
You can represent it with a fundamental or basso continuo either as +15 or 15+.
As you can see, once the seventh and eleventh degrees of a thirteenth chord are altered—relative to their approximate pitch within the natural series—the eight component sounds of the augmented-fifteenth chord could be divided in two superimposed tetrads:
Take for instance the following:
This order of sounds is entirely unalterable, both in the inversion of the
two tetrads that make it up, as well as in the pitch of each of their
Moreover, the lower tetrad can be in either close or open harmony, while keeping its seventh degree on top in either case; whereas the upper tetrad should always remain in close harmony. For instance:
Although the upper tetrad must always remain in close position, this,
however, does not hinder it in the higher pitch range from being
This latter option is more suitable for piano and string instrument scoring because these instruments are sufficiently rich in harmonics and homogenous in sound to bridge such a large harmonic interval. Take for instance:
The union of these two tetrads that form the augmented-fifteenth chord now
comes to us as the live embodiment of a harmonic alliance between the
secular dominant-seventh chord (lower tetrad)
This chord is in fact the most emblematic icon of impressionist harmony (cf., Claire de Lune). Therefore, this union consisting of both seventh chords could have been of great historical importance to music, considering it represented a genealogical relationship between an ancestor (the dominant major-seventh chord) and its analogous descendant (the secondary major-seventh chord), which has ever since habitually practiced its harmonic function over the first and fourth degrees of tonality.
(Precedent: J.S. Bach began writing his 24 preludes and fugues for The Well-Tempered Clavier in 1722. Take note that on the 12th measure of his first prelude, you can already see the broken chord consisting of C major seventh in its third inversion, as well as secondary seventh chords over the 2nd, 4th, and 6th degrees of the tonality across the entire prelude. A century and a half later, these chords would become the first flashes of musical impressionism at the dawn of its stylistic history.)
Given its well-balanced sound, the complete or incomplete use of this hitherto unnoticed chord could have harmonically emulated the novel effect caused by the free motion of parallel ninths, which constituted the first wonders of musical impressionism.
As for its harmonic lineage, the augmented-fifteenth chord could have been perhaps the last fruit borne of the genealogical tree of musical impressionism—a bright, crystalline, compact chord, both in the lower and upper registers.
Notwithstanding, I recommend the use of this chord only within an adequate range to preserve its natural features: It will not lose its harmonic characteristics if its root starts at the C note of the small octave, progressing upward.
But, if the lower tetrad is open (C-G-E-Bb), the chord root could descend to the C note of the great octave.
By observing this wide range, I have obtained good results using this chord in some of my first works published long ago. A word to the wise: If we choose to score this chord as a new compositional element, we should do so rather soberly within a kindred musical context where it makes sense. This way it may result in an enchanting chord that surprises the ear.
Now, as we all know, the microtonal gamut of the natural series departs exactly from the 17th overtone (C#).
Had this chord, however, stood out with this crowning overtone at the start of the 20th century, we would probably be pointing it out today as the first tertian chord of superimposed thirds to build onto its structure a representation of the microtonal gamut, without losing its impressionist harmonic features.
(Note well: It is precisely the 17th overtone (C#)—and not the 13th—that delimits the chordal bounds preserving the distinctive traits of this style. Be aware that, beyond this limit, the next major third—E# [the 21st overtone]—would corrupt such stylistic features, if this harmonic were to become the top sound of the chord; this is especially so if you place this chord in the lower and medium registers of the general scale.)
For the impressionist harmony of times past, the thirteenth chord was like a grand curtain falling on the most sensuous era of music. It was, and still is indeed, a sort of king among chords.
But for those who consider the potential of the augmented-fifteenth chord and still cannot see why it did not succeed the thirteenth chord in chronological order, this is merely an arbitrary way of looking at the story.
Albeit it may seem as though a discontinuity somehow occurred in the last days of this harmonic evolution, blocking the way toward the microtonal gamut, one could equally argue that the thirteenth chord was rather a regent awaiting his crown in the form of the augmented-fifteenth chord, which simply did not arrive in his own time.
After the thirteenth chord was enthroned, several atonal chords went beyond it to add on to themselves the five remaining sounds of the chromatic scale.
But none of these atonal chords kept the features of impressionist style in its harmonic character, as does the augmented-fifteenth chord.
They simply did not follow the tertian order in its respective builds; instead, they linked the 12 sounds in a varied interval order. Among these chords are the so-called Mother and Pyramid chords (both invented by Fritz Klein in 1921) and the Grandmother chord (invented by Nicolas Slonimsky in 1938).
I have excluded both the pandiatonic and pentatonic tone clusters from the group mentioned above because they are not really chords. They are more akin to instrumental noises of graduated pitch and intensity from pounding one's hand or forearm over a keyboard. (Domestic cats and dogs could likely lay claim to the source of this aural invention. We'll never know for sure, as only the originally pounded keyboard can bear witness to which animal got to it first.)
Today, as the era of musical impressionism lies a century behind us, one can only behold this chord as one would a rare gem never before seen, as though the undertow of time were to wash up a buried relic of the past onto our shores, so that we may now ponder it in perplexed admiration.
We should therefore lament that the augmented-fifteenth chord does not appear in the current literature of harmony, deserving its place as a posthumous legacy that French musical impressionism should have bestowed us.
If it turns out that all this is not just a mirage from the sands of times past, then we have arguably found an unnoticed gap in the history of music.
Copyright © 2002 by Enrique Ubieta