Although the augmented-fifteenth chord should not be subject to any sort of
alteration, it could, however, be reduced to seven or six of its eight notes
by eliminating the fifth degree of one or both tetrads of the chord,
C-E-[ ]-Bb—D-F#-[ ]-C#
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 remain in close position, this, however, does not
hinder it in the higher pitch range from being
doubled to its high octave, or
placed a major-tenth chord apart from the lower (close or open) tetrad.
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:
[close or open]
[an octave apart]
[open or close]
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)
plus the major-seventh chord (upper tetrad), a chord whose repeated use,
goes back to the early days of musical impressionism, and which becomes
mundane later on in western pop music.
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
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
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,
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
(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
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
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
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.