The Plaintive Sigh of a Sonic Doppelgänger: Why are Minor Chords Perceived as “Sad”? Part 1

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Preamble

Daniel Levitin, in his popular bestseller entitled This is Your Brain on Music: The Science of a Human Obsession from 2006, characterizes the perception of the minor chord, which lowers the third of a major chord by a half-step, as follows:

All of us, even without musical training, can tell the difference between these two [referring to a major and minor chord with the same root] even if we don't have the terminology to name them; we hear the major chord as sounding happy and the minor chord as sounding sad, or reflective, or even exotic. (Levitin 38)

The perception of the minor chord and its minor key as being sad, reflective, introspective, melancholic, defeated or even "exotic" as Levitin suggests, is incontrovertible and found in virtually every genre—classical music, jazz, rock, pop, EDM, country, folk music, etc. Why do adults[1] and children[2] alike perceive the minor chord/key as sad, introspective, tragic or melancholic, while the major chord is perceived as the opposite—happy, confident, optimistic, virile or strong?

This article will attempt to answer that question by first providing some historical context on the emergence of both the major and minor chords in the history of Western music. We will see that the minor chord is a sonic doppelgänger that evokes sadness, melancholy, tragedy, and introspection. Why does lowering the major third in a major chord by half a step carry such profound emotional weight? This article explores the historical and scientific roots of this phenomenon.

I. The Rise of the Major Chord

I propose to call this science acoustique, from the Greek akoustikos, meaning pertaining to hearing, to distinguish it from the general study of music. (Rossing 3)

This is where the term acoustics first appears, penned by Joseph Saveur in 1700 at the dawn of the Enlightenment. Long before then, however, "natural philosophers" (i.e., scientists, as they are called today) were studying sound and its perception from a scientific perspective. One of the primary questions had to do with the major chord, something we may think of as odd, given the ubiquity of the major chord in today's music of all kinds.

The major chord was not, however, always accepted as a consonance; in fact, the earliest Western music we have eschews the major chord entirely. The oldest known piece of notated music is "Hurrian Hymn #6," which was carved into a cuneiform tablet around 1400 BCE.

There are no chords as we know them—instead, we find many open fifths and the occasional major or minor thirds or sixths as the only "dissonances" allowed. It may be difficult for us to believe that a major or minor third or sixth was heard as dissonant, but the thirds and sixths, both of which are entirely uncontroversial for modern ears, were once heard as dissonances.

From ancient hymns, Western music evolved to medieval chant. The earliest church music, Gregorian Chant (800-1200 CE), avoided dyads (two notes played simultaneously) entirely—the modal melodies were monophonic.

These developments progressed, with an increased vocal range and expression, as seen in the music of Hildegard von Bingen (1098-1179).

By the 13th century, however, the monophony must have become monotonous, and more voices were added, creating dyads and triads. This introduced new pitches with new consonances and dissonances, and composers had to figure out how to incorporate them into the music.

This began with the addition of the three most consonant intervals—the octave, the fifth, and the fourth, which we can hear dominating the textures in the following example, Perotin's "Viderunt Omnes," from the end of the 13th century. In these new polyphonic textures, perfect intervals abound, but we also find a smattering of imperfect intervals that perhaps sound somewhat quirky to our modern ears. The etymology is fascinating here—they called the intervals of the octave, fifth, and fourth "perfect." In contrast, the second, third, sixth, and seventh intervals were characterized as "imperfect," which is what they are still called to this day. The nomenclature stems from the fact that they recognized the consonance in the perfect intervals, which are free of any harsh dissonances. Without any dissonance, these intervals must be a reflection of God in sound, and were therefore, like God, perfect. The other intervals, on the other hand, contained varying degrees of dissonance and were thus deemed to be imperfect, as they reflected the corruption of humankind. The terminology, therefore, directly reflects the religious worldview of the monks and clergy who wrote this music, ensconced in their monasteries and churches.

As time passed, more and more of the imperfect intervals were utilized as musicians grew accustomed to the formerly dissonant intervals. In the following example, John Dunstable's Quam pulchra es from the early 15th century, we hear thirds and sixths used freely throughout the piece, except for one significant place—the end of phrases (mm. 9, 18, and 26; see the score in the YouTube video) and the end of the piece (the last measure of the piece, m. 59). So, while they accepted more and more imperfect intervals within phrases, the important structural markers (cadences) adhered to the practice of using only perfect intervals.

By the end of the High Renaissance, composers began to regularly include the third as the closing chord of phrases and as the final chord in their compositions. We hear this in Orlando de Lassus' (1532-1594) delightful "O lá o che bon eccho" (The Echo Song), a piece written in the late 1500s, which is replete with triadic harmony from beginning to end. As the Baroque era begins in the 17th century, major and minor triads, containing a major and minor third, respectively, were used consistently as stable harmonies. From here on, the major and minor chords were both fully emancipated. Musical works ended on a major or minor chord, and the open fifths and octaves, as cadential harmonies, disappeared from Western classical music.

For the early natural philosophers, the rationale for the use of the major chord as a stable harmony was, for the most part, self-evident. The justification for its "natural origins" was clear—the major triad is found in the first five partials of the harmonic series. Thus, combining it with the other two pitches is simply reinforcing what is already sounding in the hidden realm of the harmonic series. This embrace of triads, therefore, rested on a natural phenomenon—the harmonic series—which early theorists saw as evidence of the major chord's divine origins.

II. A Short Primer on the Harmonic Series

When a note is played on any instrument, we hear that note most prominently, of course, but in the acoustical realm, it contains many other pitches. Every pitch is therefore a "compound" pitch, made up of many different pitches that are heard, but not seen in the score. This is an acoustical phenomenon that governs not only pitches but every sound that is made naturally.

The hidden pitches that sound along with the primary pitch are called "partials," "harmonics" or "overtones" [3] which can be seen in the following diagram, Figure 1. The partials that different instruments emphasize are responsible for determining the sound of each instrument. A trombone's bold sound and a flute's delicate tone come from the unique partials each emphasizes. As seen in Figure 1, the major triad is found in the first five partials, which explains its "natural" consonance. The minor triad, however, puzzled theorists, as its third appears only weakly at the 19th partial, as we'll explore later.

Figure 1: The Harmonic Series

An analogy may be helpful: The primary ingredient (the fundamental) of lentil soup is lentils, but the soup also contains many other ingredients (partials) that give it its unique flavor—salt, paprika, garlic, parsley, carrots, mushrooms, etc. The flavor of the soup is determined by the other ingredients that aren't always seen, but they are, nonetheless, present. The same is true with every pitch and every sound—we hear the primary pitch, but are unaware of the other ingredients that give it its unique sound and acoustical flavor.

Later in this article, we will examine and listen to the partials emphasized by a trombone quartet and a flute quartet, which will hopefully provide readers unfamiliar with the concept of the harmonic series with a concrete means to understand it and easily grasp its significance.

III. The Mystery of the Minor Chord

Having traced the major chord's rise, we now confront its shadowy counterpart—the minor chord. One of the issues that confounded many of these natural philosophers over the centuries was the pervasive use of the minor chord[4] as a stable chord. The major triad has its naturalistic explanation in the harmonic series, where it is found in the first five partials. The renowned German composer, theorist, and violist, Paul Hindemith (1895-1963), was one of many who grappled with this enigma.

...we must mention a chord that has always given theorists endless trouble—the minor triad. To understand and explain the major triad is a task made easy for us by Nature, who places it in our hands as a handsome gift. [i.e., The "gift" is that the major triad is found in the first five partials of the harmonic series.] But she gives us no hint about the minor triad. It does not occur in the overtone series, at least not in three successive tones. In the upper reaches of the series, minor triads can be constructed by skipping some tones (10:12:15) [E, G, B, an E minor chord]; but this seems too far-fetched an explanation of a chord that appears almost as valuable as the easily explainable major triad. (Hindemith 74)

Hindemith opines that, for the minor triad, we do not have the naturalistic rationale that we have for the major triad. The minor third (E♭ if the fundamental is C) is not found in the harmonic series of the fundamental until the 19th partial. The minor third, therefore, does not enjoy a prominent position in the harmonic series—in fact, the 19th partial is very weak and out of tune, as are all of the partials above the 16th (and a few below the 16th). In the harmonic series, we do find a minor third between the 5th and the 6th partial, which gives us the string length ratio of 6:5.

Still, as Hindemith points out about the questionable rationale of "skipping" pitches in the upper reaches of the harmonic series, it is difficult to see how the appearance of a minor third between the 5th and 6th partial provides an adequate explanation for why a minor third over the fundamental works to create a stable chord and key center. This is also not a plausible means of linking the minor chord to the harmonic series.

While the minor chord and minor key are ubiquitous today, it is interesting to chronicle their journey from dissonance to an essential consonance, without which a vast swath of music's expressive capabilities would not be possible. Without the minor chord and the minor key, music in all styles would be decimated of some of its most moving and poignant pieces—sadness, melancholy, fear, yearning, reflection, loss, tragedy, introspection, frailty and a host of other emotional perspectives would be, for the most part, impossible to convey.

In practice, over many centuries, the minor chord has, for some mysterious reason, functioned perfectly well as a stable substitute for the major chord. While earlier theorists struggled with this, by the 19th and 20th centuries, theorists generally accepted the minor triad and the minor key without needing to explain them from a naturalistic perspective. Hindemith's solution was that the major and minor triads are two versions of the same entity with distinctly different qualities.

What, then, is the minor triad in reality? I hold, following a theory which again is not entirely new, that it is a clouding of the major triad. ...I do not believe in any polarity of the two chords. They are the high and low, the strong and weak, the light and dark, the bright and dull forms of the same sound. (Hindemith 78)

Hindemith's attempt to fuse the two aside, we arrive at an obvious conclusion: the minor chord is a sonic doppelgänger of sorts. Like the two faces of Janus, the major triad and major key imply vigor, confidence, and "light," as Hindemith says. The minor triad and minor key are the opposite, reflecting sadness, weakness, frailty and other darker emotions that we often try to hide or deny. More deeply, the minor triad and minor key express our human vulnerability and impermanence as we ponder the existential nature of our existence. But the question remains: how does our sonic doppelgänger accomplish this Herculean task?

"The Head of Janus" by Martin Klein

Footnotes

[1] "A simple 'major' chord is made from the first, third and fifth notes of a major scale. This is reliably identified by Western adults and children as a happy chord. Then by simply lowering the middle note by a semitone... this is turned into a 'minor' chord, which is typically heard as sad." ("Why Are Minor Chords Sad and Major Chords Happy")

[2] "Children as young as 4 years old begin to associate minor chords with negative emotions such as sadness, though this association becomes more pronounced by age 7." (Cunningham and Sterry 31)

[3] There are differences in the definition of these terms, but they are used colloquially by musicians and are interchangeable.

[4] To turn a C major chord into a C minor chord, the third of the chord, E♮, is lowered by a half-step to E♭.

* "Doppelgänger No. 4," Sebastian Bieniek (B1EN1EK), 2018. Oil on canvas. 140 x 90 cm. From the "Doppelgänger" oeuvre and series. Used by kind permission of the artist. This piece of art will soon hang in my home.

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