Figuring Out Melody

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At the heart of the 3-Note Scale lies the most resonant sound in music: the harmonic third. Thirds form the harmonic foundation of music throughout the world. We rely on them to construct chords, contrast emotions, and harmonize songs around a campfire with our friends. What does this have to do with the 3-Note Scale? The 3-Note Scale takes this most crucial element of harmony and turns it into a little melody.

“But,” you protest, “it’s so boring. Step-step up; or step-step down. How can I write an interesting melody from such a nothing?”

That’s like asking how so much astounding architecture can arise from combining rectangles, or how so many life forms from the carbon atom. Wherever we look in our universe, we find that the most crucial building blocks are also the most humble.

The excerpts I’ve chosen barely scratch the surface of what the 3-Note Scale can do—the incredible variety of emotions and ideas it can produce. You’ll hear a folk song that captures our common desire for meaning followed by its polar opposite: a cocky, flirtatious strut. Finally, the piano concerto theme feels immensely personal, like something between a dream and a diary entry.

“Blowin’ In the Wind,” by Bob Dylan

“Cool,” by the Jonas Brothers

“Piano Concerto #3,” by Sergei Rachmaninoff

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In general use, the term “auxiliary” refers to something that adds to or extends the capabilities of something else. So when you add a printer to a computer, the printer becomes an auxiliary device.

And so it is with the melodic figure dubbed the Auxiliary. We hear its main note, a chord tone, two times: once at the beginning, then again at the end. The add-on note – the auxiliary portion of the figure – is an upper or lower neighbor note.

“Silent Night,” by Franz Xavier Gruber

As far as “extending the capabilities” of the chord tone we turn into an auxiliary, take a moment to try to imagine the melodies below with repeated notes rather than the auxiliary tones the composers heard fit to include.

“Bad Romance,” by Lady Gaga

“Toreador Song,” by Georges Bizet

To create an arpeggio, we perform the notes of a chord one at a time rather than simultaneously.

Groups of notes written first as a chord, then an arpeggio

Now there’s no rule that says we must begin at the bottom and run through the notes in order or the top and cascade down. In fact, there are many different patterns you can make with nothing but chord tones. And that’s why we have so many types of arpeggio figures.
But when we do perform the notes of a chord in order without changing direction, we get the simplest of all the arpeggios, the Arpeggio.

“Ring of Fire,” by Johnny Cash

“Sesame Street,” by Franz Xavier Gruber

“On the Beautiful Blue Danube,” by Johann Strauss Jr.

The word “run” is already in use in music. It either refers to a long scale or a somewhat fancier bit of melodic fluster (sometimes called a “riff.”) At FiguringOutMelody.com, the melodic figure we call the Run is exactly four notes long, and those notes always form a scale.

Of the many ways to use a Run, one easily comes out ahead of the rest. The Run often paints in broad or medium-long strokes. Sometimes these gestures join together to cover a large amount of registral space (as in “Penny Lane”). Other times, they don’t move very far but sway over a secure foundation (as in “As Time Goes By”) But Runs can also have a far nimbler side as we hear in “Wachet Auf.”

“As Time Goes By,” by H. Hupfeld

“Overkill,” by Colin Hay

“Wachet Auf, Ruft Uns Die Stimme,” by J.S. Bach

Here’s a case where we have two very similar figures that count as one. (The other instance is the Parkour figures.)

The Trill. Outside of FOM, a trill is a melodic embellishment produced by rapidly alternating two notes a step or semitone apart. And the term trill also applies to the way that speakers of certain languages roll their R’s (always with great gusto). We include it as a melodic figure because so many melodies use a slowed-down version of the alternating stepwise action.

The Oscillator. When we say that something oscillates, we mean that it swings back and forth in a steady motion. If you hope to cool an entire room with a small fan, get one that oscillates. The difference between a Trill and an Oscillator is that every other note in a Trill is a neighbor note, while every other note in an Oscillator is another chord tone.
The three samples here show two possible effects of the Trill. “A Modern Major General” uses the alternating notes to create interest during what is essentially a rap. The Trill figure in “Iron Man” resembles a true embellishment, though of course, slower. The third excerpt is an example of an Oscillator.

“A Modern Major General,” by Gilbert & Sullivan, with new lyrics by Randy Rainbow

“Iron Man,” by Black Sabbath

“Over the Rainbow,” by Harold Arlen

There are a lot of different types of arpeggio figures. If you hope to keep them straight, watch for two things. First, each type of arpeggio figure has a unique shape. (The one we’re looking at now, is shaped like an arch.) Second, that shape results from calculating the direction of each leap. To produce an Arch, we leap twice in one direction and once in the opposite direction. Or once in one direction, then change direction for the last two leaps.

The size of the leaps doesn’t matter, though when all the leaps are roughly the same size (as in the first two figures), we get a more balanced arch.

By far, most arch figures equally-proportioned leaps, as reflected in the excerpts below.

“I’ll Fly Away,” by Albert E. Brumley

“Royals,” by Lourde

“Surprise Symphony,” by Franz Joseph Haydn

3PN stands for a “3-Note Pentatonic” scale. Or more accurately, a 3-note slice of a pentatonic scale, because as you probably know, pentatonic scales (in either their major or minor versions) contain five notes, not three.
Notice that the pentatonic scale is a little wonky, what with its odd gaps every few notes. (Most “scales” move by step.)
We can divide a pentatonic scale into five different 3-note groups. When we do, four of those groups include one of the gaps illustrated above.
Note the similarities between the 3NP and its more symmetrical cousin, the 3NS (3-Note Scale). Whereas the 3-Note Scale always spans a third from first to last note, the 3NP always spans a 4th.

“Youngblood,” by 5 Seconds of Summer

“La Donna È Mobile,” from Rigoletto by Giuseppe Verdi

“Girl from Ipanema,” by Antonio Carlos Jobim

To pivot means to swivel or turn; to change direction. Picture a footballer using fancy footwork to drive the ball toward the goal. Don’t just “picture it.” Try to feel its kinetic momentum: moving one direction, then darting off in the opposite direction.

"Up Where We Belong" uses Pivot figures to get us to feel we are at the upper limits of what is possible.

“Up Where We Belong,” by Will Jennings, Buffy Sainte-Marie, and Jack Nitzsche

Don't miss the irony as Billy Joel sets the word "honesty" to an evasive melodic gesture.

“Honesty,” by Billy Joel

It's hard to express melancholy without sounding sentimental. Yet Rachmaninov pulls it off here by starting each Pivot figure as a strong dissonance.

“Adagio,” from Symphony #2 in E minor, by Sergei Rachmaninov

Nature abhors a vacuum. So does melody.

Any figure that ends opens up a gap (especially a leap of a third) invites the next note to fill up the little hole. So in the example below, versions A and B show the most predictable outcome for a melodic figure ending with a small leap. Versions C and D show how this same 3-note link can occur within one figure—namely, the “Little Holy Phillip” (L.H.P.)

So, about the name. A main principle in melodic figuration is that we make melody by connecting figures together. The end of one figure with the beginning of the next.

Now imagine that we could take a stop-frame video of the melodic motion between figures. Wouldn’t that help explain why some melodies feel continuous and others don’t?

THWANK! Stop imagining. We CAN INDEED observe the ways that figures link up, and no special equipment is required. Just track the steps and leaps to discover us all we need to know.

“Imagine,” by John Lennon

“Harry Potter Theme,” by John Williams

“Symphony No.8” II, by Ludwig van Beethoven

The Return figure gets its name from its proclivity to return to its starting note, as shown in the example below.

Outcome A below shows the most predictable destination of the Return figure: note #1 = note #5 (with note 5 being the first note of the next figure).

Outcome B shows another (less-) predictable path: note #5 = note #3. In other words, using this second option, the figure “returns” to the “middle” note, counting note #3 as “home.”

In the first two melodies below, the Return takes the most predictable outcomeas described above (outcome A). But in the third exceprt, the Strauss melody, we the Return doesn’t return. It LEAPS! The Return is one of many figures that is sometimes used for its smooth-as-silk behavior, and other times—when its natural connection is broken—to add a bit of complexity.

“Senorita,” by Shawn Mendez

“Bohemian Rhapsody,” by Freddie Mercury

“Voices of Spring,” by Johann Strauss, Jr.

While the names of most melodic figures serve as mnemonic devices, “Crazy Driver” one is a contender for the most quirky. How can a melodic figure act like a Crazy Driver? Let me explain.
The most predictable destination of the Crazy Driver—its “5th note”—lies a 3rd above or below the starting note.

But notice the path it takes to get there. Rather than steering directly toward its goal, the Crazy Driver figure begins with a swerve in the wrong direction! It’s a lot like an automobile driver who can’t seem to turn into a driveway on the right side of the road without first swerving left! That crazy driver!

And the name still fits when we consider another predictable destination of the Crazy Driver: to return to the original note. Here, the motion of the melody mimics a (distracted? drunk?) driver who can’t manage to drive in a straight line.

The designation “crazy” has absolutely nothing to do with how this figure sounds. There’s hardly a better choice for making smooth, gentle waves, as in the first two examples below. The third example shows quite a different sound, using the Crazy Driver as an ornate pickup to kick off a bit of syncopation.
“Joshua Fit the Battle of Jericho,” a Negro Spiritual

“Every Breath You Take,” by Sting

“Minuet” from the String Quintet in E Major by Luigi Boccherini

The bulk of this figure is an arpeggio. The “plus” note is a passing tone or neighbor note, most often added at the end to make a smooth bridge to the upcoming note or figure (though occasionally, the non-chord tone can come at the front).

“Come Sail Away,” by Styx (Dennis DeYoung)

“Ring, Ring the Banjo,” by Stephen Foster

“Morning” from Peer Gynt, by Edvard Grieg

The term “Parkour” comes from the French word “parcours,” meaning “the way through,” or “the path.” If you take this to imply “moving along a logical path to find the quickest way from point A to point B,” you’re missing a key element of Parkour the sport. The Parkour practitioner intentionally looks for obstacles to jump, bounce, or scoot over, around, or under. And those who use the barriers to execute the flashiest and most difficult stunts earn greatest respect among their peers.

Melody doesn’t always take the most logical route from point A to point B, either. We can sense a strong gymnastic spirit in the two versions of the Parkour figures illustrated below. In each case, the first and third notes are always chord tones, and there’s a clear and direct route between them. That direct route is indicated by a shadowed notehead.

As you study the Bounce and the Pounce, don’t just try to memorize the formulas. No, no, no! Instead, picture yourself crouching and leaping, or leaping then shuffling your feet to regain your balance.

“My Favorite Things,” by Rogers & Hammerstein

“I Love You,” by Billie Eilish

“Triumphal March,” from Aida, by Giuseppe Verdi

The Vault has two things in common with the two Parkour figures (the Bounce and the Pounce) 1. It’s a 3-note figure that takes an indirect route between the two outer notes, typically chord tones.* and 2. It contains a step and a leap, though not always in that order.
The main difference from the Parkour figures (the Bounce and the Pounce) is that the Vault’s step lies inside the outer notes of the figure.

“Hush, Little Baby,” by Carolina folk song

“Maria,” from West Side Story by Leonard Bernstein

“The Swan,” by Camille Saint-Saens

*At least the outside notes are usually two chord tones. Remember, with figuration, we focus on shape, which means that sometimes, chord tones and non-chord tones can get redistributed.

The Roll has two component parts: a 3-Note Scale plus a leap of a 3rd in the opposite direction to the 3-Note Scale. The result is a figure where the first and last note of the Run always match, whether the 3-Note Scale comes at the beginning or end of the figure.

“Hava Nagila,” an Hassidic folk tune

“Stand By Me,” by Ben E. King, Jerry Lieber, and Mike Stoller

“The Cancan,” from Orpheus in the Underworld, by Jacques Offenbach

The Double Neighbor figure gets its name from tabulating the number of non-chord tones present. We hear one “main note”—a chord tone—twice: at the beginning and the end.

The two notes in the middle are both neighbor notes—one higher than the chord tone; one lower. This creates a little “illegal” hole in the middle. Why is it illegal? Because one of the primary rules in melody forbids leaping between non-chord tones. But here is an immensely popular figure that does just that! Perhaps this is why the Double Neighbor figure is one of the only patterns that is already universally recognized as a melodic figure? Theorists figured they’d better proactively name one of the only acceptable exceptions to one of their staunchest rules.

“Mona Lisa,” by Nat King Cole

“If I Can’t Have You,” by Shawn Mendes

“Waltz” from the Swan Lake Ballet by Pyotr Il’yich Tchaikovsky

The Double 3rd figure gets its name from the way it melodicizes a common method for harmonizing a simple scale in thirds. But rather than playing the thirds simultaneously, they are stretched out in time.

“Invention #1,” by Johann Sebastian Bach

“Cherish,” by Terry Kirkman

“Sidewalks,” by The Weekend

The pendulum has two notes that move (or “swing”) by step as if swinging from a middle “fixed” note.

“Norwegian Wood,” by Lennon & McCartney

“Eastside,” by Benny Blanco, Halsey, and Khalid Robinson

“Juliet’s Waltz,” by Charles Gounod

The Leaping Scale is a 4-note figure made from two elements: a 3-Note Scale plus a leap to a different chord tone. (if the isolated chord tone matched the first note of the figure it would be a Roll.) Either the scale or the leap can come first. The leap can be small or large. And the direction of the leap can match the direction of the scale or contradict it.

Two factors make the Leaping Scale harmonically vivid. First, the outer notes of the 3-Note Scale are chord tones. And second, the leap occurs between two chord tones. Typically, this means that each Leaping Scale contains a root, third, and fifth.

“Old Town Road,” by Lil’ Naz

“Prelude,” from Suite #2, for unaccompanied ‘cello by J.S. Bach, bars 26-31

“The Raiders March,” by John Williams

The color-coding on the table of 24 common melodic figures shows three main categories of figures: scale, neighbor, and arpeggio. But as you look and listen closely to each of the 24 figures, you’ll hear some scale figures that include one or more leaps; You’ll notice that at least one neighbor figure contains a 3-note scale; And you’ll discover a fair bit of neighbor motion in figures that are mostly arpeggios.

In short, many of the melodic figures on the table are hybrids. But because hybridism is so rampant, there’s not much point in treating it as anything special.

So how do we decide whether to put a melodic figure in one category or another? There are two things to look for. (1) Majority rules. Is most of the figure a scale, neighbor, or arpeggio? and (2) Behavior. Does the figure act as a scale, neighbor, or arpeggio?

The Leaping Auxiliary (L.Aux.) is 3/4 neighbor figure, plus a chordal leap. The auxiliary or the leap may come first or last. The leap can be in any direction relative to the auxiliary. Here are but a few possible combinations.

“Breakdown,” by Tom Petty

“Sittin’ on the Dock of the Bay,” by Otis Redding

“Pavane,” by Gabriel Fauré

The Pendulum Auxiliary is an amalgamation of two 3-note figures: the Auxiliary and the Pendulum.

“What’s Goin’ On,” by Marvin Gaye, Al Cleveland, and Renaldo Benson

“Hold Me Now,” by Tom Bailey, Alannah Curie, and Joe Leeway

“The Hallelujah Chorus,” by George Frideric Handel

The Funnel offers some of the most convincing evidence that composers imagine shapes as we compose. How else can we explain the ever-narrowing series of leaps that make up this figure? Perhaps as a backward extension of the Little Holy Philip? Keep that in mind as you listen to “Someday My Prince Will Come,”  where the pattern stretches back even further.

We classify the Funnel as an arpeggio because it leaps until it runs out of room, not because it spells any particular harmony. In fact, the Funnel has the most ambiguous harmonic structure of all the figures, which is to say that it doesn’t fit into any particular harmony. Even if we find a way to separate chord tones from non-chord tones in one instance of the Funnel (and good luck with that!), it's not likely to work out the same way in other appearances.

“Someday My Prince Will Come,” by Larry Morey & Frank Churchill

“Dreams,” by Stevie Nicks

“Great is Thy Faithfulness,” by William Runan and Thomas Chisholm

Most of the names for the 24 Universal Melodic Figures have a mnemonic function. The name tells you something about the figure that not only helps you remember it but use it. Not so with the Cambiata figure. The figure traces back to 17th-century Italy and derives its name from an Italian verb meaning “to change.” If it were clear to anyone what sort of change occurs within this figure, that might end up being helpful. But no such luck. I only use the name Cambiata because that’s what other people call it, which brings up an interesting point about figure names.

The Cambiata is one of two figures that use standardized names. The other figure is the Double Neighbor, which sometimes goes by the name “changing tone” (in English). Why do none of the other 22 melodic figures have names? Likely because they are so ubiquitous that nobody thinks they deserve special recognition.

The behavior that merits special recognition in the Cambiata (and also the Double Neighbor) has to do with the “hole” in the middle of each figure. Music theorists have never known how to explain how a figure that leaps to and from dissonant notes can sound so graceful. So they simply provide guidelines for how to handle it, never bothering to elaborate on the “broken rules.”

We won’t go into the strict guidelines for using the Cambiata in classical styles here. More important is that the attractiveness of this figure comes from the way it goes “too far” (passing its destination) before returning to the intended goal. It’s a routine we’ve encountered in the L.H.P. and the Double Neighbor.

“There Goes My Life,” by Kenny Chesney  there-goes-my-life

“Cheek to Cheek,” by Irving Berlin

“The Washington Post March,” by John Phillip Sousa

 

The Zigzag figure changes direction after every note, making it the most indirect way to arrange the notes of a single harmony. Now typically in figuration, the more times a melodic figure changes direction within itself, the more complicated it sounds and feels. This is certainly true of the other two figures that change direction after every note: the Double Neighbor and the Double Third. But for some reason, the Zigzag figure usually makes a melody sound more playful than elaborate.

“Your Smiling Face,” by James Taylor

“Trumpet Concerto in Eb Major,” III by Franz Joseph Haydn

“Die, Die, Die,” by the Avett Brothers