Song Math
Posted by Chen on / 0 Comments
Let’s face it; pop music gets a bad rep.
There are large segments of the population who look down on pop music, claiming that it’s formulaic, generic, uninspired and that it all sounds the same. I’m sure we’ve all seen those videos on youtube where the narrator runs through fifty different pop songs, and superimposes them on the same chord progression, just to prove that point.
Maybe even you are one of those people, who don’t like what’s on the radio and think your eclectic, hip musical taste is too sophisticated to be satisfied by the “simplicity” of a Bibber, or a Gomez.
But admit it, every time Despacito comes on over the speakers at the grocery store while you are waiting in line, you bob your head and tap your toes (you might hate yourself for it, but god help you, you tap those toes!)
It’s not your fault! You are helpless to resist. Every time you can’t stop humming a catchy melody, or stop yourself from singing along with Adele’s Hello while driving down the street, there is a scientific reason for it. And it all comes down to those very formulas pop music is charged with using.
And how does pop music plead to those charges? Guilty of course! Pop is formulaic. But that’s because ALL MUSIC is formulaic. From Mozart (arguably the most famous pop star of all time) to Prince, from Bach to Britney, all music follows formulas. Be it in the composition of a melody, the structure of the harmony, or the function of each section of the form.
Sound, as a physical phenomenon, is a mathematical wonder filled with the very formulas early musicians used to bring order to the music around them. And that I think, is what pop bashers misunderstand; no songwriter sits down to write a song with a hit mathematical formula written on a whiteboard, and then inserts random words and chords into it as if they were painting by numbers. I’m sorry to say there is no secret government facility, where scientists in lab coats use sophisticated algorithms to construct the next #1 hit (although the Google AI did just write it’s own song… When is the album dropping??).
No. These formulas are just the side effects of good songwriting. If a songwriter’s tool’s and skills are sharp enough, and if they’ve familiarized them selfs with the sounds and elements of the style they are going for, you’d be able to reverse engineer and extract these formulas form their finished songs.
We have close to a hundred years of recordings of popular music. And every great songwriter in history that impacted the landscape of music, grew up listening to other iconic songwriters who changed the landscape before them. Time and time again we look at great artists, and we can trace the evolution of their sound. And we see, song after popular song how the same “math” applied to each of those hits. “Math” validated by the listener who gobbled up the music and made it the popular music of the time.
So how do we get there? How do we as songwriters get to the point where these formulas naturally appear in our melodies and lyrics? Well, as an old friend and mentor used to tell me; If you fumble around for your keys in a dark room long enough, you’ll eventually find them. But you would have found them much sooner if you just turned on the light.
For our purposes, ‘turning on the light’ would be familiarizing ourselves with “Song math.”
If you Google the term song math, you’ll get lots of youtube videos of songs teaching toddlers how to count to ten. You’d have to go pretty far down the list in Google before you found anything about songwriting (I stopped after page seven of the google search…). That’s because strictly speaking it not an actual term. Studying “Song Math” is just another way of saying, studying music. If one were to spend years studying theory, harmony, and composition, one would now have a pretty good grasp of the rules of “song math.” But many songwriters are not professionally trained musicians, and lack a background of musical training. The term Math started to be used because, while not everyone is musically trained, everyone has a basic understanding of math, and math is the bedrock of musical theory.
Take for example, Melodic Math.
For those who haven’t heard about it before, it is a term most often associated with Max Martin and his accomplices. It is one aspect of the overall “math” of a song, and deals for the most part with syllable count, symmetry, and rhyme placement.
Martin is famously tight-lipped about it. There are not many times he has talked about it fully on record, but his often collaborators Bonnie Mckee and Savan Kotecha have shed some light on it on a few occasions.
“It’s very mathematical,” McKee explained. “A line has to have a certain number of syllables, and the next line has to be its mirror image.”
Some of what Martin calls Melodic math, Pat Pattison refers to as meter and motion. What Bonnie Mckee calls “mirror image”, is simply the melodic technique of repetition, that makes something feel hooky. Let’s take a look at Teenage Dream By Katy Perry as an example (co-written by Martin and Mckee):
You make me
Feel like I’m living a
Teenage dream
The way you turn me on
I can’t sleep
Let’s runaway And don’t
I’ve divided the lines here not according to the story, but according to where the melodic phrase repeats. The syllabic pattern here is three/ six/ three/ six/ three/ six, with the “e” rhyme appearing on the last syllable of the group of three.
In the following line, Martin changes up the melody and rhythm to give us variation, but still delivers two lines with a total of syllables numbering nine, just like every group of two lines before it:
Ever look back
Don’t ever look back
Martin delivers the number of syllables our brain got used to, thus creating symmetry. The human mind loves recognizing patterns, and recognizes the syllable count as one. To give even more symmetry and hookyness to the variation at the end, Martin structures the section as a simple repeat: “Ever look back” has four syllables, with a rhythm of 2 eights notes on beat one, followed by 2 quarter notes on consecutive beats. On the fourth beat, he adds the one syllable quarter note “Don’t” (harking back to the previous measure’s fourth beat which has the same word), And then repeats “Ever look back” with the same rhythm and placement.
There are other aspects of song math beyond the melodic. Form is a big one. If the math is right, the listener naturally feels the move to the next section. If its wrong the song can appear clunky, or disjointed.
While there are many different forms we can study and get familiar with, the basic idea that seems to have stuck through the years is symmetry. There are for sure many songs out there with an uneven number of measures, but generally speaking pop songs tend to have an even number of bars to their sections. It really comes down to, I think, how we subdivide music. The entire system is based on even numbers, whole note, half note, quarter note. Music history is filled with symmetrical forms, going all the way to Bach, and before.
The movement of the harmonic progression also relies on math. A chord can change every four beats, every two beats, sometimes even every beat. But it has to follow some sort of pattern for our brain to register it as form. If the chord changes randomly, sometimes every other beat, then every beat, then held out for three beats, etc., the listener has nothing anchoring them. No guidepost to provide a point of reference and tell us where we are in the song.
The harmonic functions of chords also use patterns and formulas. Without getting into too much “music talk,” everything in music is either tension, or resolution. Chords in a progression either provide different levels of tension, or different types of resolutions. And wouldn’t you know it? One can easily extract formulas and patterns of tension/resolution, from our shared pop music history; Chord types that traditionally follow other chord types, or chords and movements that define different styles, etc.
I really could go on and on and on, (in fact, I plan on it! Look out for HitSongCoach.Com’s upcoming Song Math online course!), But for now its enough to say that there are rules to songwriting. But they are not there to limit you, or suppress your creativity. They are simply the framework that defines our art form. And once you know the rules, once you’ve internalized them and turned them into instinct, You can then find interesting and effective ways of breaking them.
To truly master all of this “Song Math,” one would have to be a lifelong student of music and songwriting. But you can get started without knowing actual music terms, simply by listening critically to popular music, and trying to identify these patterns as they occur. Once you know what to listen for, the patterns will become obvious. And the more you do it, the quicker you will internalize these formulas and turn them into instincts.
But at the end of the day, you can know all the formulas, and do all the right math, and still write a bad song. Patterns and formulas are just tools, how you use them is what counts.
Before I sign off, I want to go back for a moment, to that Google AI from before. Scientists fed it decades worth of pop music, and it extracted all sorts of algorithms from it, crunched the numbers and came up with its version of the ultimate pop song.
Listen here, to feel good about the fact that songwriters won’t lose their jobs to robots anytime soon.
Award winning and multi platinum selling songwriter/producer Chen Neeman's songs have been recorded by artists such as Miley Cyrus, Demi Lovato, Selena Gomez, Joe Jonas, Zendaya, and The Muppets, among others. Chen is dedicated to helping aspiring songwriters learn how to write better songs through personalized one-on-one coaching sessions via Skype, FaceTime, or in person at his L.A Studio.
Find out more about Chen’s Pro Songwriting Coaching, at HitSongCoach.com