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Columns | Fall 2016

Pro Song

Advanced Zippering

A Mathematical Exploration of the Zipper Song Form

Anybody in children’s music likely knows a few zipper songs. “Old McDonald” is a prime example. A zipper song’s verses usually differ by only a few words that get “zipped” in each time. The zipper song structure wields incredible built-in powers of listener engagement. You can’t go wrong with a zipper song at a get-together or sing-along!

So how do you write a great zipper song?

Zipper Songs Are Built on Mathematical Functions

A zipper song’s verses follow a set pattern, with one key word that changes from verse to verse. Usually one or more other words change as well in response to the changing key word. Delight comes in hearing the result when you plug in a new key word, whether it’s predictable, surprising, or both.

The engine driving a zipper song is like a mathematical function. A function is a rule that generates one response (or output) for each example (or input) pulled from a given category (or domain). Typically we label the input “X,” the function “f,” and the output “f(X)” (pronounced “eff of ex”).

By specifying a domain—e.g., types of farm animals—and a function on that domain, we can write all the possible verses to “Old McDonald” using a single “model verse”: If X is a type of farm animal, let f(X) be the word for the sound X makes. Then our model verse is:

Old McDonald had a farm, E-I-E-I-O
And on that farm he had a X, E-I-E-I-O
With a f(X) f(X) here, a f(X) f(X) there
Here a f(X), there a f(X), everywhere a f(X) f(X)
Old McDonald had a farm, E-I-E-I-O

To generate a particular verse, replace the “X” with a type of farm animal and replace every “f(X)” with the sound that animal makes. Try generating three verses of “Old McDonald” using the model verse above and the following table:

X f(X)
Verse 1: Cow Moo
Verse 2: Pig Oink
Verse 3: Duck Quack

See if you can identify another zipper song from its domain and function: “If X is something or someone you would find on a bus, let f(X) be a defining sound and/or motion X makes.”

Engaging the Listener

The domain and function at the heart of any zipper song provide a conceptual hook. This is what makes the song engaging. The listener will interact 1) by trying to deduce the domain of the function (so these are farm animals we’re talking about!); 2) by anticipating possible inputs (will there be a turkey?); 3) by anticipating the output your function will generate from a given input (what sound will the turkey make?); and 4) by anticipating and enjoying how each output interacts with the rest of the verse (gobble gobble here, gobble gobble there, here a gobble, there a gobble—oh, yeah!).

In a live performance you might ask audience members to provide the input X for each verse. This heightens interest even further as the singer responds spontaneously to whatever the audience has provided!

The Verse Is the Chorus

Did you notice that the “Old McDonald” verse starts and ends with the song’s title? You’re far more likely to see this happen in a chorus. Many zipper songs include only verses, so the verse must pull double duty. In addition to the changing material, your zipper verse may include the song title, the hook, some rhyme and/or repetition, and some rhythmic contrast to keep things interesting. Can you find all these elements in the “Old McDonald” verse?

Zippy Endings

Some zipper songs end naturally. After verses for spring, summer, and fall, a verse for winter is your obvious ending. But what if your domain is wide open, like things you might find on a bus? How do you end the song? Here are a few suggestions:

  • End with your favorite, most profound, or most hilarious verse.
  • Repeat the first verse as your ending verse.
  • Repeat the last line of the last verse, or alter its rhythm so that it feels like an ending.
  • End by repeating the key line from every previous verse. Susan Salidor’s song “I’ve Got Peace in My Fingers” ends this way.
  • End with a modified verse—or a whole new melodic section—that doesn’t use the X/f(X) pattern but instead summarizes the theme of the song. My own “Howdy Song” ends this way; so does Patricia Shih’s “The Color Song.”

When to Bridge a Zipper

Wiley Rankin and I wrote a zipper song called “Listening Is a Two-Way Street”: If X is an action that can be shared between two people, let f(X) be X in verb form. Our model verse:

X is a two-way, two-way street
It takes two directions to be complete
I’ll f(X) you, you’ll f(X) me
X is a two-way street

Our verses are:

X f(X)
listening listen to
sharing share with
friendship be friends with
giving give to

The function we used here is the “identity function”—what you get out is basically what you put in (allowing for grammar). Because the verse is short and the function doesn’t generate new or surprising ideas, listening to four verses in a row could get tedious.

Thus we decided to add contrast with a bridge, brilliantly constructed by Wiley:

Sharing, Caring
Loving, Living
Laughing, Hoping
Helping, Giving

Where six additional verses would definitely become tedious, this bridge merely suggests six additional verses by listing possible input words from our domain. What a simple, elegant way to expand the scope of the song!

Multiple Functions

Sometimes a model verse may require multiple functions. Susan Salidor’s “I’ve Got Peace in My Fingers” can be formulated using two functions: If X is a tool for positive interaction with others, let f(X) be the place in your body where X resides and let g(X) be a way of sharing X. Then the model verse is:

I’ve got X, X, X in my f(X)
Watch what I can do!
I’ve got X, X, X in my f(X)
I’m gonna g(X) you!

The verses are:

X f(X) g(X)
Peace Fingers Shake hands with
Words Head Talk things over with
Love Heart Give some to

The Constant Function

A constant function gives you the same answer every time, no matter what you put in, and can be used to generate a unique type of zipper song. “Six” by Trout Fishing in America is a prime example. Each verse asks a question, and the refrain that follows is always “I believe the answer is six.”

Using the language of mathematics, if X is a question whose answer is six, then define f(X) as “six” (no matter what X is). Then the model verse is just two lines and looks like this:

I believe the answer is f(X)!

Why use a function at all here? Couldn’t we just write the model verse like this?

[Put a question here]?
I believe the answer is six!

Of course! Using the function just helps show the song’s underlying structure. Perhaps you wouldn’t have thought of this song as a zipper otherwise. Turning that thought around, exploring different types of functions might help us create unique and interesting new zipper songs.

“Six” is also a rare example of a zipper song with a chorus. The verses are short and numerous, so the chorus, inserted twice, provides some needed contrast.

A Zipper With Depth

Patricia Shih’s “The Color Song” can be formulated with three functions:

If X is a color used to describe people, let f(X) be a list of things that actually are the color X, let g(X) be a negative emotional thing represented by X, and let h(X) be a positive I associate with you, inspired by X. The model verse is:

Why do they call you X man? You’re not X at all
X is the color of the
f(X) and
Yes, X is the color of all these things
But people are not the same
h(X) whenever I say your name-O

The first two verses are:

X f(X) g(X) h(X)
yellow the morning sun and dandelions and chicken soup and legal pads fearful minds You remind me of the golden rule
red climbing rose and traffic lights and tomatoes and chicken pox and bloody nose angry words I can see the rosy future

Even if we don’t sing along on first listen, the zipper aspect of this song still engages listeners of any age with a complex exploration of a difficult social topic. Now that’s advanced zippering!

Write Your Own Zipper Song

Start your own zipper song with a compelling domain and function, and then make a table to evaluate potential verses. This method allows you to tweak efficiently until you’ve built a solid foundation. Ideally your function will yield outputs that are predictable and carry consequence.

Suppose your domain is “things I might take to the beach.” F(X) could be the color of X. But who can guess the color of a bucket? And what does it matter? A better f(X) might be “why I’m taking X.” 

Once you’ve filled a table with strong ideas, construct your model verse. Leave room for your longest X and f(X) phrases. Don’t forget to make your verse as singable as a chorus. Add an ending or bridge as needed. Have fun, and let me know what you come up with!