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Fraction Attraction: composing a song inspired by math

What goes on within a musical composition that can make us *feel* the driving pulse of a beat? What makes the introduction of syncopation, or stress on the off-beat, often feel so exciting and unexpected? Building a bridge between music class and math class, fractions play an essential role here. Teachers and students alike can have fun using math to compose music, and students can witness in their own compositions how fractions are fundamental to creating different musical moods. We entered into this month’s Second Saturdays workshop with the aim of composing a piece inspired by, and that could illustrate, this facet of musical math.

New Harmony Line’s Director of Education Cecilia Roudabush kicked off this month’s Second Saturdays workshop with a lesson on this concept – the rhythmic, fractional values that make up music. Understanding a single measure as a whole that can be divided up into several pieces can be easier for many when visualizing a measure as a bar or a pie cut into different sized pieces:

After a visual primer on how a whole measure can be made up of many different combinations of half, quarter, eighth, and sixteenth notes (among other values), we discussed how stress can be placed on different beats and off-beats in the measure to create different effects. For example, in 4/4 time (when there are 4 quarter-note beats per measure), many pop songs place more emphasis on beats 1 and 3 than 2 and 4, while oftentimes in jazz music more emphasis is placed on 2 and 4.

We jumped into Hyperscore to start composing with these concepts in mind. Translating Cece’s lessons into sound, we created melody windows with motifs breaking up the measure into different rhythmic values – one whole note, two half notes, four quarter notes, and eight eighth-notes:

Then, we started layering them against each other in the sketch window to hear the ways they relate to each other. We hear the articulation of a quarter note every two eighth notes, a half note every four eighth notes, for example. We ended up with an intro with each of these motives in sequence, creating a “countdown” effect, before layering them against each other and using changes in instrumentation to make the different length notes sound out clearly against each other.

The different colors in the Sketch window each represent one of the above melody windows.

We added more complexity to the piece by creating melody windows that include rests to emphasize certain beats (and off-beats). We also decided to add more interest to the composition by contrasting the single-pitch motives we were working with against a singsongy melody window with varying pitch. A percussion window demonstrated the frequent effect that rhythm sections have of underscoring stress on certain beats of the measure:

With these different elements we gradually wove together a densely textured, bright and bouncy tune. Listen to the full piece “Fraction Attraction” below – and check out the full recording of the workshop as well to see our composition process and watch how the piece came together! Join in on the fun by registering for our free composition workshops that take place every second Saturday of each month – we look forward to making music with you!

Cover image courtesy of solod_sha via pexels.com.

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The Melt: Composing a song from an audio prompt

This month’s Second Saturdays Hyperscore composition workshop started with a sound:

Striking and familiar yet uncanny, this sound, which we encountered in this 2020 article from The Guardian, is that of Antarctic icebergs melting. The sound of rushing water is punctuated by an eerie and percussive whooshing and popping sound, which, as the article explains, is the sound of primordial air breaking out of millennia-old bubbles, held no longer by the ancient, now melting, ice.

We listened to this in the context of taking inspiration from clips of sound from the world for musical composition. How might we translate the feelings that came up, and the rhythms of the sound of the melt itself, into music? We set out to find one answer to this question during the workshop.

We began by naming the feelings and atmospheres that were evoked for each of us when we listened to the sound of the iceberg. Themes arose as we spoke of familiarity, awe, uneasiness, uncanniness, and surprise. What sounded like rushing water in the clip was a familiar, even comforting sound, but the interruption of the strange popping sound gave an edge to this feeling. The additional context that knowledge of climate change gave to the sound – the melt reaching farther into the ice, and getting louder, every year – added a somber, even grim, undercurrent. We wanted to approach composition both mirroring what we were literally hearing (a constant, smoother sound punctuated by sudden and unexpected pops) and the emotional reactions that this sound and its context created in us.

Moving into Hyperscore, we decided to start with some melody windows that could serve as an ambient, slow backdrop to the piece, using notes with long durations and in a low register, using a timpani and strings for our instrumentation.

We then created some strokes to correspond to these motifs in the Sketch window. The result was melodically tense and rather menacing.

We had our “consistent” sound which we then wanted to break up with unexpected interruptions and percussive splashes. To add a rhythmic yet unpredictable element we composed two faster-moving melodic motifs on pizzicato strings – one with a measure broken up into 3 notes of equal value (in other words, a half-note triplet), and one with a measure broken up into 4 notes of equal value (in other words, quarter notes).

When played together and layered into the Sketch window, they created a kind of rhythmic dissonance and a sense of driving momentum that broke above the surface of the steady and slow sounds we started with. We decided to emphasize this sudden and inconsistent effect to introduce these new sounds in the Sketch window (represented by the light and dark green strokes) as fragments that would pop in and out before returning in earnest and persisting for what would become the climactic moment of the composition:

To add even more emphasis to this climactic section and create a mood of mounting urgency, we created another 3-against-4 rhythmic figure on woodblock in two Percussion windows and added this in the Sketch window as well:

The intensity of the climactic section increased with the addition of the orange and purple percussion motives.

We liked it but found that we were deviating some from the unpredictable sense that we got from the popping in the initial iceberg sound clip. To reintroduce that surprise, we created a version of the green motifs that was a bit more sparse, while still maintaining the 3-against-4 feel, and applied this to the green strokes only in the latter half of our piece.

We decided to tweak the percussion windows as well, making the note attacks much more rapid and inconsistent and adding in some triangle hits:

We continued on with this process of listening to our composition, reacting to what we were hearing, then making changes and additions according to our reactions. Through this process in the course of the rest of the hour-long workshop, we added a mournful, soft ambient drone of low flute and organ, and a jerking, syncopated melody played on pizzicato strings.

We arranged all of the building blocks we had created into a form that ebbed and flowed between themes of rattling urgency and dirge-like somberness. Without planning to, we ended up creating a rather atonal and dissonant piece that nonetheless carried in its undercurrent a driving movement that enthralled us when we listened to the final product. We ended by titling it, appropriately, “The Melt”.

Listen to the final, 80-second-long composition below, along with a recording of the full workshop including our brainstorming, composing and editing process.

Iceberg image courtesy of Angie Corbett-Kuiper via Unsplash

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From silence to song: writing music from curiosity alone

For the May edition of our Second Saturdays composition workshop, we chose not to write from a prompt. It can often feel risky or intimidating to face the prospect of creating “something from nothing” – where to begin? It was precisely for this reason that we wanted to experiment with this process. Hyperscore shines when composers lead with an open mind, and can help to lower the barriers of “the blank page”. Composers of all experience can learn to trust their musical intuition with the tools of Hyperscore.

Using Hyperscore, we simply began by choosing an instrument set -folk band – and putting down some notes into a percussion window. We added one percussion instrument at a time, reacting to what we were hearing when we played it back. What does this instrument sound like? Do we want fast or slow notes, on the beat or off the beat? Most importantly, how does it feel to listen to it, and do we want it to feel different? We ended up with a steady, dense rhythm that was heavy on syncopation and evoked a slow, erratic march:

Next, we moved on to add some melodies. We agreed to start by creating a bass line riff that could repeat throughout the piece, forming a solid, catchy underpinning. Going through several iterations and asking each other what we heard and what we imagined was essential for the composition process. The bass developed into a two-instrument section, with one bouncy, quick motif complementing a swaying legato figure. After listening to them all together in a Sketch window, we made some edits to the melody windows so they would stand out and complement each other better and landed on our final versions:

Adding all three motives into the Sketch window, we decided to use the Classical harmonic mode and to experiment with creating regions of tension and release with the Harmony Line. Fine tuning these sections meant plenty of listening back, making slight changes, and then listening again.

We had rhythm, a bass line and a basic harmonic structure – now a piece was really starting to develop! It was time to bring in more melody. We created two variants on one melodic theme – a lightweight twinkling dance on a music box, and a half-speed repetition of the same theme, lower and more dramatic, on guitar:

We also decided to add an additional, more stripped down version of our main rhythm theme to add some variety and interest throughout the composition.

Weaving together all the elements in the Sketch window, making edits and additions following our intuitions and desires, we landed with a piece that had an uneven yet regimented feel. For us it was evocative of animated clocks ticking in and out of time. It reminded one of our participants of the classic tune “My Grandfather’s Clock”, after which we named the composition.

Listen to the final composition below, and watch the recording of the the full workshop, including our process of brainstorming and editing:

Photo of clocks courtesy of Andrew Seaman via Unsplash

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Creating a Character through Music

A capybara sitting in a body of water

Think of one of your favorite characters from any form of media. Chances are, they evoke some emotional response in you that has drawn you toward them. Characters can be abundant sources of joy and inspiration for all of us, as can be seen from just a glance online at the copious amounts of fan art and works created by all sorts of people motivated by their passion for all sorts of characters.

We used a character as the foundation for making music with Hyperscore at our most recent Second Saturdays Zoom workshop. We began by coming up with a character: one attendee brought up her affection for capybaras, and we soon landed on Cappy the capybara as the protagonist for our musical story.

We brainstormed a list of association words and phrases that we imagined Cappy to have, to inspire the composition of his leitmotif – a musical theme associated with him that would repeat throughout our piece. “Sleepy”, “determined”, “furry”, “plump”, “aquatic”, and “adorable” were among these descriptors. Thinking of these words, we started laying down some notes in a Hyperscore melody window that would encapsulate Cappy’s energy, using the warm sound of a french horn.

An orange Melody Window plays two variations on a five-note figure using a French Horn.
Cappy the capybara’s theme

The next question was, what’s the story? Cappy needs an exciting adventure. Imagining various scenarios prompted a second character–a hungry alligator!

A green Melody Window represents the alligator, with string notes in the lower register that rise up to peak above the water.
The alligator’s theme

There should be more than danger motivating our story. What is something that would make Cappy happy? Why, some delicious fruit, of course.

The light green Melody Window with six flute notes in two bars
The fruit theme represents Cappy’s snack

And where does all this action take place? Alligators inhabit rivers, so we needed music to suggest rippling water.

A blue polyphonic Melody Window with eight notes in two bars creates a rippling water motif.
The water theme accompanies Cappy when he goes for a swim

Now that we had our main characters and setting, what about the action? Cappy goes out for a stroll and come to a river. He starts swimming but Alligator enters the scene. When Cappy realizes he is being stalked, he starts swimming faster. There’s a race culminating in Alligator lunging at Cappy!

A yellow to-bar Percussion Window has half notes alternating between high and low toms with a wood block on the off beat that ends with a "crunch" of triangle and tambourine.
A two-bar percussion figure depicts Cappy walking and racing, as well as munching on fruit

Here’s “Cappy’s Day.” Listen to hear the different themes and find out Cappy’s fate!

Hear the motifs that represent the characters and story elements, as well as the final composition.

Here is the full Second Saturday workshop showing in real time how we put this composition together. Peter shares a ton of subtle Hyperscore tricks and hacks!

Want to try this out yourself? Sign up for our free Second Saturdays workshops here.

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Composing for video games

The logo of Scratch, an orange cat walking upright and smiling, next to the logo of Hyperscore, a stylized lowercase letter h.

Composing music can be a pure pleasure for its own sake, but to motivate a classroom of learners (not to mention oneself), it is hugely helpful to set a goal. And what could be more fun than making music for something kids already love: video games! Composing using Hyperscore’s easy, game-like interface makes it a great match for this theme.

We tried this idea out at our recent Second Saturdays Zoom workshop with David Casali. David presented three simple video games made by kids using Scratch. Scratch was created at the M.I.T. Media Lab, just like Hyperscore (literally across the hall). It’s a free, graphics-based programming language used by millions of children around the world who have amassed a vast, open-source trove of content, including animations and video games.

Composing for a few good games

Scratch offers a vast collection of kid-made video games. It would be overwhelming for students to search through them, so David suggests picking a few as prompts for a class. Here are the ones he chose. Each has a distinct feel. We picked Phroot Panda, in which the player has to catch pieces of fruit as they rain down from the sky.

“Frantic” and “busy” were some descriptive words for it. Putting himself in the mind of a fifth grader, David said the first thing he might do is set a fast tempo. We then went to work on the melody. Someone suggested a syncopated rhythm.

A Hyperscore melody window showing a basic syncopated rhythm on middle C.

Something jagged…

A Hyperscore melody window showing a melodic line that moves rapidly up and down with a syncopated rhythm.

We quite liked the jittery effect. Time to open a sketch window and start “painting” with this motif. We took this line for quite a hike…

A Hyperscore sketch window showing several lines moving up and down, some of them straight, some wobbly and some gently curved.

Definitely frenetic! Next we used the Harmony buttons to listen to our melody and settled on the Classical mode, tweaking the gray “harmony line” in the center to add harmonic tension and release. Peter added some punchy strings, ratcheting up the drama in the composition to match the game, and voila!

We downloaded the completed music as an MP3 file. David then showed us how to program the game to play to music. Here are David’s step by step instructions: Scratch Soundtrack Guide and Chant Remix on how to add a soundtrack to a Scratch program. You can watch the workshop in the video below and give a shot at composing music for your own games. Comments welcome!


Join in on the fun and spark your imagination for composing with Hyeprscore by registering for our Second Saturdays workshops!

We love having conversations about teaching to compose with Hyperscore. Come hang out with us at our monthly Zoom Office Hours!

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Taking a line (of music) for a walk

by June Kinoshita

The artist Paul Klee famously said that the art of drawing was like “taking a line for a walk.” What if you could take a line of music for a walk? That’s just what it felt like when we held our first-ever composing workshop over Zoom.

We were not at all sure how our experiment would work out. A group of us popped onto Zoom on November 12 at the appointed time (10:30 a.m. ET). Because we didn’t know how many participants would have Hyperscore running on their computers, we decided to take a collaborative approach. Peter shared his screen and the group proceeded to build a piece of music together.

We started with the percussion window in 4/4. To get things going, I proposed a bass drum on each quarter note to establish a steady pulse. We each took turns adding a new percussion line: a cymbal on the fourth sixteenth-note of each beat, another as a quarter note on the fourth beat, then a high-hat on the second and fourth beats. Each time we added a layer, we listened and discussed whether we liked what we were hearing. Once the percussion track had achieved a satisfying density, we played with the tempo and settled on a moderate speed that had a pleasing swing to it.

A Hyperscore percussion window four beats long with purple note droplets arranged on some of the instrument tracks
Percussion window with drum and cymbal notes

Once we were satisfied with the percussion track, we moved onto the melody. Lisa P. hummed a two-measure melody which Peter noted down in the Melody Window. After a few tweaks, he captured the tune perfectly with its subtle syncopation. What instrument should play it? A tenor saxophone felt like a good fit for the melody’s soulful, gently melancholy vibe.

A Hyperscore melody window with six purple note droplets filling two measures
Melody window with a syncopated tenor saxophone tune

With a melody (orange) and rhythm (red) in our “toolbox,” it was time to go to the Sketch Window. First, we took the orange line for a simple stroll, a straight line on middle C for two bars. Then we decided to jump it up an octave. After two bars of that, we added a second orange line underneath it to add harmony. We then took the orange line down a hill, from high C to low C. Halfway down the hill, another orange line came along and decided to head in the opposite direction, up the hill. It felt like time to add percussion, so we laid in a flat red line like a rock-steady floor. Two bars in, a yellow line joined in…a simple descending bass line that Peter had whipped up. 

A polyphonic Hyperscore melody window two measures long with four descending chords
Melody window with descending chords for use as a bass line

We quite liked where this was going, but we wondered how the descending orange line would sound if we imposed a bit of harmonic structure to it. Classical mode converted our soulful melody into C major—all wrong! General harmony worked well for the sloping orange parts but robbed the original theme of its specialness. Peter then showed us a cool trick. He could select sections and turn off the harmony function, restoring the original. That was fantastic, as we could now preserve melodies that we wanted to keep exactly as written, while allowing other parts of our piece to “collaborate” with Hyperscore’s machine intelligence. 

And that, folks, is how you take a line of music out for a walk.

If you have a basic subscription to Hyperscore, you can find our little opus on the Community board (“Composing Workshop 1”). If you want to remix it, just give it a new name and it will be saved to your account. To share it with the community, just make sure to check the “share” box. 

Our Second Saturdays workshop is held on—surprise!—the second Saturday of each month at 10:30 AM US ET over Zoom. Everyone from anywhere is welcome to join. Just register for the series to receive the link.

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