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.
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.