Glocks, Clocks, Math & Music: How Imperfections Create Emotion in Music
My dad loves clocks and has an extensive collection from different eras, with a variety of styles, materials, and faces all tucked away among his books and other trinkets he’s collected over the years. One Father’s Day or Christmas he was gifted a unique antique. It kept time perfectly but had a quirk. The tiny third arm that spun around to count seconds would go from 12 to 6 and then stutter for maybe three seconds before quickly swinging back up to 12 again. It always made up for the stutter at 6, and to me, it was perfect in its adorable imperfection. But it bugged my dad.
With tiny screwdrivers, pliers, and a magnifying glass he toiled away and made it so the third arm went full circle in an uninterrupted fluid motion. And it never kept the proper time again. I completely ascribe to finding the beauty where others might see flaws, or seeing perfection in the imperfections. This same concept, when applied to music, translates into something even more incredible.
Since the first utterance of words, humans have been drawn to singing, creating melodies, clapping and snapping to a rhythm; music is innate and inextricably linked to the definition of being human. In fact, research has shown only about 3-5% of the population don’t enjoy music, but due to a neurological condition called musical anhedonia.
With time signatures, meter, rhythm, BPM, acoustics, frequencies, timbre, sonic texture, psychoacoustics, etc., music seamlessly combines mathematics and physics into an art. But while mathematics is an essential element of music, the difference between mathematically perfect (a machine) and human lies in the slight irregularities and minor alterations. Like notes being off by micro-fractions- it's not necessarily perceivable by ear, but it's visible on a computer screen. With plugins sampling real players and more complex algorithms being written to give human expressions, a musician working in a DAW will still most likely want to make those midi notes mathematically perfect. However, in the “flaws” lies humanity; the slightly elongated notes, the quickening of others, all of those micro-expressions translate into emotion.
Mathematics is deeply embedded in music on multiple levels, but some higher-level elements are time signatures, rhythm, meter, and BPM. The time signature is marked at the beginning of a piece of music with two numbers stacked on top of each other, like a fraction. The top number denotes how many beats per bar, while the bottom denotes what type of note is considered a whole note. The notes in a bar can be comprised of half notes, quarter notes, eighth notes, sixteenth notes, etc., but will all combine and total out to the top number of the time signature. For instance, 4/4, or “common time,” denotes each bar will have 4 beats and a quarter note represents one beat. Likewise, 2/4 time denotes the quarter notes as one beat, but each bar will only have two beats. With different time signatures come different meters or rhythms.
Meter and BPM
Common time taps 4 beats out evenly, whereas a 2/4 meter will give a 1-2 rhythm reminiscent of a march. With a 3/4 time signature, the emphasis is on the first note. 1 is a down-beat followed by 2 and 3 being up-beats, creating that recognizable down-up-up, down-up-up waltz rhythm. Time signature and meter define the mathematical rhythm, or heartbeat of a song, while BPM (beats per minute) define how fast that heart is pumping. There are many tempo markings denoting speed usually written/seen in Italian or French. The following BPM are approximations: From the slow Larghissimo at 24 and below BPM, ticking up to a still languid Adagio at 66-76 BPM, to a moderate Moderato at 108-120, up to a trance favorite Allegro at 120-156 BPM, all the way to an intense Prestissimo at over 200 BPM.
Darude's Sandstorm is a 4/4 Allegro 136 BPM or 34 Bars Per Minute.
Sia's Chandelier is a 5/4 Moderato 117 BPM or 23 Bars Per Minute.
Next time you need a good laugh check out this rendition of Chandelier. Get it, Toad!
My nemesis the metronome
When I was first learning piano I had a strict and structured piano teacher... in retrospect that was a good thing. However, back then I always wanted to write my own songs and play around with the timing of other songs. Inevitably, she would whip out an old-school metronome, forcing my fingers to tap each note with the tick-tick-tick of that swinging metal arm.
Old school metronomes are mechanical devices usually made of wood with a metal arm. You slide a weight up or down the metal piece to quicken or slow the swinging motion; this is what creates that distinctive metronome tick. Now they come as plastic tiles with adjustable numbers; but they produce a regulated ticking that corresponds to a tempo, marking rhythm and pace.
When I rediscovered piano and first started playing around in Logic Pro X I would hit the record button and play in a stream-of-consciousness way. The comments from people on those songs are always centered around emotions. “It gave me chills.” “I can hear the heartbreak.” However, during a music session with a friend, an old familiar nemesis came back. My buddy sat me down at his system, let me play, and then stopped me. He pointed out some irregularities of the notes then clicked on a damn metronome. Afterward, he quantized and tweaked all of my notes so they were properly sandwiched between the corresponding lines and perfectly lined up. He made it mathematically perfect. And to me, it lost something in the process.
What's my point?
When something is too mathematically perfect, the rigidity seeps into our brains and reads as artificial, stiff, mechanic, or robotic. A musician can instinctually draw out some notes and quicken others to make up the difference and keep true to the time. However, to a computer program, this reads as incorrect.
The proof is in the comments and emotional responses, though. That's why film productions spring for a full orchestra instead of a single artist at a computer keyboard. These "imperfections" are human, and this is what creates emotion. I’m happy to say, while the rhythm of that song I worked on with my friend ticks alongside the metronome, the melody pulls it’s emotions from the subtle “flaws” that are me; so it's as if it was played by an orchestra of me's, rather than a computer.
Jake Estes, a documentary filmmaker, is currently working on a controversial and intriguing project. A conversation about guns. Terrorism, hate crimes, and school shootings make this topic a contentious one that has fractured the nation into different groups trying to find answers in different directions.
While American’s love their shoot-em-ups on the big screen -- James Bond, John Wick, Jack Ryan -- Jake Estes discusses guns in their realism. When people’s misunderstandings bleed into a family, it can be detrimental, so Jake set out to demonstrate how a family can come together and have an open-minded dialog about such a polarizing topic. Between his cousin, an NRA member and Jake himself, someone who is not a fan, they discuss the mechanics of different firearms and how to bring responsibility and accountability to gun ownership, as well as gun violence, misconceptions, beliefs, and opinions around this hot-button topic.
When scoring this documentary, I wanted to capture sentiments and avoid the politics. So I oscillated between creating ambiance and building up emotions to support the severity of the topics. Jake and his cousin pit the 2nd amendment against some complex social issues. In a scene where his cousin plays with his children, the interview overlays his sentiments about gun violence at schools. I wanted to do his cousin justice and show an NRA member/ a responsible gun owner can still grieve with the victims of gun violence. The two are not mutually exclusive.
Creating emotion in music is something I love to do with my stream-of-consciousness style of playing and Jake allowed free reign. So I layered in a simple two-track melody that would make a metronome blush, but Jake only felt the emotion. Here's a sneak peek:
Since the beginning, we have always tried to capture our passions and distill them into art and music. Music naturally blends math, physics, and art all together into something that has the power to evoke powerful emotions from almost everyone. With the advancements of technology, artists now have access to tools that can make songs mathematically 'perfect.' However, something is being lost in the structure.
Proof that audiences can feel the difference? Full orchestras are still being hired for film scores, string quartets are still being hauled in for weddings, people still go to concerts and watch bands in sticky bars. Because of the ambiance? Sure. But there is a quality that can only be achieved by humans' fallibility. Those drags and pulls here and there with notes and time creates expression, emotion and a deeper bond with the music. Humanity in its imperfection is what creates beauty and uniqueness, and music is no exception. Emotions and connections can all be captured in slightly mathematically imperfect flutters. Take that, metronomes.
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