September Collective Collaborative Blog: Mathematics in Music

In contrast to last month's minimalism collaborative blog, this month the collective took a technical turn. From indie prog rock to Eastern European folk music, this month's collab playlist features some of the most complex and mathematical equations in music.

​Noé's Pick

Song: “Sweet Silence”
Artist: Gorguts
Album: Obscura

Obscura was one of the most important albums for the progression of death metal thanks to its display of mind boggling song structures, riffs that defy songwriting conventions, and oddly coherent flow. Every song here could be analyzed to no end, but I think “Sweet Silence” deserves the mention as it is the finale to this journey. The song goes through a grotesque display of odd time signatures and musical passages that provide discomfort. However, the most interesting and mathematical moment is the outro. Gorguts strum a droughty guitar chord, isolated in complete darkness. Each time, the chord takes longer and longer to appear. I stopwatched the occurrence of each guitar strum and roughly got the time in seconds each takes to appear, being zero the first strum that starts the series. We shall call this the total time sequence:

0 - 2 - 2 - 3 - 4 - 5 - 7 - 8 - 12 - 20

We can get another sequence from this one, by calculating the difference in waiting time between each strum (e.g from 0 to 2 there is a difference of 2). This yields the following sequence, which we shall name the absolute time change sequence:

2 - 0 - 1 - 1 - 1 - 2 - 1 - 4 - 8

Gorguts play with expectations of orderly mathematical series and shatters them to provide a truly disorienting and nerve-wracking experience.To provide a clearer explanation of this wizardry, Iet’s label specific parts of the absolute time change sequence:

[2 - 0]  [1 - 1 - 1]  [2 - 1]  [4 - 8]
 A            B             C          D


Part A provides roughly the same wait time between strums (starting with two seconds and maintaining it) to provide a brief sense of familiarity and hope of being able to predict what is coming next. Part B then descends in a pattern of increased individual seconds; another one that can be easily put together mathematically. Part C breaks all comprehension by increasing the waiting time, and then returning to the usual rate of one.  Needless to say, this is utterly disorienting and shatters all confidence in trying to decrypt the numerical mystery.

Part D finishes by increasing the wait times in powers of two. These are unusually long periods of time compared to what came before, resulting in the most anxiety-inducing way possible to end the record. Given that Obscura is centered around the topic of darkness and discomfort, this is a perfect way to wrap things up. The frankenstein monster version of math presented by the band serves to unnerve and keep in tune with the insane experimentation of the album. But more importantly, it gracefully deposits us in the pitch black abyss, inviting us to embrace it. Here, only “Sweet Silence” remains.
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Noggle's Pick

Song: “Azaberi”
Artist: Seyid Shushinski, Bahram Mansurov, Vaqo Melkumov
Album: I don’t know, some Soviet TV broadcast from 1963?

Let’s take a trip around the world. How about stepping back in time - when goyls were goyls, and math was music? Or is it that music was math? The details don’t matter. Our expedition’s taking us to ancient times. There, the truth makes for exquisite excuses (especially when records are spotty) and ambiguity is as good as fact. All I can say for certain is that Pythagoras - you know, of triangular fame - decided to take a walk. The philosopher crossed some village, maybe Egyptian, but, crucially, home to a blacksmith with such a work ethic that it made for a chance encounter destined to benefit, oh, you know, all of humanity. As the story goes, Pythagoras heard the metallic clanks and became fascinated; so much so that he went on to discover - as if the joyless dross of life were beaten out of him, right there on the anvil, in front of some very confused townsfolk - the concept of music itself.*

“This is all great,” you must be thinking, “but how does it relate to the blog?” You see, like my story, evolution is messy. How neat would would it be if concept arrived in Europe, where scales are such a success that all music is written in this manner forever? Ah, but if the dawn of man can’t be summed up with a single-file line out of some lagoon, then music - humanity’s own creation - must have its own forks to account for. And herein lies Pythagoras’s brilliance: with, a simplified air, the idea could travel to Eastern Europe, specifically modern day Azerbaijan, where melodies belonging to a lineage of bards had been established as an aural expression.

The hybridizing of Ashiq, storytelling tradition, with Western music is mugham: a secular performance reserved for marriages and exclusive audiences, but also known to have roots in mysticism. The music is modal. Mughams are played in distinct movements by a trio, the khenende - one that can expand into an ensemble, or sozende - which consists of a tar (lute variant), kamancha (fiddle) and daf (tambourine), held by the singer, and all ultimately brought together by an adhesive idea. Did I mention improvised 32-bar phrases?

INT. STUDIO, BREAKFAST BAR – NIGHT

Noggle is hunched on a highchair. A dim lamp splashes light on the wall to his left. Staring at the monitor, his fingers stop moving.  From the open closet door to the right comes a sound.

                DISEMBODIED VOICE

        But is it fyyyyyeeeeee?

Thank you not at all self-indulgent use of screenwriting, you ask an excellent question. Look, I don’t expect Seyid Shusinsky to crack the Billboard Hot 100 anytime soon. If, before expiring, I come across a single person that knows of Bahram Mansurov, it would be one more than can be reasonably expected. Regardless, mugham is considered part of our shared heritage by UNESCO. I could keep going. Believe me, there’s plenty more to share; maybe something not unlike how there’s seven tones, also mugham, that correspond (as Pythagoras intended?) to seven celestial bodies visible to the naked eye. But thanks to modern technology, we can appreciate an integral part of the Azerbaijani national identity while claiming to be attuned with a musical narrative tracing back to the origin of artistic sound - not to mention, math.

*”Discover” is a strong word. Math is ultimately about logic; a closed world where proofs are valid or invalid. So much like how music wasn’t awaiting a bearded Greek to give it form, Pythagoras wasn’t interested in subjectivity (beauty’s debatable). There were no bangers to be had that B.C.E. summer, nope. But the facial-haired Mediterranean did create the musical scale, or Pythagorean tuning: that premise of moving along lines, vertically, by way octaves or Perfect Fifths, and exactly where I give up on trying to understand at *squints* 2:02 a.m.
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Parisa's Picks

Song: “Lateralus”
Artist: Tool
Album: Lateralus
While this is probably the more obvious choice for a mathematical song, “Lateralus” still stands as one the most thought-out and incredibly technical songs of all time. This song, both lyrically in the syllabic meters and instrumentally with its chord progressions and time signatures, reflects patterns of the Fibonacci sequence. Instead of trying to hash it all out here, I recommend checking out this video that breaks it all down and carefully shows just how intricate the mathematical themes of this song are. What I love most about “Lateralus”is that it’s actually so accessible and easy to listen to despite being so complex. I mean sure, it’s super show off-y. Danny Carey plays drums in 9/8, 8/8, and 7/8 time signatures just in the chorus alone.  But it’s still manages to be a song that you can easily get into, whether you wanna get real heady or just jam out.
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Song: “For Ash”
Artist: Marnie Stern
Album: Marnie Stern
What I love about Marnie Stern’s songwriting is how she’s able to use very complex, mathematically-driven riffs in order to evoke relatable emotions of love and heartbreak. In the opening track of her self-titled album, “For Ash”, a song decided to her deceased ex-boyfriend, we hear a combination of both aggressive, hectic riffs and percussion with an endearing melody. She utilizes her technical abilities not just to show off, but to stir up some uncomfortable feelings with erratic instrumentation but keeps you grounded in a nostalgic-type of reflection with poppy refrains and buoyant vocals. While all her skills are obviously indebted to no one but herself (despite what a bunch of douchebag dudes would like to argue against in the YouTube comments), I’d still like to give a nod to the fact that producer and drummer Zach Hill, one of my other favorite contemporary prog musicians from a billion other projects, compliments her stylings so harmoniously. A collaboration truly from the prog rock heavens.
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Alex's Pick

Song: “Bleed”
Artist: Meshuggah
Album: ObZen
I couldn’t let this theme go without mentioning “Bleed.” Tomas Haake’s drums on this song are a performance for the ages. He bridges two different rhythms: first, he keeps his double kick bass pedals in lock step with the guitars and bass on one of Meshuggah’s punishing signature polyrhythmic riffs. On top of this, he keeps a steady 4/4 rhythm with vocalist Jens Kidman. It’s a song that’s so heavy that it feels like it bends gravity. And there’s nothing mathier than a black hole.

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