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A Closer Look: "Cycloplex"

2019 April 98 min read

"Cycloplex" is a made-up word that, from its roots, could be literally taken to mean "a structure comprised of circular or rotating parts". It's also the name of my latest - and perhaps greatest - electronic track, and one that I think deserves a closer look. It's unique, it's different, and its use of many simple, repeating elements combining in complex ways puts me in mind of some sort of vast industrial machine with lots of gears, wheels, and spinners, all interacting in a delicate balance.

It's been far too long since I've published any music, and there are a few reasons for this. Number one is my continued enrolment in the composition course I mentioned in my blog post about Insomnia. My musical energy - what little I have left of it - has been focused there, and a lot of the work we've been doing is with styles and constraints that I have no experience in, so the music that has come out of it has been far below my usual standards. Another reason is Earth Strike, where I've been working pretty much full-time for over three months, part of which has involved producing music for promotional videos.

But on the morning of March 21, as so often happens out of nowhere, inspiration struck me on the little 61-key digital piano beside my desk, in the form of what would become the first 10 seconds of Cycloplex. Its cheerful, yet chaotic and unresolved nature is definitely a product of its time; my life has generally been like that for the past several months, and this piece reflects it. So let's get into it.

Key Signatures

The track is entirely in the Mixolydian flat-6 mode, and is my only piece of music that does not use any unaltered diatonic modes. (Even Finale from Episodes is only partially Mix-b6.) The tonal journey is achieved through a grand total of 11 key changes, covering 9 distinct tonics:


Most of these modulations are a minor-third down - this will be discussed further. The notable exceptions are in the middle part, which provides development through use of a 1-4-5 progression (G#C#D#), and the end, where the opening key returns after a 5-1 progression (F#B).

Coincidentally, shortly after writing this track I was introduced by a friend of mine to something called "axis theory", which is basically the idea of treating pitches that are a minor third apart as performing identical chord functions - either tonic, dominant, or predominant. Under this system, taking Cycloplex to be in the key of B, then:

  • the tonics are B, G#, F, D;
  • the pre-dominants are E, C#, A#, G;
  • the dominants are F#, D#, C, A.

and thus the sequence of key signatures in the track can be rewritten as:

key B G# F D B G# C# D# C A F# B
chord function T T T T T T P D D D D T

meaning, essentially, that the whole track is one big 1-4-5-1 progression. There is one instrument, however, that never changes keys, and in fact never changes what it's doing through the entire song. This is the bells, which play four C#s every 12 bars, starting at 0:15, and persisting until the very end. These C#s - both the pitches and their positions in each bar - are very carefully chosen so as never to clash with any of the notes that are played in the other instruments simultaneously, no matter what key the rest of the song is in. The constantly-changing key means that these bells perform different harmonic roles each time they occur - particularly notable is at 1:41, when during the most relaxed part of the song, the bells are actually playing the tonic (C#) to emphasize this resolution. It's one of the many subtle things that are easy to miss unless you're looking out for it.

Structure & Thematic Material

The track can be thought of as divided into three sections:

The opening is comprised almost entirely of looping elements, with a variety of fixed periods. These elements can be rhythmic, melodic, structural, etc., and they include (among others):

Element Period
the rhythm in the percussion 1/2 bars
the 8-note sequence of pitches in the ostinato 2/3 bars
the 12-note rhythm in the ostinato 1 bar
the arpeggios (initially in the piano) 1 bar
the 3-note sequence of pitches in the accompaniment 3/2 bars
the melodic line (rhythm & pitches) in the ostinato 2 bars
the melodic line in the accompaniment 3 bars
the strums in the acoustic guitar 4 bars

A lot of interest comes from how these periods clash with each other. We hear for example how the ostinato (with period 2 bars) and the accompaniment (with period 3 bars) produce different intervals depending on their relative phase. The same happens with the arpeggios. The notes here were chosen with great care so that the intervals between voices never clash, no matter what phase they're in.

I find that the time signature of the track often feels ambiguous, and what might look on paper to be an annoyingly pervasive and repetitive 1-bar rhythm is quickly disguised amongst the other rhythms, and hardly seems to repeat at all.

After the first four bars, the entire opening section is neatly divided into 6-bar phrases, each in a key that is a minor third lower than the previous. Most of the above looping elements have a period that divides evenly into 6 bars, so these phases are comparable in their overall structure. We're introduced to more repeating elements whose periods are 12 bars, including the percussive fills, the 4-note bell toll sequence, and even the arpeggios on a larger scale - they occur every 12 bars for 4 bars at a time.

To me, the minor-third modulations produce a strange effect, where it seems like each modulation is building tension, but the tension doesn't add up over the whole section, which nevertheless seems resolved throughout. It reminds me of the Shepard Tone illusion, and I think it can be partially explained by the fact that, under axis theory, this entire section is in the tonic and the modulations from tonic to tonic don't add any tension at all.

After the climax of the opening section - the first return to the initial key of B - there's a more relaxing interlude where new thematic material is introduced. The ostinato transforms into a more lyrical melodic line, the accompaniment calms down, and the percussion stops. As this section progresses, the key changes take on a different nature too; as above, instead of consistently modulating down minor thirds, they move in a more conventional pattern.

However, the one thing that remains constant throughout this section and the entire track in general is the rhythms. Each bar has the exact same rhythm in the sixteenth notes - the rhythm that occurs isolated in the first bar - and the pattern of the accompanying dotter quarter notes and dotted half notes remains pretty steady as well.

Notable in this section, as well as the next, is that the sixteenth-note rhythm is traded between instruments and disguised as such in subtle ways. At 1:23, for example, the first part of this rhythm is given to the soft high notes in the electric piano. This is done again many times afterwards, notably at 2:06 and 2:16 where it's in the left hand of the acoustic piano. This, combined with the much more prominent "alternate" time signature makes the middle section sound like it's in triple meter, heightening the ambiguity of the rhythm described above. This development section also retains the 6-bar phrase length of the opening.

In the buildup to the final climax, there are four notable things that serve to heighten the tension:

1. the opening pattern of repeated minor-third modulations comes back, although the keys that it passes through are all dominants, rather than tonics, so as to anticipate the ending;
2. we break from the established 6-bar phrase length with shorter phrases of 4 bars each, quickening the pace of the development;
3. the melodic material of the opening and the middle sections are mixed together, traded back and forth between instruments in quick succession; and
4. the melodic lines are gradually built up from single notes to parallel thirds, then triads, then larger and more varied chords, and finally the dramatic and virtuosic flute line that spans multiple octaves.

All this serves to make the sudden, dramatic release of tension at the very end that much more satisfying. An added bonus is that I wrote the ending to seamlessly transition back to the beginning, so a perfect loop edit could be made of this track simply by removing the volume automation that makes it fade out to silence at the end. I'll do that upon request. :)

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