Process: Figura
Background
In November 2021, LIA (@liasomething) sent me a DM on Twitter to ask me if I wanted to create a work for her and her partner’s new platform Endless Ways. Immediately I accepted (who wouldn’t?!) and, over a period of a few months, created Figura.
What’s Figura?
In short, Figura is a collection of compositions, where each iteration is an endless musical canon created using generative techniques and is accompanied with a visual score.
Each composition is played by a quartet of FM synths, the design of which I will describe later in this post.
CONTENTS
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THE MUSIC
- Form
- Canon
- Pitch Material
- The Instruments
VISUALS
- The Score
- Generation
OTHER THOUGHTS
- Listening notes
- Performance notes
CLOSINGThe Music
Form
In music, a large part of the composition process is devoted into thinking about form. There’s a musical form you are probably familiar with: the intro-verse-chorus-verse-chorus-bridge-chorus-outro form which we find in most songs we hear on the radio. The classical music analog to this is the Rondo form.
You may also have heard of symphonies, sonatas, or blues. They’re all forms. Specifically, they’re forms created by structures delineated by harmonic tension. In other words, the harmony defines the form.
So that’s a composition lesson in one. Form arises from the material. There’s a problem with this approach though. Harmonic forms require the creation and resolution of harmonic tension. It implies that there is a start and a beginning to it. For me, this was not suited to the open-ended generative format I was thinking about.
So I chose to use the canon.
Canon
A canon is a polyphonic (played by multiple musicians) musical composition or technique, where each voice has the same musical material, but plays it at a different time.
A super famous example of this is Johann Pachelbel’s Canon in D. First, the celli and basses play the bass line. Then, after a full cycle, the first violins play the main melody. In the next cycle, the first violins play a different melody, but the second violins enter and play the main melody. It’s nice because everything fits together like clock work.
If you’re from a German speaking background, you may know the folk songs ‘Viel Glück und viel Segen’, ‘Erwacht, ihr kleine Schläfer’ or ‘Über den Bergen am Horizont’. These songs are all canons, where one sings a few measures after the other. It’s like an IRL analog delay effect.
The cool thing about canons is that they can theoretically be performed by an infinite number of players for an infinite amount of time. Now this was a form that was well suited to what I had in mind.
Although the canon is a pretty old form, more contemporary composers are nevertheless still fascinated by it. They use a type of canon called a prolation canon, where each voice, instead of having the same tempo, plays the melody in a different tempo.
György Ligeti (whose music Stanley Kubrick used without permission) made prominent use of this technique to create densely woven textures that were ever varying. In his piano work Automne à Varsovie, the main chromatic wailing theme is deployed in various tempi across textures. Hans Abrahamsen, in his work Schnee, made it entirely about prolation canons, creating eerie ASMR-like and scintillating textures that bounced between space.
Similarly in Figura, each voice had a different tempo and entered sequentially, one after the other, sometimes earlier, other times later. This meant that as the synths performed the piece, every time a voice repeats the melody, it has a different relation to the other voices. Various harmonies arise from the ever varying cycles in a truly generative sense, like the way a wind chime rings in a gale.
Pitch Material
After deciding on the form, I needed a way to come up with the melody. I contemplated many techniques. For example, twelve-tone technique, where each pitch appears once before it is repeated again, was a really good candidate, since it lent itself well to the canon form. Still, the end result would sound austere and, to my ears, really impersonal.
Another technique I wanted to use came from pitch set theory. I planned to create a pool of random pitches for each composition. Then, from the pool, I would randomly string together the pitches to create a melody. I abandoned this idea soon after trying it, as it sounded no different than when I had just used twelve-tone technique.
In the end, I settled for a hybrid. This was what I did: I first selected two intervals for each composition. It could be a minor 2nd and a perfect 4th. Basically, any combination of two intervals. I added a further constraint to make sure that the same interval type (2nds, 3rds, 4ths) would not appear twice. In other words, a major AND a minor 2nd could not appear together. This was to lessen the chromatic character of the melody.
Once the interval pair was created, I created a pitch row — a technique borrowed from twelve-tone technique. From the base pitch, I randomly selected an interval from the pair I created and added it to the base pitch. The new resulting pitch became the second note of the row. I repeated this process to the new note to create a unique pitch row for each iteration.
This has the advantage of creating ‘moods’. For example, a pitch row that had only 4ths and 5ths would create a composition that sounded like an orchestra tuning (as string instruments usually tuned to 5ths). A pitch row with a major 3rd and a perfect 5th would create a major mood. These characters became a parameter of the generative system.
Finally, from this row, I randomly selected pitches to create the melody, making sure that a pitch isn’t repeated directly after it is selected.
With form selected and melodies prepared, the composition now needed its performers.
The instruments
As mentioned earlier on in this post, the performers are a quartet of FM synths. I chose to use 4 voices as an homage to the 4-part counterpoint so frequently used in the baroque and classical era.
Each voice is an FM synth with four oscillators, This is partly inspired by the Yamaha DX7, which had 6 sine wave oscillators and 32 preset algorithms. Unlike the DX7, the Figura voice’s algorithms were generatively patched. Since WebAudio prevents feedback between the oscillators, there could only be 6 unique algorithms for the 4 oscillators. Also unlike the DX7, I used not only sine waves, but also triangle, sawtooth and square waves.
The patching matrix can be seen in the live view of Figura by pressing F12 to bring up the developer console.
OSCILLATOR MATRIX
_________________
| 0 | 1 | 2 | 3 |
0 |—M—|—A—|—I—|—N—|——→ OUT
1 | ▲ | | | |
2 | ▲ | ▲ | | |
3 | ▲ | | ▲ | |a sample oscillator matrix table
In addition to the 6 algorithms, the modulation amount and ratio for each modulating operator is different for each composition, except for the output operator.
Since there already were a lot of variation in timbre, I decided to restrict the articulation (envelope) to only using sharp attacks and long decays, like the way a wind chime or a piano would work. This made sure that, even in the densest compositions, the texture would still be transparent enough to listen to and understand.
This pretty much makes up for much of Figura’s musical side. With the musical composition in check, I now needed a way to visually represent the music.
Visuals
The score
In western tradition, music is notated with the 5-line system. With the rise of aleatoric compositions in the post-war period, visual systems were being experimented with to represent music.
George Crumb rearranged the staves to create playable graphic collages. Morton Feldman’s Projections and Notations used graphs and charts to roughly indicate pitch, timbre and rhythm. Iannis Xenakis’s Psappha uses a chart similar to a punch card or a midi-roll.
Still others removed their scores further from the music. Earle Browne’s FO-LIO consists of vertical and horizontal etches. Cornelius Cardew’s Treatises lines draw the eyes to follow a visual narrative, carving out imaginary music in the mind. Stockhausen’s Studie II is a complete parametric map of the electronics programmed to create the piece. Roman Haubenstock-Ramati’s scores were like colorful mobiles reminiscent of Kandinsky.
Each style and each score embodied a visual grammar that coerces the mind to think that there is musical meaning.
Contemplating this, I wanted a precise style that resembled modern notation and was clean and legible. I also wanted to create something the sat on a single page as a whole on its own, like a painting.
Generation
In truth, the process of creating the score isn’t the most interesting. First, the selected pitches are visualized on the page like a midi-roll. This formed the skeleton of the score.
I then added embellishments around the notes. There are several parameters to each ‘note’.
- Each note can have a lined-rule through it
- Each lined-rule can be decorated, with a different styles of decoration
- Lined-rules can be decorated with triangle flags, rectangle flags or cascading rectangle flags
- Each note can be decorated with clusters of vertical lines
After decorating the notes, they are ‘beamed’. Beams can be
- straight, directly connecting two notes with a single line
- single-armed, connecting two notes with two lines
- double-armed, connecting two notes with three lines
The score is also fitted with a ‘staff’, which is a single horizontal line around the middle of the page. This staff represents a timeline and is also fitted with ‘repeat’ marks, similar to classical notation, indicating that these pitches are played as a loop.
There are two possible kinds of decorative elements around the score as well.
- A flock of circles
- a cascade of lines that symbolize quantized soundwaves
That’s pretty much it as far as the score is concerned.
Other thoughts
Listening notes
On first listening, it maybe jarring to hear disjointed melodies clashing together. Here are some tips to make it a more stimulating, if not enjoyable, process.
- Try to identify the base melody and see how it relates to the score
- Try to listen to how the four voices relate to each other, as the cycle through the melody
- Take a while to enjoy how the resulting clashes between the voices differ from the actual base melody
- If you are musically inclined, try to transcribe the melody
Performance notes
While there are already digital instruments specifically designed to perform these scores, there isn’t a way to faithfully reproduce the music from the score, since the music was created before the score. The score ends up being an abstract symbol of the music.
Still, I can imagine four musicians sitting in front of the score and interpreting it together, following the constraints of the canon form. That would be fun, if not interesting, to do!
Closing
I hope you enjoyed reading this article about the process of creating Figura. Feel free to write me on Twitter to discuss or talk about it. I also want to thank Lia and Damian for creating the Endless Ways platform and inviting me to be part of the first exhibition!
