Music based on the Fibonacci word, golden ratio time signature

This is a song based on the Fibonacci word 010010100100101001..., and can be thought of as being in the golden mean time signature.

Some math:

The Fibonacci word is a sort of noncommutative version of the usual number-theoretic Fibonacci sequence, in the sense that we start with 1 and 0 and then recursively put them together based on the Fibonacci recurrence, but instead of adding them as numbers, we concatenate them as words: 1, 0, 01, 010, 01001, 01001010... More precisely the Fibonacci word is the infinite word obtained as the limit of this procedure.

There are many other ways to construct this infinite word, and in the video I instead visualize its construction as a mechanical word, meaning I take a particle traveling on a square with the left and right side glued together, and the top and bottom glued together (this is called a torus/donut), and I give the particle velocity (φ, 1) where φ is the golden ratio. I write a bit when the particle crosses the torus horizontally, and whether I write is 0 or 1 is determined by whether it crosses the top edge before it the next horizontal crossing. This generates the same infinite word as the previous procedure.

To explain the title and the picture, this song is, arguably, in time signature φ/4, in the sense that for integer n/4, one obtains the standard count 1, 2, ..., n used in music from a similar coding strategy (at least up to dynamical isomorphism) of a toral flow, when the velocity is (n, 1), and here it is (φ, 1). There are also other ways to interpret a time signature of φ/4, and the present one is not necessarily the most obvious one. But in my corner of mathematics and music, it is the most natural one.

Some notes on the music:

I have been playing the sequence as a monotonic guitar string skipping exercise for probably a decade. It is quite meditative. I have composed many things on top, but this is my first "finished" product out of this. As a song intentionally doesn't feel very complete. I suppose this is meant to reflect the fact that the word is infinite and never (strictly) repeats. I like to keep open the possibility of extending it infinitely.

The keyboard solo is somewhat liberal with the time signature, so quite hard to play while actually following and feeling the background beat.

The bass solo in turn is basically improvised (in many takes). It uses long notes, and illustrates some rhythmic phenomena e.g. there's two slow arpeggios that can be interpreted to have a 54444 type "feel" i.e. five notes in sequence and the first is 25% longer. Since 5+4+4+4+4 = 21 is a Fibonacci number, such rhythms align with the background beat.

Tracking, video, technology, etc.:

My guitar, bass and synth tracked with line in into M-Audio FastTrack. Many synth tracks also played from midi score by Surge. Drums are midi score fed into MT-PowerDrumKit. I used Reaper for the tracking and for putting the video together. For recording video I used my cellphone. The background visualization is made in Python together with PIL (for writing frame data), Sympy (I use actual golden ratio rotation without cheating) and moviepy (for generating mpg), and I used pygame for testing. The silly quake effect is done with a Reaper script in Lua. Anthropic's Claude was a lot of help in learning how the Reaper API and PIL&moviepy work.

Everything is "mimed", in the sense that video is filmed after tracking, except the synth solo I actually tracked while filming, so I made it audible (but surge plays the same on top anyway).

Further math note to experts:

Readers/listeners with sufficient musical and combinatorics-on-wordsial background may be interested in knowing that I'm really thinking of the sequence as morphic word, where first I take the limit point of the substitution
0 to 01011
1 to 01011011
and to the limit point I apply finally
0 to 01001
1 to 01001001
This turns out to produce the same sequence, you can check it in Walnut as an exercise. I tend to feel the Fibonacci word this way naturally.