AlgoMotion | Toothpick Sequence with Circle of Fifths Harmony #math #fractal #visualization #music @AlgoMotion | Uploaded March 2024 | Updated October 2024, 1 hour ago.
Visualizing the Toothpick Sequence to 16 steps, with musical harmony based on the circle of fifths.
Longer version (256 steps): youtu.be/_7oxzD9SFKo
In the The On-Line Encyclopedia of Integer Sequences (OEIS), the Toothpick Sequence is sequence number A139250: oeis.org/A139250
To generate the toothpick sequence, at each step add a toothpick to the end of every "exposed" toothpick. Two toothpicks may never overlap, and the midpoint of each new toothpick must touch the endpoint of exactly one existing toothpick. An endpoint is "exposed" if it does not touch any other toothpick.
At steps of the form 2^k (powers of 2), the number of new toothpicks at those steps are equal to 2^k, and they are always placed along two lines perpendicular to the initial toothpick.
Chord Selection:
=============
The chords move through the circle of fifths until a "power of 2" step is reached. Each chord is selected so that every time we arrive at a "power of 2" step, the chord is a C.
The exact quality of each chord was manually selected for each pitch class (i.e. for all 12 notes). The number of notes in each chord and the MIDI velocity of each note are functions of how many new toothpicks are placed at a given step.
The code for creating this video was written in Java using the Processing graphical library (processing.org/).
#math #art #music #toothpick #sequence #circleoffifths #musictheory #algorithmicmusic #visualization #mathematics #cellularautomata #algorithm #java #code #computerscience #fractal #hypnotic #mesmerizing #calming #calmingmusic #audiovisual #studymusic #focusmusic
Visualizing the Toothpick Sequence to 16 steps, with musical harmony based on the circle of fifths.
Longer version (256 steps): youtu.be/_7oxzD9SFKo
In the The On-Line Encyclopedia of Integer Sequences (OEIS), the Toothpick Sequence is sequence number A139250: oeis.org/A139250
To generate the toothpick sequence, at each step add a toothpick to the end of every "exposed" toothpick. Two toothpicks may never overlap, and the midpoint of each new toothpick must touch the endpoint of exactly one existing toothpick. An endpoint is "exposed" if it does not touch any other toothpick.
At steps of the form 2^k (powers of 2), the number of new toothpicks at those steps are equal to 2^k, and they are always placed along two lines perpendicular to the initial toothpick.
Chord Selection:
=============
The chords move through the circle of fifths until a "power of 2" step is reached. Each chord is selected so that every time we arrive at a "power of 2" step, the chord is a C.
The exact quality of each chord was manually selected for each pitch class (i.e. for all 12 notes). The number of notes in each chord and the MIDI velocity of each note are functions of how many new toothpicks are placed at a given step.
The code for creating this video was written in Java using the Processing graphical library (processing.org/).
#math #art #music #toothpick #sequence #circleoffifths #musictheory #algorithmicmusic #visualization #mathematics #cellularautomata #algorithm #java #code #computerscience #fractal #hypnotic #mesmerizing #calming #calmingmusic #audiovisual #studymusic #focusmusic
