Fractal Tuning
What is "Fractal Tuning"?
Fractal Tuning is a new math-based, alternative musical tuning system. Musicians use tuning systems when composing and performing their music ... although contemporary musicians are often not aware that their choice of musical instrument can come with built-in limitations on the tuning system they can use.
For most modern music played with standard pianos and guitars, the tuning system employed is more accurately called a Temperament, rather than a tuning ... and is commonly known as Western 12-EDO (12 Equal Divisions of the Octave), which is created from repeating, consecutive 12√2 Intervals. (A musical "Interval" can be thought of as the distance or space between two musical tones.)
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The Western 12-EDO musical temperament has grown over the past 200 years to become the defacto standard for today's contemporary music. Nearly every song, melody and film score you hear these days is using this 12-EDO tuning standard.
​Why "Fractal"?
So, what is it about this new tuning that makes it "Fractal"? To explain, here is a brief excerpt from Park Anderson's upcoming book, "If God Created the Integers, Then Why Did we Stop Using Them for Music?":
Book Excerpt:
Fractal Tuning is "fractal", because of the strong relationship that Integers have with core Fractals such as the Cantor Set and the Koch Snowflake. The Cantor Set is often shown as intervals on a number line, displayed between 0 and 1 … which is very similar to how Fractal Tuning maps on a number line between 1 and 2:
And, the Koch Snowflake is a basic design of an integer-based pattern that is one of the earliest fractals to have been described. Below, from left to right, the first 4 iterations of a Koch Snowflake:
In addition, as Fractal Tuning Pitch patterns are extended, they form a spiral pattern. This is reminiscent of some of the more advanced Fractals, such as the Mandelbrot Set, where the combination of Integers, Irrational Numbers and Imaginary Numbers form complex self-similar patterns that seem to go on infinitely the deeper the zoom goes.
However, with Fractal Tuning, we set limits on the patterns, so the end of one spiral connects to its own beginning, forming a 3D torus shape, instead of an endlessly descending continuous spiral.
How is Fractal Tuning Implemented?
Fractal Tuning can be achieved when musicians implement our spArxx Tonal Palettes™ Tuning Patches, which are generated by our patented SaaS platform, spArxx Genesys™. Our unique spArxx Tonal Palettes™ are perfect for composing, writing and creating new music, because the interwoven patterns of resonant intervals combine to nudge creative minds into fresh neural pathways.
How Does Fractal Tuning Sound?
Fractal Tuning sounds great! Depending upon the tunings and keys selected by the musician, highly resonant harmonies are possible. At the other end of the spectrum, some intervals have a very dissonant quality, which is perfect for adding sonic texture to film scores and sound effects.
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To hear some music created with our spArxx Tonal Palettes™, and for a general overview of Fractal Tuning, click the image below to watch our video:
Interested in further exploring Fractal Tuning?
If you're a professional musician, then free consulations are available. Get in touch so we can start working together!