The connections between music, musical scales, and fractals can be illustrated through the concept of self-similarity

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The connections between music, musical scales, and fractals can be illustrated through the concept of self-similarity. 

Fractals in Music

Definition: Fractals are patterns that repeat at different scales. In music, this can manifest as smaller melodic or rhythmic phrases combining to form larger structures.

- Example: Bach's Cello Suite No. 3 exemplifies fractal music, where short motifs repeat and expand into longer phrases, akin to a Cantor set structure[1].

Musical Scales and Fractals

- Scale Invariance: Musical elements like pitch intervals and rhythm often follow power-law distributions, revealing fractal characteristics. This means patterns in music can resemble themselves at various levels of complexity[3].

- Computer Algorithms: Tools can generate melodies based on fractal algorithms, allowing exploration of different musical scales and their relationships to fractal patterns[2].

In summary, the interplay of fractals and music enriches our understanding of musical composition and perception, revealing deeper connections to natural patterns.

Citations:

[1] https://www.gracenotes-music.org/post/fractal-music

[2] https://asmir.info/lib/Fractals_Chaos_Music.htm

[3] https://www.ethanhein.com/wp/2014/fractal-music/

[4] https://www.reddit.com/r/WeAreTheMusicMakers/comments/f94ws/musical_fractals/

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