*Time Tree Sketches*(2016–), work-in-progress

Thirteen Algorithmic Trees / for Sound Installation

Image credit: Thomas Chaplin

In 2016, I wrote

“ In my piece I have rendered the image of this primordial tree as the overtone series: not as a simple ascending integer series, but rather as a 2nd dimensional tree-type data structure: each of its inner nodes has its own overtone sub-branches.

This structural foundation of musical materials led me to try to portray trees “graphically” as well. To render the infinite variations of tree forms and physiognomies, I adopted Barnsley’s Fern model, which uses a transformation matrix with probability variables, in a mathematical formula of self-similarity: Iterated Function System (IFS.)”

The spatial geographical data generated by Barnsley’s algorithm is mapped onto the frequency domain, and sonified by reinterpreting the process of iteration as sonic events happening at different time-points. Through the sonification process, I generated more than a hundred versions of Barnsley’s ferns, and chose several outputs and refined, revised, and notated them on the paper.

For

Here I upload three data sonification results that I generated for

Tree 57

init dur = 30 / max frequency = 4246.89 / dist factor = 1 / fund frequency = 28.5851 / max depth = 10 / each repeat = 3 / left leaf ratio = 1.3333333333333 / right leaf ratio = 1.1666666666667 / each repeat decrement = -0.25 / duration decrement = 0

Frequencies (first three lines): 28.59 57.17 57.17 85.76 171.51 85.76 114.34 38.11 171.51 343.02 343.02 686.04 128.63 686.04 514.53 1372.08 1372.08 257.27 114.34 47.64 514.53 686.04 192.95 1029.06 214.39 2058.13 1372.08 257.27 686.04 1029.06 1543.6 1372.08 2058.13 257.27 1029.06 289.42 428.78 2058.13 428.78 2744.17 3087.19 343.02 228.68 95.28 385.9 2058.13 1543.6 343.02 2058.13 1286.33 1372.08 2058.13 257.27 4116.25 321.58

Tree 64

init dur = 30 / max frequency = 4246.89 / dist factor = 1 / fund frequency = 65.4064 / max depth = 10 / each repeat = 3 / left leaf ratio = 1.2083333333333 / right leaf ratio = 1.4375 / each repeat decrement = -0.3 / duration decrement = 0.1

Frequencies (first three lines): 65.41 130.81 130.81 261.63 94.02 261.63 392.44 196.22 261.63 523.25 523.25 188.04 1046.5 196.22 1046.5 523.25 1308.13 523.25 2093 392.44 784.88 1569.75 392.44 188.04 117.53 1635.16 2616.26 392.44 1046.5 1569.75 1046.5 1046.5 3270.32 245.27 2093 327.03 3924.38 282.07 588.66 2093 3139.51 261.63

Tree 95

init dur = 30 / max frequency = 4246.89 / dist factor = 1.1818181818182 / fund frequency = 32.7032 / max depth = 12 / each repeat = 3 / left leaf ratio = 1.5454545454545 / right leaf ratio = 1.2222222222222 / each repeat decrement = -0.3 / duration decrement = 0.2

Frequencies (first three lines): 61.66 139.87 139.87 317.32 317.32 103.13 512.39 225.86 317.32 413.07 719.88 182.08 937.11 937.11 233.97 413.07 719.88 2125.94 2125.94 182.08 1162.43 667.01 413.07 3432.88 413.07 4822.96 937.11 1513.2 937.11 1077.06 233.97 1513.2 5543.28 667.01 233.97 937.11 413.07 3432.88 2125.94 937.11

In 2016, I wrote

*Goethe’s Garden*for two pianos tuned a quarter-tone apart, by using a recursive fractal algorithm:“ In my piece I have rendered the image of this primordial tree as the overtone series: not as a simple ascending integer series, but rather as a 2nd dimensional tree-type data structure: each of its inner nodes has its own overtone sub-branches.

This structural foundation of musical materials led me to try to portray trees “graphically” as well. To render the infinite variations of tree forms and physiognomies, I adopted Barnsley’s Fern model, which uses a transformation matrix with probability variables, in a mathematical formula of self-similarity: Iterated Function System (IFS.)”

The spatial geographical data generated by Barnsley’s algorithm is mapped onto the frequency domain, and sonified by reinterpreting the process of iteration as sonic events happening at different time-points. Through the sonification process, I generated more than a hundred versions of Barnsley’s ferns, and chose several outputs and refined, revised, and notated them on the paper.

For

*Time Tree Sketches*, I will use the other tree data that was not used in*Goethe’s Garden*, and will develop the recursive algorithm in harmonic and rhythmic directions on a deeper level to transform the shapes and colors of trees more dramatically and ecologically. The computer will infinitely create ever-changing sonified images of different trees (as Goethe dreamed), now without the limit of tunings, instruments, and time.Here I upload three data sonification results that I generated for

*Goethe’s Garden*.Tree 57

init dur = 30 / max frequency = 4246.89 / dist factor = 1 / fund frequency = 28.5851 / max depth = 10 / each repeat = 3 / left leaf ratio = 1.3333333333333 / right leaf ratio = 1.1666666666667 / each repeat decrement = -0.25 / duration decrement = 0

Frequencies (first three lines): 28.59 57.17 57.17 85.76 171.51 85.76 114.34 38.11 171.51 343.02 343.02 686.04 128.63 686.04 514.53 1372.08 1372.08 257.27 114.34 47.64 514.53 686.04 192.95 1029.06 214.39 2058.13 1372.08 257.27 686.04 1029.06 1543.6 1372.08 2058.13 257.27 1029.06 289.42 428.78 2058.13 428.78 2744.17 3087.19 343.02 228.68 95.28 385.9 2058.13 1543.6 343.02 2058.13 1286.33 1372.08 2058.13 257.27 4116.25 321.58

Tree 64

init dur = 30 / max frequency = 4246.89 / dist factor = 1 / fund frequency = 65.4064 / max depth = 10 / each repeat = 3 / left leaf ratio = 1.2083333333333 / right leaf ratio = 1.4375 / each repeat decrement = -0.3 / duration decrement = 0.1

Frequencies (first three lines): 65.41 130.81 130.81 261.63 94.02 261.63 392.44 196.22 261.63 523.25 523.25 188.04 1046.5 196.22 1046.5 523.25 1308.13 523.25 2093 392.44 784.88 1569.75 392.44 188.04 117.53 1635.16 2616.26 392.44 1046.5 1569.75 1046.5 1046.5 3270.32 245.27 2093 327.03 3924.38 282.07 588.66 2093 3139.51 261.63

Tree 95

init dur = 30 / max frequency = 4246.89 / dist factor = 1.1818181818182 / fund frequency = 32.7032 / max depth = 12 / each repeat = 3 / left leaf ratio = 1.5454545454545 / right leaf ratio = 1.2222222222222 / each repeat decrement = -0.3 / duration decrement = 0.2

Frequencies (first three lines): 61.66 139.87 139.87 317.32 317.32 103.13 512.39 225.86 317.32 413.07 719.88 182.08 937.11 937.11 233.97 413.07 719.88 2125.94 2125.94 182.08 1162.43 667.01 413.07 3432.88 413.07 4822.96 937.11 1513.2 937.11 1077.06 233.97 1513.2 5543.28 667.01 233.97 937.11 413.07 3432.88 2125.94 937.11