DeBach

—the Visualization of Bach’s “Well-Tempered Clavichord”
M.F.A. Thesis
RIVES BFK printmaking paper light weight, PVA Sheet, vellum; inkjet print;
Fall 2016–Spring 2017; Chicago, IL



I started to learn both painting and piano performing when I was four, and I love both of them. Since I chose visual art as my career, I always hold the thoughts to use visual arts as a form to visualize music. The M.F.A. Thesis is a perfect timing for me to dive into this area.

Bach’s “Well-Tempered Clavichord”  is famous for being recognized as the “Old Testament” in music. When I was looking through the whole score sheets collection, I found out a very interesting and mysterious phenomenon that there are different patterns repeating within different pieces, which triggered my curiosity of Bach’s secret composing equation. (The image below is Bach’s manuscript of the first Prelude from his “Well-Tempered Clavichord,” whose ascending–descending–ascending pattern is happening all over the piece.)


Based on numerous research and experimentation, I created my own geometric, architectural, mathematical, and logical visual language to translate Bach’s “Well-Tempered Clavichord” into appealing and seductive sculptural forms to offer a better and easier way to understand his music.


SAIC 2017 M.F.A. Show
April 28th–May 16th, 2017
Sullivan Galleries, School of the Art Institute of Chicago












Experimentation & Calculation
The math happening in the simple ones such as an octahedeon nesting in a cube is pretty easy to calculate. But I was stuck at one of the most intricate ones—a dodecahedron nesting in an icosahedron—for quite a long time, almost two months. Eventually, I did “antatomy”  to this interrelationship using a physical and visual way to figure out how it spatially works on one single unit and how units are connected together. Here is the anatomical structure that I was using: 




After figuring out the spatial and mathematic nesting relationship, I utilized what I found onto the layering structure of Bach’s Fugue structure to test it out—An Octahedron in a Hexahedron/Cube in a Dodecahedron in an Icosahedron.




Exploration & Analysing
Base on numerals experimentations and mathematical calculation (mainly Pythagorean Theorem), each one of the transparent sculptures solidifies and visualizes the intertwining, interlocking, layering, and nesting structures of the Preludes and Fugues. 

The two volumes of Bach’s “Well-Tempered Clavichord” is more than just two books containing 24 separate pieces. The tonalities of them are in the exact arrangement of an octave from & C minor all to way to B major & B minor, which is followed by C major again to complete a loop. The one below is the visualization of the looping orchestration.    Stationary Views:



The structural form is an Invertible Cube with two Keys being nested in a dodecahedron. The outside layer—dodecahedron—is the shield to embrace all the pieces as a whole. When it is being opened, the invertible cube can be revealed and the main body of the Invertible Cube can be twisted inward and outward and can go back to the original position repeatedly and continuously, which shares the same pattern as Bach’s “Well-Tempered Clavichord’s” tonalities—starting from the cube position/C major and ends at the same.    Motional Views:


Fugue, Layering & Nesting Structure
An Octahedron in a Hexahedron/Cube in a Dodecahedron in an Icosahedron

Fugues from the “Well-Tempered Clavichord” is of layering and nesting structure. Each piece is composed of “themes” composed of “motifs” composed of “motif in motifs,” which is literally the same as the architectural structure of an edifice—the facades out of interior spaces out of skeletons out of constructional functionalities. Due to this logic, the fugues are considered architectural, sculptural, and mathematical. Therefore, long story short, the mapping of the musical and geometric structure realizes the visualization.
Icosahedron—the Whole Fugue
Dodecahedron—Theme
Hexahedron—Motif
Octahedron—Motif in Motif





Comments from My Thesis Advisor
“Many many wows, Li. It’s fantastic, mesmerizing, intellectual, ‘fancy,’ AND ‘high-end.’ You maintained quality and the thread of inquiry through the entire process, right up until the end—we are all very proud of what you’ve accomplished and that you are representing Visual Communication Department in the show. You are onto something here in a visual language that speaks Bach in a whole new way.”—Stephen Farrell



Special Thanks to

Stephen Farrell
Jacob Ristau
闫 大卫 [Dawei (David) Yan]
Daniel Morgenthaler
Shawn Decker
Myungah Hyon/현 명아
郭 烨 (Ye Guo)
陈 思 (Si Chen)
李 劭恆 (Shau Heng Li)






#music visualization
#paper sculpture
#mathematics
#artist’s book
#self-generated project
© 2018 Li Han.