"Musical innovation is full of danger to the State, for when modes of music change, the fundamental laws of the State always change with them." — Plato, The Republic

"The theory of relativity occurred to be by intuition, and music is the driving force behind this intuition. My parents had me study the violin from the time I was six. My new discovery is the result of musical perception." — Albert Einstein in Shinishi Suzuki's 1969 Nurtured by Love: A New Approach to Education

Musics that are improvised, or invite an improvisational element, can challenge and encourage personal and collective imagination in an array of fascinating ways. The solo improvisor may constantly seek new avenues that can be explored and learned from. A group of improvisors embark together on an adventure involving cooperation, intense listening, considerate response, and collaborative creation.

While there are infinite approaches to improvisation and composition, one angle is to become well-versed in the vast range of scales and intervals available through one’s instrument(s). Toward this end, a multi-sensory practice that includes visualizing, as well as listening to, the patterns inherent in tonal combinations may be useful.

A tertiary color wheel containing twelve colors (three primaries — red, yellow and blue; three secondaries — orange, green, and violet; and their six descendants) can be used to represent relationships in a 12-tone musical system.

Clockwise from top: Red, red-orange, orange, yellow-orange, yellow, yellow-green, green, blue-green, blue, blue-violet, violet, red-violet. Colors directly opposite one another on the color wheel are known as “complements” (red and green, for example).

The musical system exemplified here contains twelve tones, each a half-step apart:

C — C#/Db — D — D#/Eb — E — F — F#/Gb — G — G#/Ab — A — A#/Bb — B

The Tonal Relativity charts illustrate relative pitches (or the space between pitches). One can therefore begin on any pitch (or color) and extrapolate the relationships represented in each set of charts. Playing each interval or mode over a drone of the tonic (the tone the scale or interval begins on) will audibly illustrate the relationships.

While any twelve different colors could be used to make the patterns inherent in the scales visible, the use of twelve hues that form a gradient allows for a more direct correspondence  between the 12-tone chromatic scale and the 12-color tertiary color wheel.

When the Tonal Relativity project began in 2015, we chose squares to indicate whole steps and half-squares (rectangles and triangles) to indicate half-steps (in both color and pitch). The 2020 version has taken on a circular shape that reveals additional information.

All of the pieces in color began as paintings in gouache on paper at a scale of ½ inch = ½ step in both color and pitch (one octave therefore equals 6”) and later digitally altered. Please see Instagram for views of these original sketches in the studio. Various incarnations of the Tonal Relativity project linked at left.

While the color wheel at the top of this page can be used as a key to the color relationships, the image below can be used as a key to the patterns depicted in the seven Modes of the Major Scale. A large dot represents a whole step, a small dot represents a half step:

A 3-part rotating wheel such as the one below may be used to quickly identify intervals (for example, the wheel makes it immediately apparent that, while any color can be aligned with any note, tritones are always represented by complementary colors):

Click below to download a PDF containing DIY wheel parts (print on heavy stock, cut out, connect with split clip):

"Begin anywhere."John Cage

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All parts of the Tonal Relativity project are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.