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, visualizations that reveal inherent repeating patterns 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) along with relatively-sized shapes/spaces can be used to represent relationships in a 12-tone musical system.

These charts are intended as a starting point — patterns derived from scales containing any number of tones can be depicted using similar methods.

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 an equally-tempered 12-tone chromatic scale and a 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 original sketches in the studio. Various incarnations of the Tonal Relativity project are linked at left.

While the color wheel at the top of this page can be used as a key to the color relationships, the images below can be used as keys to the patterns depicted in the sets of seven Modes of the Major Scale, Modes of the Ascending Melodic Minor Scale, and Modes of the Harmonic Minor. We have also charted two sets of Pentatonic Scales.

Dot sizes are relative, with smallest dot representing half a step, dot with twice the diameter representing a whole step, dot with 1.5 times the diameter representing a step and a half, etc.

High-resolution PDFs of the following graphics in worksheet form are freely available for download here. For examples of worksheets in use, please see Instagram.

Audio-visualization of the Modes of the Harmonic Minor Scale:

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):

"Color deceives visual perception there is a discrepancy between physical fact and psychic effect. What counts here — first and last — is not so-called knowledge of so-called facts, but vision — seeing." — Joseph Albers, introduction to Interaction of Color

"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

“I think music is an instrument. It can create the initial thought patterns that can change the thinking of the people.” — John Coltrane, 1966 Interview with Frank Kofsky for KPFK Radio

"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

"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.