Harmonic Coloring

A method for assigning colors to musical pitches

Pitch Height, Pitch Class, and the Circle of Fifths

There are many kinds of relationships between musical pitches. One of the (and perhaps the) most fundamental is called pitch height; this is what we're referring to when we say "this note is higher than that note" or "the melody goes up."

When pitch height changes by an octave (corresponding to a frequency ratio of 2:1), there's a sense that we're at "the same note." So, depending on how many notes we say there are within an octave, the number of pitch classes (pitches that might differ in pitch height but not otherwise), will be some smaller number. In most western music, this number is considered to be twelve.

The most fundamental relationship between pitch classes, then, is how close two notes with the same pitch height but a different pitch are. So, C-natural is relatively close to C-sharp, but relatively distant from F-sharp. This gives the pitch class ordering of: C, C-sharp, D, D-sharp, E, F, F-sharp, G, G-sharp, A, A-sharp, B. And then, back to C. We can say that this ordering of pitch classes is circular, because we get back where we started after going through all twelve pitch classes.

Another (possibly the second most) fundamental relationship between pitch classes is the one where the frequency ratio is (approximately) 3:2, known as the perfect fifth. Using this, we get the ordering: F, C, G, D, A, E, B, F-sharp, C-sharp, G-sharp, D-sharp, A-sharp (and then, back to F, more or less). This ordering is called the circle of fifths.

Because it's hard to keep track of twelve separate pitches (see this), most musical styles limit themselves to a smaller subset of pitches at any one time, typically five (pentatonic music) or seven (diatonic music). Typically, these are pitches that are contiguous on the circle of fifths (since this will give the 3:2 ratio between the largest number of pitches).

Assigning Colors to the Circle of Fifths

In the proposed method for assigning colors to the circle of fifths, we take advantage of the fact that both can be considered to be circular, and pick twelve (approximately) equally-different colors to assign to the twelve pitch classes:

I've assigned blue to be the "home pitch" (the tonic, notataed Roman numeral "I") because that seeme the most "settled," and chosen the blue-toward-red direction as the I-toward-V direction because motion toward the dominant ("V") seems more "active" compared with motion toward the subdominant ("IV").

When these colors are applied to the pitches of a major scale, it looks like this (here's a video):

Using this coloring method, we can see how sets of pitches are used in various musical compositions; following are some examples ...

Tallis, Spem in alium (YouTube)

This piece is typical of much polyphonic Renaissance music in that it is mostly modal, and, as such, mostly stays within a single set of seven pitches. Toward the end, you can see a section where it shifts briefly toward the dominant, followed by a brief shift toward the subdominant, before settling back on the tonic.

Contrast that with ...

Kodaly, String Quartet No. 1, third movement (YouTube)

... this piece by Kodaly which has strong, obvious tonal shifts at many points (indicated with vertical lines).

That's pretty dramatic; music of the Baroque, Classical and early Romantic periods is typically less dramatic. For example ...

Bach, Brandenburg Concerto No. 3, G major, first movement (YouTube)

... this piece by Bach changes pitch sets less dramatically and less abruptly ...

Beethoven, String Quartet No. 14, movements 1-4 (YouTube)

... and even this late Beethoven string quartet movement, though it changes key significantly, is relatively stable.

By the time of Brahms, however ...

Brahms, Piano Quartet in C minor, opus 60, second movement, Scherzo (YouTube)

... frequent modulations are more common, and in Debussy's music ...

Debussy, Prelude to "The Afternoon of a Faun" (YouTube)

... quick, abrupt modulations had become an essential part of the musical language.

Stravinsky, The Right of Spring (part 1) (YouTube)

Stravinsky learned a lot from Debussy, and applied the "quick+abrupt" idea to both changes in tonality and changes of texture.

Stravinsky, The Right of Spring (part 2) (YouTube)

Stravinsky often deviates from simple diatonic tonality, so the pitch sets used are often more diverse, color-wise.
(More complex examples of harmonic coloring in The Rite of Spring are given in section 3 of this PDF.)

For more videos using Harmonic Coloring, see this playlist.

See also:

  • Visual and Aural: Visualization of Harmony in Music with Colour
  • Harmonic Visualizations of Tonal Music
  • Isochords: Visualizing Structure in Music