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Pitch • Intervals • Scales • Chords • Modes • Circle of Fifths

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Back to Music Theory

Chroma Wheel I: The Chromatic Scale

Picturing pitch-space

Pitch describes the frequency of tonal vibration in Hertz (cycles per second) and we perceive this as how high or low the sounds are. The range of human hearing is between 20 and 20,000 Hz. The Western 12 tone equal temperament (12-TET) tuning model gives us the chromatic scale, a repeating cycle of octaves, each containing 12 tones of equal value shown on ChromaWheel as 30° segments.

Chromatic scales of different octaves have the same quality except for being transposed into higher and lower registers. Moving up an octave doubles the frequency of a tone, while moving down an octave halves it. This can be seen by halving the length of a vibrating string to get a pitch an octave higher – e.g. fretting the 12th fret on a guitar. This is because the shorter the string, the higher the pitch generated.

The gap between any given tones is called an interval and moving from a segment to one next to it represents a somewhat confusingly named semitone or half-step, the fundamental unit of interval (pitch-change) in this tuning system, and so the building block of melody and harmony. In the wheels above semitone intervals are shown by each side of the inner white dodecagon.

Chroma means colour and ChromaWheel presents the spectrum of pitch as analagous to a colour scale, which shows adjacent and nearby tones to be similar in hue as they are in pitch, whereas complementary or opposite tones on the wheel can be heard as more distant in pitch and seen as contrasting in hue. Some tones when played together (chords, harmony) or sequentially (melody) will appear consonant while others will seem dissonant. Consonance isn’t objective however and depends on cultural factors.

Octaves can be divided into other fractions. Though 12 is a useful number to divide mathematically, ChromaWheel may be adapted for, for instance, an 8-tone, 24-tone chromatic scale, or indeed any number that can be reasonably represented on a wheel.

Colours are arbitrary and are intended to show gradation of the scale. Do is movable – i.e. it can be any tone, not necessarily C. Tones and their intervals are always relative to each other. The 1, Do in solfège, Sa in sargam is the tonic or tonal key centre, the scale degree which sounds most resolved. It represents unison or octave intervals.

Chroma modes

Chroma phrases

Chroma Wheel II: The Circle of 5ths

Clockwise: cycling ascending Fifths or descending Fourths

Anticlockwise: cycling ascending Fourths or descending Fifths

Comparing Chroma Wheel I & II

To go from Chroma wheel I to II you rotate one whole tone scale 180 degrees, i.e. a tritone, keeping the other in the same position so that every other note has been replaced by its tritone, its complementary (opposite) colour.

Although octaves are a natural phenomenon, which is what Chroma Wheel encapsulates, The Chromatic scale is not. It is a tuning system among many. Tuning in 5ths, called Pythagorean tuning is the original way. Being the 3rd partial of the harmonic series of notes of natural resonance, Fifths are very consonant. It is naturally harmonious.

The chromatic scale was invented as way to mitigate the problem keyboards faced with the ‘Just Intonation’ of Pythagorean tuning: scales didn’t sound the same in different keys and you can’t retune pianos on the fly.

[more info here]

So although Fifths are primary, they are shown on Chroma Wheel II because Chroma Wheel I represents not simply the 12 degrees of 12-TET but its colour gradations symbolise the spectrum of sound, pitch “space,” with octaves which as mentioned can be divided up into any number of degrees.

The circle helps us to see the cycling nature of octaves – again, the halving/ halving the frequency – and how the tones interact harmonically, bringing a certain colour palette.

Cycles of Fifths and Thirds

Tertiary harmony

Diatonic triads

More to come…

Chroma for guitar

Glossary

Modes

• Scale shape rotations

Flats ♭ and Sharps ♯

• relative to key

Equal-temperament

• vs. just intonation

What is an octave?

• Frequency – Hz
• spiral

Symmetry

• Reflectional
• Palindromic

Circle of 5ths

• triads
• 7 chords
• extended