Intervals • Scales • Chords • Arpeggios

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The Chromatic Scale

Picturing pitch-space

**fixed tones:**
letters represent assigned frequencies (Hertz) – e.g. A=440 Hz (pitch standard)

**scale degrees:**
1 is always the tonic (degrees relative to it). 360° represents one octave

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.