The Architecture of Music


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Chord Interval Diagrams

“A chord is a combination of three or more tones sounded simultaneously for which the distances (called intervals) between the tones are based on a particular formula” Monath (1984, p. 37). Chord formulas can be expressed numerically using semitones to describe the intervals between the notes. For example, the maj3 = 4 3 5 (below). Interval diagrams are the graphic representations of numeric chord and scale formulas. As can be seen below, a lot of information can be extracted from a simple numeric chord formula. Since chord formulas always add up to 12, interval diagrams represent an octave and any generic note in between starting from any bass note.

Chord Interval Diagram

Every chord has a unique formula and that formula can be graphically depicted as an interval diagram. The formulas and interval diagrams for each chord are all unique and different and their formulas and interval diagrams never change. Standard musical notation is condensed musical notation. If the musical staff were to be expanded to include a line for every note you would have interval diagrams and chords would look the same no matter which bass note they started from.

Traditional music theory chord formulas using interval names have been integrated into the interval diagram to name the intervals of a chord. In traditional music theory maj3 = P5 M3 as can be seen on the right side of the interval diagram above. However, using a numeric sequence to describe the semitones between the notes of a chord is useful in many ways. For one, interval diagrams can be created from numeric chord formulas and a universal graphical representation of a chord can be made. Interval diagrams visually depict the semitone distances, or intervals, between the notes of a chord and help to visually describe what a chord will sound like. Study the diagram above to understand the parts of a chord interval diagram.