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” Norman Monath, How To Play Popular Piano In 10 Easy Lessons (Fireside Books, 1984), p.37. Chord formulas can be expressed numerically to describe the intervals in semitones between the notes. For example, the maj3 = 4 3 5 (below). Interval diagrams are the graphic representations of numeric chord formulas (and, as we will see later on, 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. Interval diagrams work very much like an expanded musical staff. Standard musical notation is condensed musical notation. If the staff were expanded to have a line for every note you would have the interval diagram and chords would look exactly the same no matter which note they started from. Interval diagrams are in a sense universal depictions of chords.

Chord Interval Diagram

Every chord has a unique formula and that formula can be graphically depicted as an interval diagram. 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, what I am calling maj3 would be described as being built out of a M3 and a P5 (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 has advantages to the traditional model. 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.