chordless

Chordless is an adjective used in music and in graph theory contexts. In music, a chordless chord refers to a triadic chord from which the third has been omitted. Without the third, the chord lacks a defined major or minor quality, producing a suspended or neutral sound. This is common in voicings that omit the third to emphasize the bass or texture, in jazz and contemporary harmony, and in suspended chords such as sus2 or sus4, where the tension is resolved by reintroducing the third.

In practical terms, chordless voicings can help avoid tonal ambiguity or create space for melodies and bass lines to define the harmony. They are often used in arranging, composition, and guitar or keyboard voicings to achieve a particular color or to allow other voices to articulate the harmony more clearly. The concept is closely related to the idea that the third of a chord determines its quality (major or minor), so removing it changes how the chord is perceived.

In graph theory, chordless has a separate meaning. A chordless cycle, also called an induced cycle, is a cycle that has no chords—no edges joining nonconsecutive vertices of the cycle. This concept is central to the study of induced cycles or holes in graphs. Related terminology includes chordality: a graph is chordal if every cycle of length four or more has a chord, equivalently, if the graph contains no induced cycles of length four or more. Thus chordless describes a structural property in contrast to chordal structures.