The missing fundamentals of harmonic theory: Chord roots and their ambiguity in arrangements of jazz standards

Abstract

Since Lippius and Rameau, chords have roots that are often voiced in the bass, doubled, and used as labels. Psychological experiments and analyses of databases of Western classical music have not produced clear evidence for the psychological reality of chord roots. We analyzed a symbolic database of 100 arrangements of jazz standards (musical instrument digital interface [MIDI] files from midkar.com and thejazzpage.de). Selection criteria were representativeness and quality.The original songs had been composed in the 1930s and 1950s, and each file had a beat track. Files were converted to chord progressions by identifying tone onsets near beat locations (±10% of beat duration). Chords were classified as triads (major, minor, diminished, suspended) or seventh chords (major–minor, minor, major, half-diminished, diminished, and suspended) plus extra tones. Roots that were theoretically less ambiguous were more often in the bass or (to a lesser extent) doubled. The root of the minor triad was ambiguous, as predicted (conventional root or third). Of the sevenths, the major–minor had the clearest root. The diminished triad was often part of a major–minor seventh chord; the half-diminished seventh, of a dominant ninth. Added notes (“tensions”) tended to minimize dissonance (roughness or inharmonicity). In arrangements of songs from the 1950s, diminished triads and sevenths were less common, and suspended triads more common, relative to the 1930s. Results confirm the psychological reality of chord roots and their specific ambiguities. Results are consistent with Terhardt’s virtual pitch theory and the idea that musical chords emerge gradually from cultural and historic processes. The approach can enrich music theory (including pitch-class set analysis) and jazz pedagogy.