Macroharmonic Progressions through the Discrete Fourier Transform

This article examines macroharmony through the lens of the discrete Fourier transform (DFT) using computational analysis. It first introduces the DFT, giving an interpretive framework to understand the theory of chord quality first introduced by Ian Quinn (2007) before extending the theory to macroharmonies. Subsequently, the paper discusses different approaches—including different weighting and windowing procedures—to retrieving pitch data for computational analysis. An analysis of macroharmony in Domine Jesu from Maurice Duruflé’s Requiem, Op. 9 follows. I show that the DFT reflects intuition, reveals form-functional macroharmonies in the movement, and provides us with a perspective to find novel hearings.

Diachronic Changes in Jazz Harmony

The present study examines both gradual and rapid changes occurring in 20th-century jazz harmonic practice. A newly-assembled corpus of 1,086 jazz compositions was used to test the idea that jazz music exhibits a mid-century decline in traditionally “tonal” chord usage. Evidence was found for slow, incremental changes in zeroth-order chord quality distributions, consistent with gradual, unconscious changes in harmonic usage. Typical tonal chord-to-chord transitions became less common between the 1920s and the 1960s, consistent with the hypothesis of tonal decline. Finally, use of root motion of an ascending perfect fourth dropped suddenly in the 1950s, suggesting that chord-to-chord transitions might be more susceptible to rapid change than chord frequency. Possible constraints on stylistic evolution are discussed.

Computer-Based Recognition of Perceptual Patterns in Chord Quality Dictation Exercises

This experiment measured achievement of 18 freshman music majors in the GUIDO chord quality program and determined the pattern of student responses to chord quality dictation exercises. A two-part test to measure student achievement on chords in close position and on chords in open position was administered before any training began, at the end of the first semester after training on chords in close position but before training in open position, and at the end of the second semester after training on chords in open position. Correlated t-test comparisons of scores showed significant learning gains on the basis of chords in close position during the first semester and on open position chords during the second semester. Additional significant increases on the basis of chords in open position during the first semester and chords in close position during the second semester indicated existence of a transfer mechanism. Analysis of responses to the third set of tests led to the identification of five principles of chord-quality confusions.