Volume 10, Number 2, June 2004
Copyright © 2004 Society for Music Theory
Bret Aarden and Paul T. von Hippel
Rules for Chord Doubling (and Spacing): Which Ones Do We Need?
 If beneath every musical surface is an idealized homophony, then the primary mechanism working to obscure it is probably rhythm. The implicit--or sometimes explicit(77)--assumption of idealized harmony is that triads occur at strong metrical positions. We chose to limit our study to strong metrical positions, since triads in weak positions are less likely to be functional harmonies.
 To define "metrical strong points," we used the first two levels of the metrical hierarchy for time signatures with 3, 6, or 9 in the numerator; and we used the first three metrical levels for numerators of 2, 4, or 12. In the case of 6/8 this would correspond to the dotted-half and dotted-quarter levels; and in 4/4 this would include the whole-note, half-note, and quarter-note levels.
 Some strong-beat sonorities include nonharmonic tones that only later resolve to notes of the triad. These sonorities pose difficult problems for computer analysis, and may not be good candidates for the study of doubling practice. We chose to ignore them and restrict our attention to more simply stated triads--i.e., strong-beat sonorities containing only the root, third, and fifth.
Brent Yorgason, Managing Editor
Updated 03 June 2004