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?

5.1 Coding Triad Features

[1] Competing theories suggest certain features that might discriminate composed triads from random triads in four voices. (See 2.) These features include:

  1. the triad's spacing,
  2. the scale degree of the doubled tone,
  3. and the triad member of the doubled tone.
[2] We used effect coding(79) to represent these qualitative features in quantitative form. The resulting variables were as follows.

Doubled Scale Degree

[3] One set of variables indicated which scale degree was doubled. The possibilities were:

[4] Unfortunately, we could not make finer distinctions among the chromatic scale degrees. As it was, there were very few doubled chromatics; had we broken them into smaller groups, our statistical estimates would have become too uncertain.

Doubled Triad Member

[5] Another set of variables indicated which triad member was doubled. The possibilities were:

[6] In all then, this variable had 27 possible values: 3 triad members X 3 triad qualities X 3 triad inversions.

Good Spacing

[7] A final variable was necessary as a control because doubling rules are confounded with rules for spacing. (See 2.2.) This necessary control variable indicated whether or not the triad had its largest space between its two lowest voices, i.e.,

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Prepared by
Brent Yorgason, Managing Editor
Updated 03 June 2004