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?

2.2 Spacing Rule

[1] Although this essay is focused on doubling, we found it necessary to control for the effects of chord spacing. The reason is that the usual spacing rule makes some doublings more convenient than others.

[2] Theory textbooks commonly recommend that a chord have its largest space between its lowest voices. The psychological reason for this is well-established. The human auditory system has poorer resolution at low pitch levels; hence, if a chord is to sound transparent, extra space is necessary between low voices.(67)

[3] Following this rule will often lead a composer to double the bass.(68) If we assume that all upper voices are separated by less than an octave, then a chord with its largest space at the bottom will have three convenient ways to double the bass, but only one convenient way to avoid it (see Figure 2.2a).

Figure 2.2a.
A schematic showing a possible well-spaced chord (made of dots)
with a large space between the bass and tenor. The lines represent possible
convenient ways to double a PC. Three involve the bass, but only one avoids it.


[4] This observation can be made more concrete by reference to our samples of triads from chorale harmonizations by Bach and string quartets by Haydn and Mozart. (See 4.1.) Among triads whose largest space is between the two lowest parts, 85% double the bass in the chorales, and 73% double the bass in the quartets. By contrast, when the largest space is not between the two lowest parts, only 57% double the bass in the chorales, and only 46% do so in the quartets.(69)

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Prepared by
Brent Yorgason, Managing Editor
Updated 03 June 2004