MTO 10.2: Aarden and Hippel, Rules for Chord Doubling, 4.1

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?

4.1 "Composed" Triads

[1] Our analyses used large samples of triads drawn from the chorale harmonizations of Bach and the string quartets of Haydn and Mozart. The following guidelines formed the basis of our procedures for sampling triads.

Four-voice sonorities in the home-key regions

were searched to find complete triads
at strong metrical positions.

A triad was discarded if any pair of voices approached or departed the triad using parallel motion at the octave, or if two voices met or crossed.
We did not attempt to identify triads below the musical surface.

[2] In order to increase the size of our sample, we made use of computer software to automate the analysis and sampling of music. In order to turn the process over to a computer, it was necessary to operationalize some basic musical definitions, in particular:

where are tonal centers unambiguous (see §4.1.1); and
what is a strong metrical position, and is a triad a triad without one? (See §4.1.2.)

[3] The sampling process benefited immensely from the use of existing resources, particularly electronic scores and computer analysis software. All of the scores were taken from the MuseData database created by CCARH,⁽⁷¹⁾ and were analyzed using both the Humdrum Toolkit⁽⁷²⁾ and the Melisma harmonic analysis software.⁽⁷³⁾

[4] The complete process resulted in a total sample of 2643 triads from the chorales, and 960 triads from the string quartets. Some triads taken randomly from the sample are shown in Figure 4.1a.

Figure 4.1a. Some triads taken at random from the sample:

the Bach chorale "Den Vater dort oben" (BWV 292), measure 9,
a Haydn string quartet, opus 74 number 3 ("The Rider"), third movement, measure 3,
the Bach chorale "Wie bist du Seele in mir so gar betrübt" (BWV 435), measure 1, and
a Mozart string quartet, K. 169 ("Haydn" #2), fourth movement, measure 73.

1.	2.
3.	4.

◄ Back to §4 (Data)

Go on to §4.1.1 (Tonal Context) ►
Go on to §4.2 ("Random" Triads) ►

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Prepared by
Brent Yorgason, Managing Editor
Updated 03 June 2004