Keeping It Simple

Bret Aarden and Paul von Hippel have written a much-needed article about teaching partwriting rules in undergraduate music theory. They have focused only on rules about chord doubling and chord spacing, but the results certainly suggest potential extrapolations.

Chord doubling -- deciding which note of a triad to double in two different voices, especially in four-voice settings -- can be described by two different sets of rules. The first set, which Aarden and von Hippel call triad member rules, tell the student which member of the triad (root, third, or fifth) to double as determined by the chord quality (major, minor, or diminished) and the inversion of the chord (which triad member is in the bass voice). Two examples: 1) root position major or minor triads should have the root doubled; 2) first inversion diminished triads should have the third doubled.

The other set of rules is called the scale degree rules. These rules do not care what quality or inversion of chord is used, looking only at the notes of the triad as notes in of the major or minor scale. Tendency tones, typically the leading tone, should not be doubled.

The authors develop a program that can look at chords and determine whether they have proper doubling and follow the spacing (put the largest interval between the lowest voices). This is tested by having the computer program compare two chords and determine which chord is from an authentic piece and which chord was randomly created. By changing the program to used different sets of rules, the authors discovered that both sets of rules had the same level of accuracy, interpreting this result to mean that the two sets were redundant. Because they feel both sets are not needed, they suggest going with the simpler set of rules, the scale-degree rules.

I applaud the results, as I feel most textbooks overload the rules for partwriting. The focus should be on creating smooth lines that avoid dependency between voices (e.g. parallel fifths and octaves), without codifying every possible instance of chord progression as a different rule. However, I find their label of scale degree rules to be misleading. The typical rule is about tendency tones, of which only two are specific scale degrees (the leading tone and the flattened second scale degree). The other main tendency tone is the chordal seventh, which changes scale degrees depending on the root of the chord. Thus I would call the set of rules tendency rules.

Now let's see them tackle voice crossing and voice overlap!