Acoustics & Music Theory
why it sounds like that
Concept

Common-tone — where it appears

A pitch class present in both of two successive chords, which a voice can hold rather than move. Counting them is the cheapest measure of how far apart two chords are, and it is what makes some progressions smoother than others.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

How far the voices have to move. Three chord changes with their voices joined by the assignment that moves the least in total. The distance is computed over every way of pairing the notes, so a change that shares two of its three notes shows as two flat lines.

The shortest move, which is what a chord change is

Between any two chords there is an assignment of voices that moves the least. Compute it and the changes that composers actually use turn out to be the short ones.

harmony · Voice-leading Both criteria, measured from C major. The 23 chords other than C major placed by the smallest total voice motion and by how many notes are held in common. Agreement between the two criteria would be a staircase; the cells drawn in the discrepancy colour are the ones that break it, and over the whole set of 24 chords the two criteria order a pair of destinations oppositely in 72 of 6072 comparisons. A minimal assignment drops a common tone it could have held in 0 of the 552 pairs.

Two criteria that are taught as one

Move the least and keep the common tones arrive in one breath, as though they were one instruction. They are two different functions, and enumerating every pair of chords settles exactly where they agree: as a way of connecting two given chords they never once disagree, and as a way of saying which chord is nearer they disagree about one comparison in eighty.

harmony · Voice-leading

Named alongside it

The objects these essays reach for when they reach for this one.

Neo-Riemannian transformationParsimonyVoice-leadingContrary motionDominant seventhTriad

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