Thirteen chords of just-tuned harmony can accumulate a semitone of flatness.

Evidence

The predicted pitch drift for just tuning of the chords in the exercise shown in Figure 4.42 is shown in Figure 4.43. It is based on the tuning of the just scale (see Section 3.4.2), and it can be seen that the prediction is for the pitch to drift a semitone flat (rather surprising for an exercise consisting of only 13 chords!). — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1381

Categorization

• CANDY: A semitone of pitch drift from just thirteen chords is a great ‘wait, what?’ dinner fact.
• SEED: Essay angle: how small rounding errors in pure intervals compound into audible pitch catastrophe in choral singing.
• XREF: connects to: Just-tuned chord progressions predict key drift of a full semitone; A 34-cent tuning difference changes a chord’s identity and residue pitch

Broader Connections

• Just-tuned chord progressions predict key drift of a full semitone #expands (0.90)
• A 34-cent tuning difference changes a chord’s identity and residue pitch #qualifies (0.85)