Chords sound consonant when singers’ fundamental frequencies are integer-related.

Evidence

When singing a chord, each harmonic of the note produced by one singer will have a nearest neighbor in the set of harmonics produced by another singer, and the overall consonance of the result will depend heavily on the tuning accuracy. This is maximized when the fundamental frequencies are in an integer relationship and are harmonics of each other (see Section 3.3.3). — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1377

Categorization

• DEFINE: Clarifies consonance as harmonic overlap between voices, defining it operationally via integer frequency ratios.
• SEED: An essay angle: why a cappella groups ‘lock in’ and why unaccompanied choirs drift—acoustics explains an everyday ensemble experience.
• XREF: Extends the just-intonation and harmonic-series material introduced in Section 3.3.3. — connects to: Chord consonance is maximized when singers’ fundamentals are integer-related harmonics; Harmony is sustained through chords of two or more simultaneous notes; Simple integer frequency ratios between notes produce the greatest measured consonance — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1296 (+14 more)

Broader Connections

• Chord consonance is maximized when singers’ fundamentals are integer-related harmonics #corroborates (0.95)
• Simple integer frequency ratios between notes produce the greatest measured consonance #corroborates (0.95) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1296
• Whether two vibration frequencies are commensurate with small integer ratios shapes their musical meaning #corroborates (0.95) — Eric J. Heller, Why You Hear What You Hear- An…, 309
• Chord consonance is computed from individual harmonic proximity across the notes #qualifies (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 943
• Harmony is sustained through chords of two or more simultaneous notes #complicates (0.75)
• Musical scales universally favor intervals with small integer frequency ratios #complicates (0.75)
• String-length ratios of small integers produce the most consonant musical intervals. #complicates (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 2359
• Chord dissonance rises as harmonic number increases and interval shrinks #complicates (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 998
• Musical intervals trace directly to harmonic-series frequency ratios #complicates (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 811
• A 34-cent tuning difference changes a chord’s identity and residue pitch #complicates (0.75)
• Whether combination tones are musical depends on the tuning system #complicates (0.75)
• Consecutive intervals of equal magnitude and opposite sign create repeated tones in pitch sequences #complicates (0.75)
• Higher-order combination tones can be misheard as actual played notes #complicates (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1589
• Singing just-tuned chords predicts rapid pitch drift flat #complicates (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1384
• Organists shape timbre by selectively reinforcing harmonics of one series #complicates (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1526