Simple integer frequency ratios produce local consonance maxima between tones

Evidence

Dissonance has been measured for different ratios between the fundamental frequencies of two notes. Figure 11.14 shows the degree of dissonance and consonance when the fundamental frequency of one of the sounds stays at 250 Hz, and the frequency of the other sound changes from 250 Hz to 530 Hz (Plomp and Levelt, 1965). Each sound consists of the fundamental frequency and five harmonic components. Perfect consonance is obtained with frequency ratios 1:1 and 1:2. Consonance has a local maximum with all simple integer ratios, such as 2:3, 3:4, 3:5, and so on, and a minimum in between. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1296

Categorization

Category: Factual Claims

• XREF: Connects to the psychoacoustic ground of why just intonation and the harmonic series matter in music theory — Pythagorean/just vs. equal temperament tension.

Related

• Simple integer frequency ratios between notes produce the greatest measured consonance (similarity 0.96)
• Chord consonance is computed from individual harmonic proximity across the notes (similarity 0.85)
• No tuning system can make all diatonic intervals have simple ratios (similarity 0.84)
• Simple integer frequency ratios minimize partial interference and thus dissonance (similarity 0.84)
• Interval consonance ranking derives from critical-bandwidth proximity between harmonics (similarity 0.84)
• Equal tempered intervals stay consonant because mistuning falls within critical bandwidth (similarity 0.83)
• Dissonance depends on musical interval, not a fixed beat rate across frequencies (similarity 0.83)
• No pure integer-ratio system can tune musical intervals without compromise. (similarity 0.82)
• Peak dissonance between two tones occurs at a quarter critical band separation (similarity 0.82)
• Chord consonance is maximized when singers’ fundamentals are integer-related harmonics (similarity 0.82)
• No tuning system can make all diatonic scale intervals perfectly consonant (similarity 0.81)
• Interval dissonance increases with position higher in the harmonic series (similarity 0.81)
• Consonance is a continuous sensation while dissonance is an intermittent one (similarity 0.81)
• Untrained listeners judge two-tone consonance continuously without musical interval prominence (similarity 0.80)
• Equal frequency ratios occupy equal perceptual distances regardless of starting pitch (similarity 0.80)