Equal tempered intervals stay consonant because mistuning falls within critical bandwidth

Evidence

The roughness phenomenon is, on the other hand, much more easily obtained when two notes are played at the same time. If the fundamental frequencies are different, the distances of their harmonics on the frequency scale define the roughness. If some of the harmonics are located at distances relative to each other that create roughness, a dissonant sound is perceived, as shown for three intervals in Figure 11.13. When the frequency ratio is near 3:2, as shown in the uppermost case in the figure, most of the partials of the spectra are either located very near to each other or far enough away from each other to cause no roughness. Only partials with number 10 or higher are at frequencies influencing each other. When the frequency ratio is about 5:4, a larger number of partials are seen to have such a ratio with each other that higher roughness is perceived. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1294 (#qualifies, via linked claim)

Categorization

• XREF: connects to: Dissonance depends on proportional separation falling inside the critical bandwidth, not absolute frequency difference; The rate of beating between close partials determines whether they sound consonant or rough; Interval dissonance increases with position higher in the harmonic series — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1294

Related

• Simple integer frequency ratios minimize partial interference and thus dissonance (similarity 0.91)
• Interval dissonance increases with position higher in the harmonic series (similarity 0.90)
• Dissonance depends on musical interval, not a fixed beat rate across frequencies (similarity 0.90)
• Dissonance arises from inconsistent stretch of notes versus partials (similarity 0.89)
• Equal temperament beats stay within the 5% critical bandwidth so consonance survives (similarity 0.87)
• The rate of beating between close partials determines whether they sound consonant or rough (similarity 0.85)
• Clashing tones within one critical band produce roughness that underlies dissonance (similarity 0.85)
• Roughness between note partials determines perceived musical dissonance (similarity 0.85)
• Simple integer frequency ratios produce local consonance maxima between tones (similarity 0.84)
• Perceived dissonance arises when nearby harmonics fall within critical bandwidth (similarity 0.83)
• The same musical interval’s dissonance changes with pitch register (similarity 0.83)
• Simple integer frequency ratios between notes produce the greatest measured consonance (similarity 0.83)
• Interval consonance ranking derives from critical-bandwidth proximity between harmonics (similarity 0.83)
• Consonance judgments rest on psychoacoustic critical bandwidth (similarity 0.83)
• Consonance perception is continuous and not tied to musical intervals (similarity 0.83)

Broader Connections

• Dissonance depends on proportional separation falling inside the critical bandwidth, not absolute frequency difference #expands (0.92)
• The rate of beating between close partials determines whether they sound consonant or rough #corroborates (0.78)
• Interval dissonance increases with position higher in the harmonic series #qualifies (0.75) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1294