Tonal consonance and critical bandwidth are explored in this paper. The authors review theories explaining tonal consonance as the singular nature of intervals with small integer frequency ratios. They evaluate these theories in light of experimental studies, supporting von Helmholtz's hypothesis that consonance and dissonance relate to beats between adjacent partials. Experiments showed that as frequency increases, the transition between consonant and dissonant intervals relates to critical bandwidth. Simple-tone intervals are consonant when frequency differences exceed this bandwidth, while the most dissonant intervals correspond to about a quarter of this bandwidth. These results explain properties of consonant intervals with complex tones. The authors analyzed chords from two musical compositions (Bach's Trio Sonata and Dvořák's String Quartet) and found that critical bandwidth plays a significant role in music. For a number of harmonics representative of musical instruments, the "density" of simultaneous partials changes with frequency in the same way as critical bandwidth. This suggests that critical bandwidth is important in music, as it influences the perception of consonance and dissonance. The results indicate that critical bandwidth is related to the perception of consonance, with the most consonant intervals occurring when frequency differences exceed critical bandwidth. The authors conclude that critical bandwidth plays an important role in music, as it influences the perception of consonance and dissonance. The results suggest that critical bandwidth is related to the perception of consonance, with the most consonant intervals occurring when frequency differences exceed critical bandwidth. The authors conclude that critical bandwidth plays an important role in music, as it influences the perception of consonance and dissonance.Tonal consonance and critical bandwidth are explored in this paper. The authors review theories explaining tonal consonance as the singular nature of intervals with small integer frequency ratios. They evaluate these theories in light of experimental studies, supporting von Helmholtz's hypothesis that consonance and dissonance relate to beats between adjacent partials. Experiments showed that as frequency increases, the transition between consonant and dissonant intervals relates to critical bandwidth. Simple-tone intervals are consonant when frequency differences exceed this bandwidth, while the most dissonant intervals correspond to about a quarter of this bandwidth. These results explain properties of consonant intervals with complex tones. The authors analyzed chords from two musical compositions (Bach's Trio Sonata and Dvořák's String Quartet) and found that critical bandwidth plays a significant role in music. For a number of harmonics representative of musical instruments, the "density" of simultaneous partials changes with frequency in the same way as critical bandwidth. This suggests that critical bandwidth is important in music, as it influences the perception of consonance and dissonance. The results indicate that critical bandwidth is related to the perception of consonance, with the most consonant intervals occurring when frequency differences exceed critical bandwidth. The authors conclude that critical bandwidth plays an important role in music, as it influences the perception of consonance and dissonance. The results suggest that critical bandwidth is related to the perception of consonance, with the most consonant intervals occurring when frequency differences exceed critical bandwidth. The authors conclude that critical bandwidth plays an important role in music, as it influences the perception of consonance and dissonance.