The same two notes can clash in Bach and soothe in Debussy
Play C and D together and in a Bach prelude from the 1700s the pair counts as a clash that must be resolved. Put the identical interval in a Debussy piece from the early 1900s and it can sound perfectly settled. Whether notes agree depends on physics, but also on style and on what listeners are used to.
Consonance and dissonance look like simple opposites, each defined as whatever the other is not, but in practice they form a sliding scale from very smooth to very harsh. Paul Hindemith observed that nobody had ever fully explained them and that definitions had shifted for a thousand years. Since around the sixteenth century most accounts have equated consonance with pleasant and dissonance with unpleasant, yet that confuses dissonance with noise, and a well-placed clash is often exactly what makes music enjoyable.
Ancient theorists measured intervals by the lengths of vibrating strings; from the early seventeenth century people spoke of frequency ratios instead. The simpler the ratio, the smoother the sound tends to be. One explanation is that the overtones of the two notes line up. A note and the note an octave above blend so well because every overtone of the upper note is also an overtone of the lower one. Another account links it to how regularly nerve cells fire in step with the waves.
The physical side is about interference. Two tones at slightly different pitches alternately reinforce and cancel each other, and the loudness wobbles at a rate equal to the gap between their frequencies. Below roughly 20 wobbles a second the ear hears beating; faster than that it turns into a gritty roughness, which peaks and then fades away somewhere between 75 and 150 per second, depending on the tones involved.
Some traditions chase that roughness. Organs have a stop called the voix celeste built on deliberate beating, and Bosnian ganga singing, the buzz of the Indian tambura and Indonesian gamelan all prize it. In Western harmony, dissonance does a different job: it creates tension that pulls the music forward. In a G7 chord in C major, the F is the unstable note, and it typically slides down to E as the harmony comes to rest on C.
Source: Consonance and dissonance
