Short answers, pulled from the story.
Consonance refers to combinations of sounds perceived as stable, restful, or blending, while dissonance refers to combinations perceived as tense, harsh, or requiring resolution. The distinction forms a gradation rather than a strict binary, and it depends on acoustics, cultural context, musical style, and period. As Paul Hindemith noted, the definitions have varied for a thousand years.
Dissonance in acoustic terms arises from amplitude fluctuations produced by wave interference when two sounds with different frequencies interact. When these fluctuations fall within a certain rate range, the ear perceives roughness or beating rather than a smooth blend. Researchers Pankovski and Pankovska also proposed that dissonance triggers a P300 brainwave response, signalling an unexpected or rare sound event.
Hucbald of Saint Amand defined consonance as the "measured and concordant blending of two sounds" that occurs when two simultaneous sounds from different sources combine into a single musical whole. He identified six consonances: the octave, the fifth, the fourth, the octave-plus-fifth, the octave-plus-fourth, and the double octave.
In the opening aria of Cantata BWV 54, Widerstehe doch der Sunde, nearly every strong beat carries a dissonance; of the thirty-two continuo notes in the first four bars, only four are consonant. At the close of the St Matthew Passion, Bach inserted what conductor John Eliot Gardiner called an "unexpected and almost excruciating dissonance" over the final chord, with melody instruments insisting on B natural before resolving to a C minor cadence.
The finale of Beethoven's Symphony No. 9 opens with a B flat inserted into a D minor chord, which Roger Scruton, following Wagner, described as a "horror fanfare." When the passage returns just before the voices enter, a diminished seventh chord is added, creating what Scruton called "the most atrocious dissonance that Beethoven ever wrote, a first inversion D-minor triad containing all the notes of the D minor harmonic scale."
George Russell's Lydian Chromatic Concept of Tonal Organization, published in 1953, argued that the tritone over the tonic is relatively consonant because it derives from the Lydian dominant thirteenth chord and from harmonic series ratios. Russell extended this to grant consonance to the sharp eleventh note in jazz's 12-tone equal temperament, which is the sole pitch difference between the major scale and the Lydian mode.