Short answers, pulled from the story.
The distinction changed from a rigid binary to a fluid spectrum in the year 1536 when music theory underwent a quiet revolution. Before this date, certain intervals were inherently sweet and others were inherently harsh. This shift established a historical constant where definitions varied wildly over a thousand years.
Sensory dissonance is caused by the collision of sound waves that create a rapid fluctuation in amplitude within the critical band of human hearing. The ear perceives this fluctuation as beating or roughness, which the brain interprets as tension. This biological alarm system triggers an EEG pattern known as the P300 response to irregularities in sound.
Pythagoras defined consonance as intervals corresponding to simple numerical ratios of string lengths such as 2:1 for the octave and 3:2 for the fifth. He considered these ratios to be the only true consonances while labeling all other intervals as diaphonos or discordant. This mathematical purity held sway for centuries until the early Middle Ages.
Johann Sebastian Bach used dissonance to convey the agony of Christ's betrayal in the St Matthew Passion. He inserted an unexpected and almost excruciating dissonance over the very last chord where melody instruments insisted on B natural before melting into a C minor cadence. Conductor John Eliot Gardiner heard this moment as a final reminder of the suffering.
The year 1913 marked the turning point with the premiere of Igor Stravinsky's The Rite of Spring. The Sacrificial Dance featured a rhythmic and harmonic language that shattered the conventions of the past. This work along with the experiments of Henry Cowell signaled the emancipation of dissonance.
George Russell grants consonance to the septimal minor seventh, major ninth, neutral eleventh, neutral thirteenth, and diminished fifteenth in the Lydian Chromatic Concept of Tonal Organization. He argues that these intervals are truly non-dissonant when they correctly reproduce the mathematical ratios of the harmonic series. This theory extends to the 12TET tuning system of Jazz and the 12-note octave of the piano.