Final answer:
The strongest relationship between the tonic triad and the dominant triad in major-minor tonality is the harmonic relationship, responsible for tension and resolution in Western music.
Step-by-step explanation:
In major-minor tonality, the strongest relationship that exists between the tonic triad and the dominant triad is the harmonic relationship. The tonic triad is the chord built on the first degree of a scale, which is considered the 'home' chord or the key center. The dominant triad, on the other hand, is built on the fifth degree of the scale and has a strong tendency to resolve back to the tonic. This tension and resolution are critical to tonal music and form the basis of Western harmonic progression.
The tonic and dominant triads share two notes in common when in root position, and the movement from the dominant to the tonic (known as a perfect cadence or authentic cadence) is considered the most conclusive and stable in tonal music. This relationship underlines the sense of closure and finality at the end of a musical phrase or piece and is particularly prominent in the compositions by J.S. Bach and the tonal system of the Baroque, Classical, and Romantic periods.