What is the quality of the triad if the interval between the root and third is m3 and the interval between the third and fifth is M3?

A. major
B. minor
C. Augmented
D. diminished

The quality of the triad, based on the given intervals, is A. major.

The quality of the triad can be determined based on the intervals between the root, third, and fifth. In this case, if the interval between the root and third is a minor third (m3) and the interval between the third and fifth is a major third (M3), the quality of the triad is diminished. Therefore, the correct answer is D. diminished.

To determine the quality of a triad, we need to understand the intervals between its notes. In this case, the interval between the root and third is a minor third (m3), and the interval between the third and fifth is a major third (M3).

In a major triad, the interval between the root and third is a major third, and the interval between the third and fifth is a minor third. So, option A can be eliminated.

In a minor triad, the interval between the root and third is a minor third, and the interval between the third and fifth is also a minor third. So, option B can also be eliminated.

In an augmented triad, the interval between the root and third is a major third, and the interval between the third and fifth is an augmented third. Since the interval between the third and fifth in this triad is a major third and not an augmented third, option C can be eliminated.

In a diminished triad, the interval between the root and third is a minor third, and the interval between the third and fifth is a diminished third. Since the interval between the third and fifth in this triad is a major third and not a diminished third, option D can be eliminated.

Therefore, the correct answer is A. major, and the explanation demonstrates how to arrive at this answer.