MUSIC THEORY FUNDAMENTALS - Chapter 5, Exercise 1 Solution
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Building a Diminished Triad on C

PROBLEM
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Using this chapter's own triad-construction table, build a diminished
triad starting on C, and identify the two real interval qualities
stacked to produce it.

SOLUTION
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The chapter's own table defines a diminished triad as a minor 3rd with
another minor 3rd stacked on top (minor 3rd + minor 3rd).

Starting on C and stacking a minor 3rd (3 semitones):

    C -> Eb   (C to Eb is 3 semitones = minor 3rd)

Stacking a second minor 3rd (3 semitones) on top of Eb:

    Eb -> Gb  (Eb to Gb is 3 semitones = minor 3rd)

ANSWER: The diminished triad on C is C-Eb-Gb. The two interval qualities
stacked to produce it are a minor 3rd (C to Eb) and a second minor 3rd
(Eb to Gb).

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WHY THIS WORKS AS AN ANSWER

This directly follows the chapter's own construction rule for the
diminished quality specifically - unlike the major and minor triads,
which mix a major 3rd and a minor 3rd in different orders, the
diminished triad is the only one of the four qualities built from two
identical intervals (both minor 3rds), which is exactly what gives it
its own distinctively unstable, tension-filled sound compared to the
major and minor triads.