MUSIC THEORY FUNDAMENTALS - Chapter 4, Exercise 2 Solution
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Finding the Inversion of a Minor 7th

PROBLEM
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Using the real inversion rule from this chapter (number + inversion
number = 9; major<->minor, perfect<->perfect), find the inversion of a
minor 7th.

SOLUTION
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Apply the number rule first:

    original number + inversion number = 9
    7 + inversion number = 9
    inversion number = 9 - 7 = 2

Apply the quality rule second:

    minor inverts to major

ANSWER: The inversion of a minor 7th is a major 2nd.

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WHY THIS WORKS AS AN ANSWER

This is a direct, two-step application of the chapter's own stated
inversion rule: the number component (7 -> 2) comes from the fixed
"sum to 9" relationship, and the quality component (minor -> major)
comes from the fixed major/minor swap rule. As a real check: the
chapter's own worked example showed a major 3rd inverting to a minor
6th (3+6=9, major->minor) - this exercise runs the identical two-step
logic in the opposite direction (minor->major) on a different starting
interval, confirming the same rule holds regardless of which specific
interval you start from.