MUSIC THEORY FUNDAMENTALS - Chapter 4, Exercise 1 Solution
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Identifying a 7-Semitone Interval

PROBLEM
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Using this chapter's own real semitone-count table, identify the
interval quality and number for a distance of exactly 7 semitones, and
explain why this specific interval is called "perfect" rather than
"major" or "minor."

SOLUTION
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Scanning the chapter's own semitone-count table for the value 7:

    5th - Perfect - 7 semitones

ANSWER: A distance of 7 semitones is a perfect 5th.

It is called "perfect" rather than major or minor because the perfect
5th is one of only four interval numbers (unison, 4th, 5th, octave) that
ever take the "perfect" quality at all - the chapter established that
this category exists because these four intervals correspond to real,
simple, low-integer frequency ratios drawn directly from the overtone
series (the perfect 5th specifically is a 3:2 ratio). Historically, that
acoustic simplicity made them sound so stable and consonant that they
were treated as a separate quality category entirely, rather than being
classified as "major" or "minor" the way 2nds, 3rds, 6ths, and 7ths are.

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WHY THIS WORKS AS AN ANSWER

This is a direct lookup against the chapter's own real semitone-count
table, cross-checked against the chapter's own explanation for why the
"perfect" category exists in the first place - it is exactly the same
3:2 ratio Chapter 1 first introduced as the physical basis of the
perfect fifth's own consonance.