AA major 3rd — quality stays the same, size inverts
BA minor 3rd — size changes (6+3=9), quality flips from major to minor
CA perfect 5th — quality becomes perfect when inverted
DAn augmented 4th — the tritone is the inversion of a major 6th
Apply both rules. Generic size: 6 + ? = 9, so ? = 3 — it becomes a 3rd. Quality: major inverts to minor. Therefore a major 6th inverts to a minor 3rd. Option A fails to apply the quality-flip rule. The sum-to-9 rule and quality-flip rules must both be applied together; neither alone gives the correct answer.
Question 2 Multiple Choice
A melody and bass note are a perfect 5th apart, with the melody on top. The bass note is moved up an octave so it is now above the melody. What interval do they now form?
AA perfect 5th — 'perfect stays perfect' means the size is also preserved
BA perfect 4th — size changes (5+4=9) but quality stays perfect
CAn augmented 4th — inverting a 5th produces the tritone
DA diminished 5th — quality flips when the voices cross
Option A is the classic trap: 'perfect stays perfect' refers to the quality (the word 'perfect'), not the numeric size. The size still changes by the sum-to-9 rule: 5 + 4 = 9, so a 5th inverts to a 4th. Since perfect quality is preserved under inversion, a perfect 5th inverts to a perfect 4th. The rule is: number changes (add to 9), quality follows its own pattern (major↔minor, perfect stays, aug↔dim).
Question 3 True / False
An inverted interval contains the same two pitch classes as the original interval, just with their registers swapped.
TTrue
FFalse
Answer: True
Inversion moves one note by exactly one octave — no new pitches are introduced. If the original interval is C up to E (a major 3rd), the inversion E up to C (a minor 6th) still involves only C and E. This shared pitch-class content is why inverted intervals have a sonic connection and why theorists in some contexts treat an interval and its inversion as related — they literally contain the same notes, just voiced differently.
Question 4 True / False
The inversion of a major 2nd is a major 7th.
TTrue
FFalse
Answer: False
The size rule is correct: 2 + 7 = 9, so a 2nd inverts to a 7th. But the quality flips: major inverts to minor, not major. A major 2nd inverts to a minor 7th. A student who remembers the sum-to-9 rule but forgets the quality-flip will make exactly this error. To get the full answer, both rules must be applied: size follows the sum-to-9, and quality follows the major↔minor / perfect↔perfect / aug↔dim pattern.
Question 5 Short Answer
A student says 'interval inversion just flips the interval upside down, so the two sounds are completely unrelated.' What's right and what's wrong about this?
Think about your answer, then reveal below.
Model answer: The student is right that the interval is flipped — one note moves an octave, changing which is on top. But wrong that the sounds are completely unrelated. An inverted interval shares the exact same two pitch classes as the original; only the voicing changes. A major 3rd (C–E) and its inversion, a minor 6th (E–C), both contain C and E — they are closely related in pitch content despite sounding different.
The misconception that inversions are unrelated sounds prevents understanding of why chord inversions are considered variants of the same chord rather than entirely different harmonies. The sum-to-9 and quality-flip rules tell you precisely how the interval name changes, but the preservation of pitch-class content is what ties the original and its inversion together sonically and functionally. This connection is foundational for understanding voice leading and counterpoint.