A major sixth (M6) is inverted. What interval does it become?
AMinor sixth (m6)
BMajor third (M3)
CMinor third (m3)
DPerfect fifth (P5)
Interval inversion follows two rules: the size numbers sum to 9 (6 + 3 = 9), and major inverts to minor (and vice versa). So a major sixth inverts to a minor third. The common error is option B — choosing major third — which gets the size right (9 − 6 = 3) but forgets that quality flips: major becomes minor. Perfect intervals stay perfect (P4 ↔ P5), major ↔ minor, augmented ↔ diminished.
Question 2 Multiple Choice
A student hears a major third (C up to E) played, then hears the inversion voiced as a simple interval within an octave. What should she recognize?
AA major sixth — inversions of major intervals are always major
BA minor sixth — because major inverts to minor and 3 + 6 = 9
CA perfect fourth — because C and E are a fourth apart when rearranged
DA minor third — the same quality but a larger interval
A major third inverts to a minor sixth: 3 + 6 = 9 (size rule), and major → minor (quality rule). Option A gets the size right but forgets the quality flip — a major interval does not invert to another major interval. The quality flip from major to minor is the key recognition skill: the minor sixth has a distinctly more open, expansive sound than the compact major third that preceded it.
Question 3 True / False
Inverting a minor interval usually produces another minor interval.
TTrue
FFalse
Answer: False
Inverting a minor interval produces a MAJOR interval (e.g., minor third → major sixth; minor second → major seventh). The quality-flip rule states: major ↔ minor, augmented ↔ diminished, and perfect ↔ perfect. Only perfect intervals invert to the same quality. This is one of the most important rules of interval inversion and the most common source of error: students expect quality to be preserved and are surprised to find it changes.
Question 4 True / False
The interval numbers of an interval and its inversion always sum to 9.
TTrue
FFalse
Answer: True
For simple intervals, the sizes always sum to 9: unison (1) inverts to octave (8), 2nd inverts to 7th, 3rd to 6th, 4th to 5th. 1+8=9, 2+7=9, 3+6=9, 4+5=9. This is because an octave spans 8 diatonic steps, and splitting it into two intervals that together fill an octave always gives pairs summing to 9 (not 8, because both endpoints count the starting note). Memorizing the complementary pairs — 2nds/7ths, 3rds/6ths, 4ths/5ths — is the practical takeaway.
Question 5 Short Answer
Why does inverting an interval change its quality (e.g., major to minor), and how does this affect the sound of the inversion compared to the original interval?
Think about your answer, then reveal below.
Model answer: When you invert an interval by moving the lower note up an octave (or the upper note down an octave), the distance changes and with it the arrangement of half steps. A major third (4 half steps) inverts to a minor sixth (8 half steps): the half-step count is different, producing a different quality. Major intervals have one more half step than the corresponding minor interval, and inversion redistributes those half steps across the octave complement. Sonically, the inversion sounds distinctly different — a minor sixth is more open and expansive than the compact major third.
The quality flip happens because quality is determined by the exact number of half steps, not just the diatonic letter span. When you invert, the half steps that made the interval 'major' get redistributed across the octave. This is why ear training for inversion requires listening for quality, not just size: the two intervals in a complementary pair (e.g., M3 and m6) share no perceptual quality — they sound different and must be recognized as distinct sounds that happen to be mathematically related.