Interval inversions : When the top member of an interval is moved to the octave below the bottom member ( or vice versa ), the interval is said to be inverted.
Just wondering…I know nothing about music theory, but I thought does it mean that the interval changes in relation to the other two notes? So taking joules example C major in first inversion is stacked E-5,G-5,C-6. The distance between note G and C is 5 semitones (perfect 4th). When you move the top note down an octave to become C-5,E-5,G-5, the interval between C and G is now 7 semitones (perfect 5th). Likewise a distance change between E and C. That’s how I kinda interpret it, but I could be wrong.