Inversions of Musical Intervals

When the lowest note (root note) of an interval or chord is shifted one octave higher, or if the highest note of the same is shifted one octave below, the interval or chord is said to have been inverted.

When the shift is only of one interval, the inversion is simple, while if the note being shifted is moved more than an octave the inversion is termed compound.

When we invert the interval or chord, new intervals are formed and the lowest (bass) played note changes to become the highest pitched, or vice versa. As this shift is by one whole octave, the changes have a certain relation with the original chord or interval. It is simple Mathematics. Let us consider the intervals P4 3rd (5 semitones from unison) – moving the root up by an octave makes this P4 note the new bass. The root is now (12-5=) 7 semitones from it, making the inverted interval a perfect 5th.

Similarly, we can deduce the following dicta about the quality of the interval –

1. 2nds become 7ths, 3rds become 6ths, 4ths become 5ths, and so on till, obviously we reach our own alteration of making root into octave
2. Any minor interval (m2, m3, m6, m7) becomes a major interval and vice versa
3. A perfect interval remains perfect
4. An augmented interval becomes diminished and vice versa

http://basicmusictheory.blogspot.com/2009/10/inversions-of-musical-intervals.html

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Inversions of Musical Intervals