INVERSION

Inverting an interval means moving the lower note and octave above or moving the top note an octave lower.

When Inverted a:

Unison Becomes aOctave
Secondseventh
Thirdsixth
Fourthfifth
Fifthfourth
Sixththird
Seventhsecond
Octaveunison

The ordinal number of an interval plus the ordinal number of its inversion always adds up to 9

Unison 1+Octave8=9
Second2+seventh7=9
Third3+sixth6=9
Fourth4+fifth5=9
Fifth5+fourth4=9
Sixth6+third3=9
Seventh7+second2=9
Octave8+unison1=9

Since an interval plus its inversion is an octave the sum of both sets of half steps will always be 12 -

 If an interval has 3 half steps the inversion will have 9

IntervalPLUSInversionadds up to 12
012
111
210
39
48
57
66
75
84
93
102
111
120

QUALITY

The inversion ofPerfect isPerfect
MajorMinor
MinorMajor
AugmentedDiminished
DiminishedAugmented