Inverting Intervals

To invert an interval means to move one note (out of the two) up or down by an octave. For example, to invert a 3rd (C and the E above), I can move the C up an octave. This effectively puts the C above the E. So, the new order from lower to higher is E up to C. Furthermore, this creates a different interval: the 3rd became a 6th.

Here's a visual, which matches the style of a previous post on reading intervals from a staff:

When you invert an interval on the staff, its line/space category becomes reversed (same to different, or different to same). Click to enlarge.

You'll see that interval numbers of each inversion pair always add up to 9:

• A unison inverts to an octave (1+8=9)
• A 2nd inverts to a 7th (2+7=9)
• A 3rd inverts to a 6th (3+6=9)
• A 4th inverts to a 5th (4+5=9)
• And vice versa