**Interval inversion** refers to the process by which the notes of an [[intervals|interval]] are rearranged so that the lower note becomes the upper note and vice versa. **Example 1a** shows the inversion of a third (F–A), where the lower note F is transposed one octave higher, resulting in a sixth (A–F). As shown in **Example 1b**, an interval and its inversion (or complement) form an octave. **Example 1.** Major third and its complement. ![[example interval inversion major third and its complement.png]] As noted above, the [[interval size|size of an interval]] changes when it is inverted. For intervals smaller than an octave, the size of the new interval can easily be determined by subtracting the size of the old interval from 9. This is known by some as the “rule of nine.” As shown in **Example 2** below, when inverted, a 2nd becomes a 7th, a 3rd becomes a sixth, and a 4th becomes a 5th, and vice versa. **Example 2.** Simple intervals and their complements. ![[example interval inversion size.png]] We can generalize the information above even further by identifying three classes of mutually invertible intervals: 1. 2nds ↔ 7ths 2. 3rds ↔ 6ths 3. 4ths ↔ 5ths In addition to changing size, most intervals also undergo a change in quality when inverted. Major intervals become minor intervals and vice versa (**Example 3a**). Augmented intervals become diminished intervals and vice versa (**Example 3b**). However, perfect intervals remain perfect (**Example 3c**). **Example 3.** Change in quality ![[example interval inversion quality.png]]