Inverted Intervals

So far we’ve only talked above ascending intervals, or intervals whose “base” or “root” note is the lower one. But what if the root note is the higher of the two notes? Then you get something called an “inverted” interval.

The formula to figure out an inversion is: 9 – (interval) = (inverted interval). However, once you’ve found the new number value, you must flip the major/minor and diminished/augmented quality of the interval. Perfect intervals stay perfect when inverted.

Ex: A major 3rd is an inverted minor 6th. 9 – 3 = 6, then switch the “major” to “minor.” A perfect fourth is an inverted perfect fifth because 9 – 4 = 5, and the quality (perfect) stays the same.

Here are some more:

Ascending intervalInversion
Minor 2ndMajor 7th
Major 2ndMinor 7th
Minor 3rdMajor 6th
Major 3rdMinor 6th
Perfect 4thPerfect 5th
Augmented 5thDiminished 4th
Perfect 5thPerfect 4th
Minor 6thMajor 3rd
Major 6thMinor 3rd
Minor 7thMajor 2nd
Major 7thMinor 2nd
OctaveOctave

 

The formula for inverting intervals works in the reverse manner, too. You can “un-invert” an inverted interval.

Ex: An inverted 4th is a regular 5th, and an inverted minor 7th is a major 2nd.

TL;DR: inverted intervals are intervals whose root note is the top note, rather than the bottom one. The formula for converting regular intervals to inverted ones, and vice versa, is: 9 – (interval) = (inverted interval). If the interval is major/minor, or augmented/diminished, you must flip its quality. Major becomes minor, augmented becomes diminished, perfects stay perfect.