Understanding Intervals and Inversions
Picture the C major scale; C D E F G A B C. Count on your fingers from C to F. If you have enough fingers, you reached 4. Count backwards from C to F. This time, it was 5 steps away. The distance between C up to F is four steps, but if you count backwards it is 5 steps. An interval from C to F is called a perfect fourth. The interval from F up to C is called a perfect fifth. This is the confusing part: depending on which direction you go to reach a note (up or down) a different musical interval is created.
Examples of All Intervals
Interval Name  Notes  Example 
Unison  C to C 

Minor Second  C to D♭ 

Major Second  C to D 

Augmented Second  C to D♯ 

Minor Third  C to E♭  
Major Third  C to E 

Perfect Fourth  C to F 

Augmented Fourth  C to F♯ 

Diminished Fifth  C to G♭  
Perfect Fifth  C to G 

Augmented Fifth  C to G♯ 

Minor Sixth  C to A♭  
Major Sixth  C to A 

Augmented Sixth  C to A♯ 

Minor Seventh  C to B♭  
Major Seventh  C to B 

Octave  C to C 

When we take an interval of C up to F and move the F from the top to the bottom, we create an inversion. The resulting interval will have a different name entirely, although no notes have changed. An inversion is when you flip an interval and put the top note on the bottom. There is an easy formula for remembering the results of an inversion:
Inversion Formula: Flipping the Quality
Beginning Quality  Flipped Quality 
Major  Minor 
Minor  Major 
Perfect  Perfect 
Diminished  Augmented 
Augmented  Diminished 
Inversion Formula: Flipping the Number
Beginning Number  Flipped Number 
2  7 
3  6 
4  5 
5  4 
6  3 
7  2 
Note: in the chart above, if you add any beginning number to any flipped number, the result always equals 9.
When we “flip” our interval to create a new one, we can learn what it is by flipping both of its two properties: its number, and its quality. A major third interval, inverted, becomes a minor sixth interval.
Key Questions
 Which interval quality (major, minor, etc.) is symmetrical? (The same when it’s flipped)
 What is the inversion of a major interval?
 What is the inversion of a diminished interval?
 What is the inversion of a second?
 What is the inversion of a fifth?
 What is the inversion of a sixth?