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 An interval of a Perfect 4^th is five half steps above or below the starting note.

 From A to D is an interval of a Perfect 4^th

 How to Find Perfect 4ths Above and Below any Note.

You remember how to find a Perfect 5^th above or below a note. Just count two steps forward (above) or backward (below) in the Cycle of Thirds. To find Perfect 4^ths above or below a note just do the opposite.

 A Perfect 5^th above is two steps forward, therefore a Perfect 4^th above is two steps backward.

A Perfect 5^th below is two steps backward, therefore a Perfect 4^th below is two steps forward.

 If you want to see the structure behind why Perfect 4^ths are found in the opposite direction as Perfect 5^ths, study the illustration below.

 The Principle of Inversion

When the same note name that is a Perfect 5^th above a note is also a Perfect 4^th below the same note (such as the E’s above and below A in the preceding illustration), this is known as the principle of inversion. The interval of A up to E becomes inverted when you keep the same A but refer to the E below it (E up to A). Perfect 5ths invert to Perfect 4^ths. This is why you count in the opposite direction of the Perfect 5^th to find the Perfect 4^th. Because the cycle is in thirds, the note that is a perfect 4th above will be two steps backward, not forward. And a note that is a Perfect 4th below will be two steps forward. For example, if you look at the image above, two steps backward from A (counting in thirds) is F, then D. D is shown as a P4 above A.

 Finding Perfect 4^ths

Focus on mastering finding Perfect 5^ths first. Then just count in the opposite direction for 4^ths. To find a Perfect 4^th above D, remember that a Perfect 5^th above is two steps forward in the Cycle of Thirds, then just count in the opposite direction (backward) two steps in the cycle to G. G is a Perfect 4^th above D. A Perfect 4^th above E is two steps backward to A.

To find a Perfect 4^th below D, remember that a Perfect 5^th below is two steps backward in the Cycle of Thirds, then count in the opposite direction (forward) two steps. A is a Perfect 4^th below D. A Perfect 4^th below E is two steps forward in the Cycle of Thirds to B.

Remember that the bunny (B) is looking up to the fly (F), so when moving from B to F you must raise F one half step to F#. Also, the fly (F) is looking down at the bunny (B). This means that when moving from F to B you must lower B by one half step to Bb. 

 From B to F                 From F to B
Raise F 1/2 Step            Lower B 1/2 Step

 B# to F##                   F## to B#
B to F#                       F# to B
Bb to F                       F to Bb
Bbb to Fb                    Fb to Bbb

      
    Notice that when finding either Perfect 5^ths or Perfect 4^ths, you must always raise F and lower B. It works the same for both Perfect 5 ^ths and Perfect 4 ^ths.

 Summary for Finding Perfect 4^ths

First master finding Perfect 5^ths above or below a note. To find Perfect 4^ths just count two steps in the opposite direction. Remember that the signs match. If a Perfect 4^th below G is D, then a perfect 4^th below G# is D# and so on.

Exercise:

Fill in the blanks with the note that is a Perfect 4^th above the given note. Remember to count two steps backward in the Cycle of Thirds. Also, remember F to B (lower B one half step). Use the interval Answer Charts to check your answers. 

Exercise:

Fill in the blanks with the note that is a Perfect 4^th below the given note. Remember to count two steps forwards in the Cycle of Thirds. Also, remember B to F (raise F one half step). Use the interval Answer Charts to check your answers. 

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