EXAMPLE 1) 

1. Figure out the size.
* Ignore the sharps or flats when you count the size.
* Count each pitch, including the bottom and top.
C – D – E – F
so, the size is 4th.

2. Figure out the number of half steps.
The pitches within the range are C# – D – D# – E – F
(C#-D, D-D#, D#-E, and E-F),
so the number of half steps is 4.

3. To be a perfect 4th, it needs five half steps. This interval has four half steps in size 4, so it is a diminished 4th.

EXAMPLE 2)

1. Figure out the size.
* Ignore the sharps or flats when you count the size.
* Count each pitch, including the bottom and top.
A – B – C – D – E – F
The size is 6th.

2. Figure out the number of half steps.

The pitches within the range are Ab – A – A# – B – C – C# – D – D# – E – F – F#,
 so the number of the half steps is 10.

3. A major 6^th has nine half steps, but this interval has ten half steps in size 6. It is an augmented 6th.

EXAMPLE 3)

To build a diminished 7th on B:

1. Figure out the 7th from B.
B – C – D – E – F – G – A, 
so the top pitch should be A (or A something [A# or Ab]).

2. Figure out the number of half steps.
A major 7th has eleven half steps, so a diminished 7th has nine half steps.
B – C – C# – D – D# – E – F – F# – G – G#(or Ab)

3. Since the top pitch should be an A (or A something), the answer is Ab.