2 
'Rule of 9'
Inversion offers a neat way of working out the names of intervals larger than an augmented fourth. If you remember the inversional relationships in the table above, you only have to memorize the interval types to the augmented fourth. If you have an interval larger than an augmented fourth, simply invert it, identify the interval, then invert that. For example, the interval DB flat is a sixth. Instead of counting semitones (half steps) to determine the type of sixth, invert it to B flatD. Now you have a third, you can count the semitones (half steps), four, and determine that it is a major third. Therefore, your original interval is a minor sixth, the inversion of the major third
For diatonicallynamed intervals, there is a useful rule applying to all simple intervals (that is those of one octave or less). The number of any interval and the number of its inversion always add up to nine. Thus a fifth (number 5) and its inverse or complement, a fourth (number is 4) add up to 9.
Where intervals are identified by ratio, (for example, a fifth may be expressed as 3/2), the inversion is determined by reversing the ratio and multiplying by 2, in this case 4/3, which is the ratio of a fourth. Multiplying them together gives an octave 3/2 x 4/3 = 2/1.
