The Complementary Interval
By complementary interval, we mean the inversion of an interval. Simply take the upper note and move it down an octave.
For this article, you should already be a little familiar with intervals and also be able to distinguish and hear them.
For example, the complementary interval of a fourth -> is a fifth.
Does it even sound the same?
It actually sounds the same. Provided you automatically recognize octaves.
In the first measure, we have a perfect fifth. From C to G. In the second measure, we play from G to C.
Now there are two ways to see or hear these intervals. On the one hand, I could say in the second measure, it’s a perfect fourth upwards, from G to C.
Or, it’s a perfect fifth, from C to G (i.e. downwards).
But why is that so?
Fortunately, there are “only” 12 notes. Within a scale only seven (there are also scales with more or less! For example, the pentatonic has only five notes).
Generally, we think in intervals, so for example, the fifth of C is G. Or the minor third is minor and the minor seventh belongs to a dominant 7th chord.
But there are also ways to think differently. Namely in half steps. For example, instead of thinking of a fifth, you think of 7 half steps. But I would start with the normal intervals and either not do the half steps at all, or sometime, as soon as the normal way becomes too easy! :)
Like a die with 6 faces, the complete number must always add up to 7. So if the die shows you a 6, then you know that on the opposite side there MUST be a 1.
With intervals, this number must always add up to 9. So if you hear/see a perfect fourth (4), the inversion of it must be a perfect fifth (5).
If you have a third (3), the counterpart must be a sixth (6).
Minor and major intervals
Now, as always, there is a problem! Namely, we still think a bit in half steps. We just name them differently.
Minor intervals must be major intervals in the inversion. So complementary intervals are then really complementary if you also include the half steps.
So the complementary interval of a minor third must be a major sixth. With the fourth and the fifth this is not necessary, since both are “perfect” and have neither major nor minor. The counterpart to this is called diminished and augmented for the fourth and fifth.
The inversion of an augmented fourth (#4) must therefore be a diminished (b5) fifth (which, incidentally, is exactly the same note in both cases!).
List of complementary intervals
Each measure starts with a major or perfect interval. Then the complementary interval to it. The root is always C.
Here each measure starts with a minor interval. The root is always C.
