Intervals can be tough. One thing you always have to think about (especially if you play a harmonic instrument) is what happens when you go “around the horn” (my fancy way for saying past the octave) and you need to maintain the same notes in your harmony. For example: if you play a power chord, you play the root, the fifth, and then the root again. But what is the distance between the fifth and the root, not the root and the fifth?
Read on, dear theoretician…
Interval Inversions Equal 9
All intervals are relative to another interval. The reason this occurs is because notes displace in different positions will have a different relative difference between the same notes, or in other words, the distance between C and D traveling in a single direction is a different distance between D and C. If we examine a C major scale we can see this more clearly
Before traveling, remember that you always count the note you are starting on. To go from C to D it is a single move traveling to the right, also known as a 2nd. If we wanted to play the inversion of those same two notes, we would have to travel 7 more moves to the right before we hit a C again. That distance is a 7th.
If we apply the same logic to all the notes excluding unison and the repeat of the octave:
A pattern emerges. Looking across between the root to scale degree column and the inversions column horizontally, the distances all add up to 9. 2+7, 3+6, 4+5, 5+4, 6+3, 7+2, all add up to 9. Therefore, subtracting the initial distance known from 9 will give you the distance of the inversion.
But wait…there is more! You want a video version you say?