How to think of Intervals and their Inversions

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?

@ianbassett Thanks and love the new avatar, so fancy!

I am learning more about inversions and understand that there are two types: First and second - with each of those just replacing the triad’s bass note with either the 3rd or 5th respectively. Is that correct? In the musical toolbox, what are some of the main reasons you would invert a chord? Does it change the “color” of the music?

Thanks man!

For intervals - yes, for standard triads there is first and second inversions. If you add chord tones on (such as the 7th, which is very common) you get third inversion, and so on. That is correct - you only have to know what the lowest tone is in order to know what inversion you are at. Our ears hear from the bass note up, so however the chord is organized on top of the bass (in terms of naming your inversion) is inconsequential so long as the chord tones are there.

There are lots of reasons you would choose to invert a chord. Inversions give you the harmony you might need to fill in the puzzle, but often have a softer impact. They generally tend to indicate “travel” more than always using the root, so if you want to keep something moving you can invert your chord instead of giving it the solidity of a root in your bass. From a “good harmony” perspective, you can also use intervals to avoid parallel fifths and octaves. It gives you the chance to spell chords out differently so you aren’t stuck (in some cases) with parallelisms.

Finally, you may have a bass line that you want to do, and it may have some descending or ascending step-wise motion. It’s hard to maintain all the rules of voice leading in those cases (as mentioned above, parallelism with adjacent chords is a concern) so you can harmonize using chords that are farther away, but use the inversions of those chords to grab bass notes that maintain step-wise motion in the bass.

From a guitarist standpoint, if you are playing with a band, you may not need to play your full chords all the time. Having a bit of knowledge about inversions gives you the option to play thinner chords and grab only the tones you need if your bass player is covering the lower register for you.

I’d love to hear more about this, perhaps it’s a topic for another post.

Is this why power chords exist?

Ah yes. The rules of voice leading - most definitely will post a topic about that in the future.

Not really, power chords are more take one note and “fatten it up” by actually ignoring the voice leading rules mentioned above. You get the root and fifth (and no major/minor harmony) which when played in succession with other power chords gives the illusion of a “fat note” rather than hearing roots and fifths together. The reason to avoid parallel fifths and parallel octaves is your ear loses the sense of individual voices, which in power chord playing (made up of parallel roots fifths and octaves) you do exactly that. It’s a stylistic choice that works well for “power” but not for vocal independence.

I was referring more to the approach of say, playing a D major chord only from the 3rd (g string) up if you have a bass player playing a D. Not the sexiest example I could think of, but you get the idea. You’re not actually playing the root in the bass, but since someone is you can get away with a thinner chord on top. It can be useful for note choices based on ease of playing, string grouping, or wanting to separate voices from the lower octave just as a few examples.