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Inverted Chords: A closer look ...

Interval -1 = ???

What a chord inversion is was part of one of the last sessions. We will now go one step back and see what happens if a single interval is inverted. The best way to show this in a table again. All we do is take a single interval, inverting it and trying to find some rules.

Interval

Inverted interval

1. C - C# = 1 - b2 C# - C = 1 - 7
2. C - D  = 1 - 2 D - C  = 1 - b7
3. C - D# = 1 - b3 D# - C = 1 - 6
4. C - E  = 1 - 3 E - C  = 1 - #5/b6
5. C - F  = 1 - 4 F - C  = 1 - 5
6. C - F# = 1 - b5 F# - C = 1 - b5
7. C - G  = 1 - 5 G - C  = 1 - 4
8. C - G# = 1 - #5/b6 G# - C = 1 - 3
9. C - A  = 1 - 6 A - C  = 1 - b3
10. C - Bb = 1 - b7 Bb - C = 1 - 2
11. C - B  = 1 - 7 B - C  = 1 - b2

I think you would have expected these results because it's only a question of simple arithmetics. However, there are some rules for inverting intervals:

Four rules, not that difficult to remember, will guide us throught chord inversions. One last question: why does the diminished interval stay if inverted? Because this is the center of a scale, also called the tritone.

Analyzing inverted chords

Some steps back: Three-Note-Chords have two inversions, the first where the 3rd is the lowest note and the second where the fifth is the lowest note. Correct?

Aren't you curious how the interval structure of an inverted chord looks like? No? You are not a serious bass player, bass players are always interested in boring things .

The whole time I am assuming that what is valid for the C major scale is also valid for all other major scales. But that's the way it is. If you dont believe it try what we have done in the previous chapters with any other major scale. But dont blame it on me if your girl/boy friend starts looking for another companion.

Back to the question how the interval structure of a chord changes when inverting the chord, trying to find the answers, here for three-note-chords:

C major chord

Basic form

First inversion

Second inversion

C  E  G

E  G  C

G  C  E

This could be
another chord with
E as root

This could be
another chord with
G as root

So we have to analyze the interval structure for the inversions. Ok, I will do it for you:

C  E  G

E  G  C

G  C  E

Two triads:

First inversion:

Second inversion:

C - E = 3,  
E - G = b3

E - G = b3,
G - C = 4

G - C = 4,
C - E = 3

So the inversions are still a Cmaj chord but the intervals are not only triads. And the inversion type is only defined by the note which is the lowest one, so the inversions could also look like this:

C  E  G

E  C  G

G  E  C

Two triads:

First inversion:

Second inversion:

C - E = 3,  
E - G = b3

E - C= #5/b6,
C - G = 5 

G - E = 6,
E - C = #5/b6

And this very different interval structure is the reason why inverted chords sound so much different form the standard chords. They contain 4ths, 6ths and thirds. If you have tried the intervals on your bass and experienced the very different mood of each interval you will understand why the whole sound changes. Analyzing the transitions of intervals in inversions will also lead into a set of rules how and which intervals become 3rds, 4ths and 6ths. We will skip this here.

Summary

This was a lot of theory but I think this helps to understand a lot of things when you buy more advanced books and tutorials. One last chapter I would like to add. When we talked about harmonization of a scale we already had the most important parts for progressions. And after this we will stop with theory, or better said: we will apply theory.

Exercises

1. How many inversions are possible for four-note-chords (very easy)?
2. Can you find the rules for interval transitions in inverted chords (very hard)?