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I'm watching the below video about the C dominant 7th chord (C E G B♭) and its inversions. At approximately 0:40 he starts to show the 1st inversion:

I would have expected a 1st inversion to be: E C G B♭ (i.e. we move the 3rd to be the bass but otherwise the other notes are in "order").

But instead he says 1st inversion is: E B♭ C G and I don't understand why it goes from the E to the B♭?

I'd really like to understand this concept and how it works (I'm not sure if triad inversions — which I thought I understood — are maybe worked out differently for sevenths?)

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up vote 4 down vote accepted

The "first" part of the first inversion means the first note that is not the root (aka the third) is the bass note so in this case, all first inversion is telling you is that the E is in the bass instead of the C. The order of what notes come next is not really important. A more in depth explination about seventh chord inversions can be found here.

In general when talking about chords, they are treated more like sets where only what the bass note of the chord is distinguished and everything else as long as it is there is fine.

One example you can think about on guitar is when you play an open E major chord, you play the notes E, B, E, G#, B E from bottom to top. The fact that the notes aren't in the the exact order of the spelling of the chord (E, G#, B) and that there are multiple E and B notes does not matter when talking about the chord only the thing that changes is the voicing of the chord.

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aha! OK so that's good to know! Wow that was quick and easy thank you :-) – Integralist Mar 5 at 19:13
1  
It's also good to know what 'voicings' mean now as well! – Integralist Mar 5 at 19:24

You need to understand the difference between close and open voicings. In close voicings the notes are arranged in thirds or seconds. Inversions of close voicings are created by moving the lowest note up by one octave. So the close voicings of C7 are

C E G Bb (root position)

E G Bb C (first inversion)

G Bb C E (second inversion)

Bb C E G (third inversion)

Note that on the guitar most of these voicings are (close to) unplayable because they would require very wide stretches.

The type of voicings shown in the video are called drop-2 voicings. They are very easy to play on the guitar, and they also sound good. To create a drop-2 voicing, you take any of the above voicings and drop the second note from the top by one octave. So the first voicing above C E G Bb becomes G C E Bg (by dropping the second note from the top, the G, to the bass). In this way you can create all the voicings shown in the video.

As pointed out in another answer, for open voicings (and drop-2 voicings are open voicings), it is the bass note that determines the name of the inversion. So for a C7 chord, the note E in the bass means that it is the first inversion, regardless of the arrangement of the other notes in the chord.

Another popular type of voicing on the guitar is the drop-3 voicing, where the third note from the top is dropped. So, e.g., the close voicing C E G Bb becomes E C G Bb (that's the one you expected to see as the first inversion!). Unlike drop-2 voicings, drop-3 voicings are usually not played on four adjacent strings, but the bass note is played on either the low E or on the A string, and then one string is skipped, and the remaining three notes are played on the next three adjacent strings. So the voicing E C G Bb would be played as (from low to high)

12 X 10 12 12 X

or

X 7 X 5 8 7

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I'm assuming it doesn't matter what order the notes after the dropped note is played. e.g. if playing Amaj7 (A, C#, E, G#) and I make a drop 2 voicing (E, A, C#, G#) I assume that the order of A, C# and G# wouldn't matter (so I could attempt to play: E, A, C#, G# in that order - closed voice - or maybe E, C#, G#, A - open voiced - and it would still be considered a 'drop 2 voicing'). Is that right? – Integralist Mar 14 at 15:38
    
@Integralist: No, that's not right. A drop-2 voicing is constructed from a close voicing by dropping the second note from the top. Your last example E - C# - G# - A is actually a drop-3 voicing, constructed from the (close) first inversion of Amaj7: C# - E - G# - A => (drop-3): E - C# - G# - A – Matt L. Mar 14 at 16:12

Generally, the only note whose position in the chord matters is the bass note. It's the note that determines if the chord is in root position or in some inversion. After that, the other notes (in our case C,G and Bb) can be in any order you want and the result will be the same. The different ways you put these notes are called 'voicings' and it's good to know different ones so that you can play the same chord over and over again and give it color by changing the voicing.

So, you will look for ways that are handy. It might not be really practical to play E on the bass and the C,G,Bb in that order, thus you'll have to mix them up.

Also, putting E and Bb that close together creates the nice dissonant sound of the dominant 7th chord which jazzists love. If you put them further apart, the dissonance would still be there, but it'd be more subtle.

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Inversion is determined solely by the lowest note. The rest is voicing - close position or extended position.

Guitarists have a limited choice of voicings, defined by the possible "shapes" their fingers can reach. Sometimes if they can get the right note on the bottom and the right one in the melody, that has to be considered a result! Keyboardists have rather more scope to achieve the desired harmony, desired voicing AND desired voice leading. Get into sequencing or orchestrating, you can have EXACTLY what the music requires!

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Great answer, straight to the point and the keyboard/guitar difference is immediately what came to mind. – Matthew Read Mar 5 at 20:09

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