# What implications do the formal rules of inversions have for suspended chords?

I understand about the relationship between run-of-the-mill suspended chords and inverting them. For example, I know a Gsus2 (`GAD`) is an inversion of Dsus4 (`DGA`). Whatever `ADG` ought to be called, other than Gsus2 in 1st inversion or Dsus4 in 2nd inversion, I'm not sure.

Now Wikipedia insists that a chord in 1st inversion must have a third as the lowest note and the root a sixth above it, which has implications for my assumptions. If there's an unusual chord like this...

...would it be correct to say it's in 1st inversion or not? Granted there is no third—E—so, by the Wikipedia definition, it falls short. Intuitively, though, it is. At least to me.

So if the answer is no, that's not 1st inversion, would I have to name that chord Fsus2add♭9,♯11,13? Or F13♭9,♯11sus2omit7? Or Fsus2,♯4add♭9,13?

Or what if the D were lowered one octave? Would it now be Cmaj9♯11sus4 in 4th inversion? Or would that also require E to be present?

(I know, I know... context. Please remember this question is purely about formal theory and the example chord is just an example.)

• "I know, I know... context." -- Well, context is important when naming chords. Also, I doubt that Wikipedia is the best source for learning music theory.
– user39614
Jan 23, 2018 at 17:15
• @DavidBowling Can you suggest a source that discusses how to name inversions of suspended chords, then?
– trw
Jan 23, 2018 at 17:33
• There is no mystery in how you would name an inversion of a suspended chord. If the 4th is in the base, it is in first inversion. Whether you should call such a collection of notes a sus chord or something else is another question. Classical harmony considers four triads (maj, min, aug, dim), so inversions of sus triads don't make sense in this context. Jazz harmony treats sus chords differently, and sus triads are commonly referred to, at least in practice. Context.
– user39614
Jan 23, 2018 at 18:18
• I don't see a discussion of sus triads in either Piston (referenced in the Wikipedia article) or in Nettles & Graf (The Chord Scale Theory & Jazz Harmony), but this Wikipedia article about sus chords does mention sus chord inversions.
– user39614
Jan 23, 2018 at 18:18

I think it depends on the musical context. It's first worth noting that Wikipedia also states:

Each suspended chord has two inversions.

...

Suspended fourth and second chords can be represented, in integer notation, as {0, 5, 7} and {0, 2, 7} respectively. The second inversion (quartal chord) is {0, 5, 10}.

So which is it? Rather than suggest that Wikipedia is contradicting itself, I simply think the page you cited is working within a limited musical context. Sure, genres might exist which restrict the notion of an inversion to triadic chords (by which I mean chords that contain the root, third, and fifth). But in many other musical contexts, a broader conception of inverting non-triadic chords is used, as the above citation shows.

So I think the answer depends on, e.g., whether you're in a classical theory course or a jazz theory course. I doubt you'll find a jazz musician who thinks that inversion, as a concept, can only be applied to triadic chords (pure triads or 7th chords). Then again, a chord as funky as Cmaj9(#11sus4) probably only exists in genres that permit the inversion of non-triads.

In close harmony, 1st inversion of a triad will have the third at the bottom, thus fifth next, and root a sixth above the lowest note. But after that, there is nothing to say which of 5 or root has to go where. Even with a four note chord - C7 for example, the 1st inversion will have 3rd under everything else.

Calling any chord xxxsus2/4 assumes the 2 or 4 will be replacing the 3. Otherwise it's an 'add 9 or add 11'.

Trying to name inversions of such chords may be a nice technical exercise, but in real terms not a great deal of use or help. Easier to show the dots...

Edit - in response to comment - let's take a fairly straightforward Cmaj9. C E G B D. In 1st inversion it'll have E at the bottom. Now let's take Cmaj7sus4. C F G B. Now, in 1st inv. there's an F at the bottom. If it was Cmaj7 add11, then it reads C E G B F, and the F is underneath. It's an interesting question, in theory!

• But a technical exercise is exactly what I'm trying to do here. Can you help with that?
– trw
Jan 23, 2018 at 17:32

I don't think there's a formal ruling on this (who would make one, anyway?) But it seems logical to name the inversion the same as if the 3rd WASN'T suspended.

As you say, many chords may be analysed in more than one way. Sometimes it's useful to work out which would be more appropriate. Other times it isn't.

Suspensions apart, my feeling is that when you have to name a chord in a way that requires 'omit 3rd', you're probably getting it wrong.