I am learning 7th chord inversions and realize that the 3rd inversion of a minor 7th chord is a chord with a 4th and a 2nd above the bass. From learning a lot about sus chords recently, I can't help but think that there must be some kind of a similarity between the two since they are both chords with a maj 2nd and P 4th above the bass. I couldn't find any info about this so perhaps I am wrong and they are actually very different chords?
...since they are both chords with a maj 2nd and P 4th above the bass...
That will only be true for minor seventh chords and half diminished seventh chords. It's not true for major seventh and dominant seventh chords.
Dm7/C(omit 5) superficially is similar to
C(sus2)(sus4)(omit5). But, notice all that parenthetical commentary in the chord symbols? We need to add all that detail to voice the chords partially, to get the two chords to look the same. It matters a lot that you omit the fifth for both chords, because this is exactly what creates the ambiguity. If you had the chord fifths, then you could tell unambiguously what is the root, and from there you could say whether the other tones were chord tones or non-chord tones. Basically, a root and fifth above will help you sort out the tones in a tertian stack.
I think the rest of this comes down to voice leading and looking at the next chord to make clear what the partial chords actually function as. We want to know what is a third and what is a seventh. The tones in ascending order are
C D F. If
C is a root, then there isn't a third or seventh, the
D F are suspensions.
F descends to
D descends to
C and we resolve to another partial chord of
C major. In terms of thirds and sevenths and the notion this is a suspension we should expect to look at the previous chord to see the
F actual was a chord tone, and if so, it commonly would have been a seventh, like the
F in a
G7 chord. If
D is the root, then
C is the seventh and it would resolve down to
B in the next chord, a likely partial
Bdim functioning as dominant.
So, the point of this is if you omit chord tones it can make chords ambiguous. The way to make chords clear is to either:
- voice chords fully with chord tones
- use typical voice leading to make the role of each voice tonally clear.
If you put these into Roman numeral analysis you have either
C: I with
2-1 suspensions - a tonic chord, or a
C: ii4/2 chord - a subdominant. So, when the harmonic context is sorted out they are two very different chords.
Another thing that may interest you is the harmonic pattern called the quiscenza. It's a tonic pedal with figured bass of 4 chords above it
5/3. Or, in jazz symbols
C. The third chord is the one that matches your
4/2 type. But, interestingly, you wouldn't really call it a suspension, because in this case the non-chord tone is the pedal bass. So, the interval stack matches the
4/2, but the voice leading details are different.
On the assumption that you mean major seventh chords, rather than any of the (several) other seventh chords:
All chords will have intervals between their notes, that's the nature of them, and our quest to make sense of how various notes fit with others.
The fact that there are two similar intervals that occur in sus and maj.7 chords is co-incidental. Let's take C maj.7. CEGB, in whatever configuration. Those particuar notes won't make any sus chord, they simply make C maj7.
Consider that a major triad contains M3 and m3. A minor triad contains m3 and M3! That certainly doesn't make them similar! They are, in your words 'very different chords'!
Probably you're over-thinking things. The intervals between consecutive notes in any chord are the telling ones. Or more accurately, the interval each note has in relation to the root of the chord.
There are very few chords which have more than one incarnation. Two come to mind - minor 7 and major 6 -as in Am7 has the same notes as C6; and m7♭5 and m6 - as in Am7♭5 has the same notes as Cm6. And of course several diminished and augmented chords, for obvious reasons there.
There is a similarity between sus2 (hate that) and sus4 chord make ups, but that's a story for another time.
All seventh chords, regardless of type, in third inversion will have a second and a fourth above the bass. Since sus4/2 chords also have a fourth and a second, there is a trivial similarity at that level.
If one is using chord symbols for the purpose of indicating the notes in a chord, then, in theory, it doesn't matter if one calls [B♭ C E♭] C-7/B♭ or B♭sus4/2.
What distinguishes them is chord function.
Given the above example, suppose the chord after [B♭ C E♭] is [A C E♭ F]. In that case, we have a minor seventh chord moving to a dominant seventh chord — typical of a major ii-V progression, for example. So to best convey the chord function, it should be named C-7/B♭ followed by F7/A.
However, suppose the chord following [B♭ C E♭] is [B♭ D F]. In that case, it's clear the first chord is operating as a suspension. It would be more appropriate to name the chord B♭sus4/2, because this gives a hint of what's coming next: B♭maj.