These chords are essentially 9sus4 chords.
E.g., an F/G has the notes G F A C which are with respect to the root G 1 b7 9 4
The only note missing from a complete G9sus4 chord is the fifth (D).
Leaving out the fifth does not change the quality or basic sound of the chord.
You can get the fifth of the G9sus4 chord if you use Dm7
/G instead of
F/G. However, the function of these two chords is the same and they are interchangeable.
You find both versions frequently in jazz lead sheets.
Another frequently used option is to add the major seventh to the top triad, i.e., Fmaj7/G, which would give you a G13sus4 chord.
These chords are used extensively in modern jazz and advanced pop music.
Read more about this type of chord in this blog post .
The vanilla example for the application of this type of chord is the piece Maiden Voyage by Herbie Hancock.
music.stackexchange.com/users/9724/Matt L.
In a jazz context, Dom's answer is perfect.
However, I also want to say that this chord has become extremely common in pop/rock piano-driven music, for example Elton John, Billy Joel, and Stevie Wonder.
And especially in musical theater of this style, for example Jason Robert Brown, Stephen Schwartz, and the "straight to off-off-Broadway" duos like Kerrigan-Lowdermilk and Salzman-Cunningham.
In this context, when you have a chord like F/G resolving to C, I think the simplest explanation is that it's primarily an F chord (and thus you have a plagal cadence), with a 5->1 in the bass that strengthens it a bit by adding a bit of dissonance to be resolved, plus outlining an authentic cadence.
If you think of it this way, then F/G is really the end of the story.
It's an F chord, with a G in the bass.
music.stackexchange.com/users/10290/MattPutnam
They are called "Slash chords".
Often they exploit the fact that just about ANYTHING can act as a dominant if rooted strongly by the dominant note.
You could analyze all the chords here as some flavour of G chord.
But slash notation is much more helpful.
You could also describe this sort of thing as various chords over a "dominant pedal".
music.stackexchange.com/users/17003/Laurence Payne
It does get called an 11th.
As in, for example, E,G#,B over an F# bass is F#11.
Not an E based chord as expected, but F# (root), E (b7),
G# (9), B (4 or 11)
A nice example of several of these is David Nichtern's 'Midnight at the Oasis'.
Another way to look at it is an 'E add 2' chord.
In this case, in first inversion, putting the F# at the bottom.
Not a sus 2 which takes the 3 out and puts 2 in instead.
music.stackexchange.com/users/2808/Tim
There isn't really a name for these chords, but there is a reason they are used and that may allude to what someone can call them.
These chords are way more quartal/quintal in nature.
Let's look at the F/G and look at how the notes compare to G as looking from the bass note of each and since the 5th of the bass note is typically implied we'll include the D also.
Notice how we get a quartal stack of G - C - F and a quintal stack of G - (D) -
A looking at G as the bass.
We also can add both together
so it looks like the quartal stack of F - C - G - (D) - A or the quintal stack of A
- (D)
- G - C - F .
This shows that the chord is completely quartal or quintal in nature
In general quartal and quintal chords don't really have names besides the 6/9 chord which is very quintal in nature.
Since the full quartal stack root is also the root note of the chord in the slash chord, I'd call it a second inversion quartal quintad .
It's a mouthful, but accurate.
music.stackexchange.com/users/7222/Dom
I agree - as a genre they are often called slash chords.
Though if you want to instruct someone to play e.g.
F/G - you could say play "an F over G".
I've heard a few people use this.
music.stackexchange.com/users/26787/Daviiiide
Chords like F/G and C/D are really quite common in jazz, blues and soul music yet I have never heard or been able to find a concise name for them.   To be clear, I am referring to any major (or indeed minor) triad with the chord's supertonic in the bass.  I hope someone has heard of a term for these even if it is not an official term.
Is there a term for chords like F/G and C/D?
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music.stackexchange.com/users/8482/Tim Hargreaves
Chords like F/G and C/D are known as Slash chords. Often they exploit the fact that just about ANYTHING can act as a dominant if rooted strongly by the dominant note.  You could also describe this sort of thing as various chords over a "dominant pedal".  They are called "Slash chords".  
Chords exploit the fact that anything can act as a dominant if rooted strongly by the dominant note. They are called "Slash chords" Chords are often played over a "dominant pedal"