After studying pop music composition for a while I noticed that many composers use slash chords in their music. How do I use those in my own composition? When is it more preferable to use slash chords than traditional chords?
Here are some cases where slash chords might be used:
The most boring case. The bass holds (or repeats) a note while the harmonies change. Useful in everything from bagpipe drones to the codas of Bach organ fugues.
Sort the reverse of the above. The bass is moving around while the harmony is staying relatively static, leading to passing tones and such.
You're probably already used to seeing these types of chords.
- 1st (3rd in bass) -- a slightly less stable version of the chord, with a strong desire for the bass to resolve stepwise upward to the root of the next chord. C/E wants to resolve to F.
- 2nd (5th in bass) -- an even less stable version of the chord, typically used as a passing chord, or in a "cadential 6 4" formula, as in classical music, where the bass stays put, and the upper voices resolve downward. C/G wants to resolve to G.
- 3rd (7th in bass) -- This inversion tends to slap you in the face, and has a feeling of things wanting to fall apart. The bass typically resolves downward to become the third of the next chord. C/Bb wants to resolve to F/A.
This is where things get interesting, and is what I think you're probably asking about.
Jazz-based styles, especially, are prone to building harmonies beyond 7th chords by stacking thirds. So you get 9th chords, 11th chords, even 13th chords. Often these chords will also omit notes. Sometimes it seems like just about any note can be thrown into a chord (sometimes even if its not in the scale) but I'm pretty sure that's not the case. A full discussion of chord extensions is outside the scope of this question, but here's how they can lead to slash chords.
First a simple case (that you wouldn't typically see): Let's say you have CM7 (C, E, G, B). This could technically be written as an E minor chord over a C (Em/C). If you play an E minor chord with your right hand, then add a C in the left hand, you can see how the CM7 chord retains some of the meloncholy "flavor" of the E minor chord, even though CM7 is technically a major. You can try this with other seventh chords as well, playing all but the bass note, then adding the bass note.
Now lets take it up a third higher. Say you have a C9 (C, E, G, Bb, D), which is an extended version of a dominant C7. One possibility is to omit the 3rd completely, giving a Gm/C. Another possibility is to make the 3rd a suspended 4th, which gives a C9sus4: (C, F, G, Bb, D), or Gm7/C. Finally, you might choose to omit the 5th (G), giving a Bb/C. This might be the same situation as your Eb/F chord that you mentioned: you have the IV chord over the 5th scale degree. This specific combination is a common enough occurrence that wikipedia calls it a "jazz sus chord". Note that, classically, a sus4 chord would be expected to resolve, but that is not the case here. Instead, the dissonance is embraced, and the sus4 is used as a substitution for the dominant. Essentially, it acts like a dominant chord, but with less urgency (since there's no leading tone), seasoned with the "sweetness" of a subdominant IV chord. Since this is a dominant chord, it should resolve to a tonic. You could try resolving to an FM7 chord, (voiced as an Am/F), so the progression looks like C9sus4 -> FM7 (or in slash chords: Bb/C -> Am/F).
Hopefully the "mixing flavors" metaphor will give you an idea of how to approach experimenting with extended chords.
The most common way to play "slash" chords (more properly known as chord inversions) is to take a major chord and play it over it's III or V. However any chord with a non-I note as its bass note would be consider an inversion.
For example, the root note for the D major chord is the note D. So playing a D major chord with a root note that is anything but the note D would considered an inversion of D major.
John Mayer's Free Fallin is a cool example. The chord progression F - Bb - F - C. However John is inverting the F chord and playing it over an A note. He does it the whole song. It gives a sort of "suspension" feeling because your brain expects to hear an F chord over an F note, and the playing of the A gives it a some suspense.
Oh The Blood by Gateway Worship is another awesome example as it has two slashes in a row in the chorus. D/F# - C/E - G. You'll hear it at the start of the chorus at the 47 second mark. If you want a treat then wait for the bridge when Kari goes into super-angel-voice-overdrive.
By The Way by RHCP is a cool example. Right away the first chord is strummed 8 times and then inverted by playing the root note down 1 step.
And the classic, I'll Make A Man Out Of You from Mulan. It starts with Em - D/F# - G.
Really though, the best way to add this to your own writing is to listen to a butt-ton of songs and learn them. Add them to all your songs then listen to them. Your ear will tell you when not to use them.