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Let's get something cleared up right away: slash chords are *not* different from the chords you already know. When you hear someone using the term slash chords, this person is simply applying a different way of looking at an existing chord.
Example: E7 can be written as E/D. Now, hold your horses before you go and play this. That E/D is a pretty ugly E7. In other words, it really doesn't sound like an E7. It isn't a "proper" E7. It doesn't get invited to E7 Christmas parties, and A would be mortified at the thought of being preceded by this E/D. Why? We're getting away from the main point, but it's important to explain: ya don't want to have the 7th of a dom 7 in the bass. You want the first or the fifth. In this case, that means the E or the B.
Okay. Back to the E/D. What's great about notating E/D is that, unlike reading "E7," reading "E/D" gives you a clue about the voicing of the chord. That is, you know the D is in the bass. The "E7" notation doesn't tell you that.
Where would you see slash chords notated? You'll see them all over the place, but you'll see a lot of them when the composer is *creating a melody in the bass line* -- especially a chromatically descending bass line. Let's illustrate this:
Check out that first chord. What the heck is that? Well, if you forget about slash chord notation for a moment, you might call it a Gmaj#11, add 9, or something like that. But, who wants to read that?
Bring our memory of slash chord notation back into your mind, and you'll call that first chord simply a F#minor/G . Highly hip. That's a heckuva lot cleaner looking than Gmaj# blah, blah, blah, isn't it? And, the slash chord notation also communicates more clearly the true progression: it's just a ii-V-I in E. However, running along the bottom of that ii-V-I, I decided I wanted a bluesey bass line. Play the tab again, and you'll hear what I mean: G, F#, E. We're in the key of E major, but I dig the blues, so I put the blue G in there.
The next time you're struggling with the chords when reading a piece of music, and you don't see the chords notated in slash notation, take a look at the bass line. Is there a melodic bass line going on there? If so, rewrite the chords in slash notation and see if they don't make more sense.
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