Naming chord inversions

Question

I'm pretty new to piano (but not to instruments) and everything i learnt before was from watching videos or listening to someones play, rarely tabs. But now i decided to learn reading some scores and chords and other basic music theory.

I decided to learn Bach's prelude BWV 846, so i took the score http://www.sheetmusic2print.com/Media/Bach/Prelude-1-BWV-846.gif and someone's performance (learning starts at 1:18)

So he gives chords one by one : C, Dm7, ...

What I have learnt before is that Dm7 is 1,3b,5,7b but he plays C in the base, so it would be third inversion of Dm7. Is there no difference in saying: "now we play normal Dm7, and now we play it's third inversion"? I'm confused why he didn't write Dm7/C.

Do we only use slashes (like C/G#) when the base note is out of the chord (in C it is C E G)?

I'd really love to hear some explanation about this, because i'm confused about it for some long time. Cheers!

Answer 1

Slash chords have been around a while, and seem to have two interpretations. On one instrument - guitar, mainly, but also piano, the note after the slash says what the bottom note of that chord should be. If there's a bass player present, then that's what he'll play, and it doesn't matter much what the rest of the band do. Lots of music does not always use root 'inversions', but still doesn't put which to play. Yes, Dm/C is the 3rd inversion of Dm, and it could have been stated. It's more often used as a passing chord.

And the note after the slash can be any note out of 12. He does actually quote some slash cords, but seems inconsistent.