Replacing "D-minor" and "G-Major" with "F-major" and "G 7 no 5" (in a 2-5-1 chord progression)?

Question

This "warm-up" video first goes over what it calls as "bookkeeping" (from 21-to-35).

They establish that the "warm-up" will take place in c-major and will follow the chord progression: 2-5-1

So first she begins by playing the D-minor, G-major, then C-major.

Then she says that she's "minding the voice leading", and switches to playing a set of new chords that are not actually inversions of the previously played chords. (I had to look up what chords she plays) It appears as though she's playing: F Major, "G 7 no 5", and then C-major.

It sounds quite nice and similar to the previous progression, but I have no idea how someone comes up with that, or how this is still a "2-5-1" progression.

Any intution or understanding here would be greatly appreciated!

Answer 1

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The necessary observation is that her left hand is always playing the roots of the ii-V-I progression: D-G-C.

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Going step by step through her modifications:

1. ii-V-I in root position (Dmin - Gmaj - Cmaj)

"Ok let's mind the voice-leading"

2. Looking only at her right hand, she appears to play Fmaj - G7(omit 5) - Cmaj. However, you have to consider her left hand. In actuality, she's playing Dmin7 - G7 - Cmaj. It's okay to omit the 5 in a seventh chord, because that pitch contributes relatively little to the overall sound of the chord.

"Better"

3. Now she plays Dmin9 - G7add13 - Cmaj9 omitting the 5 of all three chords. Again, she's using standard piano voicings for those chords.

"Still missing something..."

4. Here she just adds pedal and a gentler touch to the chords.

"Better" #2

5. Finally, she re-voices the chords again and plays Dmin7(include 5) - G7(omit 5) - Cmaj7. Again, if one considers only her right hand, then she's playing F/C - G7(omit 5) - Emin/B. But one has to include all tones, including the left hand, to interpret chords, so in fact she's playing an ordinary jazz ii-V-I progression.

"Yes..."