What are mixed inversion practice tables?

Please have a look at the image below first, to see what a “mixed inversion practice table” looks like. I have attached a PDF file with seven of those tables. One for each tone of the major scale. Each table follows the same set of rules. The colored row holds a tone from the major scale that is always part of 4 different seventh chords. Those 4 chords are built upon the 4 tones that together form a descending seventh chord from the note in the colored row. For example, if you look at the first table, the colored row holds tone 1 from the major scale. If you go down a third in the scale, you’ll get tone 6. Down a third again, and you’ll get tone 4. Another third down, and you’ll get tone 2. So you’ll end up with: 2 4 6 1 , which is the 2 chord. If you build a seventh chord on each of those tones, you’ll note that all of them have tone 1 in them. On the other hand, if you’d built seventh chords on top of the tones that form the 1 chord (1 3 5 7), you’ll note that none of them use tone 1. (except for the 1 chord itself of course)

How to use those tables in your practice routine and why should you?

I use each different day of the week for a particular tone of the major scale. On Monday, I practice tone 1. On Tuesday I practice tone 2, etc. So on Monday I will play chord arpeggios from the table where tone 1 is in the colored row. I mostly practice to start from tone 1 in ascending and descending ways. On Tuesday I’ll do the same thing, but then using table 2.
After a week I have not only practiced all 7 seventh chords, but also their inversions. A common pitfall is to only practice seventh chords arpeggios starting from the root. With this practice routine, you are forced to learn them from any given tone within the chord. You also are practicing them outside the context of the chord itself. It is relatively easy to hear an inversion of a chord, when you are already playing it from the root for example. But when you play a random note and you are asked to hear the current note as the seventh note of the 3 chord, that is quite a challenge for your ears if you’ve never practiced it in such a way. And that is exactly what these tables are for.

You can download the PDF here.