What he's pointing out is that you can use multiple names (homonyms) for the same combination of notes.
For example, with three notes, C-E-G is obviously a C major chord. But you can also describe it as E minor, with the 5th (B) omitted, and a 6th (C) as the bottom note. In his notation, "Em/6 no 5"
I would read this as "E minor over sixth no five".
The notes are described in the first part of the item - "1 - 2 - 3 - 6", with each number describing the number of semitones to the next note. So if you were to start on B (I picked B because it results in no sharps/flats).
- B+1 = C
- C+2 = D
- D+3 = F
- F+6 = back to B
What Hober has done is, for each shape, he's picked the "simplest" name for that chord, then applied that to a root note of C, then used the notes in that chord as the basis for picking the root note for naming it other ways.
That's a bit complicated, so let's step through the example.
He's decided that 1-2-3-6 is most simply named as
X7/11 no R. That applies no matter what note
X is, but he's written
C7/11 no R.
- A C major chord - C,E,G
- Plus the dominant 7th - C,E,G,Bb
- Over the 11th - C,E,F,G,Bb
- Minus the root - E,F,G,Bb
... and you can see that it fits the numeric description:
- E to F is 1 semitone
- F to G is 2 semitones
- G to Bb is 3 semitones
- Bb back to E is 6 semitones
Then he picks what he considers the next simplest name for the chord:
Ym7/6 no 5.
Since he's already picked the notes E,F,G,Bb, in this case Y = G:
- G minor - G,Bb,D
- Plus the dominant 7th - G,Bb,D,F
- Over the 6th - E,G,Bb,D,F
- minus the 5th - E,G,Bb,F
... the same notes as
C7/11 no R.
Perhaps the easiest example is 2-4-3-3. He treats inversions as equivalent. So 4-3-3-2 is equivalent to 2-4-3-3. Experienced musicians can immediately see that the intervals 4-3-3-2 correspond to the third, fifth, dominant 7th, octave, so that's a
X7 chord. If X=C, that's
C7: C,E,G,Bb. Or you could call those same four notes
F#b9b5 no R.