Is there a scientific or logical explanation to why these chords
"lead" to the specified chords,
Albrecht already answered as to the musical logic regarding 'leading.' Basically, half steps have a strong pull.
But I think something should be said about 'common patterns.'
or is it simply just a result of common patterns in popular music?
Yes, common patterns are important. In fact I think several of the options for progressions in the chart come from common patterns. But the chart doesn't explain the connection to such patterns.
This the following is a loosely organized list of some patterns you might look into:
- 'functional harmony' which groups chords in predominant, dominant, and tonic categories and defines a syntax of progressions from predominant to dominant to tonic.
- 'strong progressions' generally considered root movement by descending fifth, descending third (from the tonic), or ascending step (from IV to V)
- hugely important are 'harmonic sequences' where typically a two chord progression like a descending fifth or fourth is then repeated a step higher or lower, one very well known sequence is the circle of fifths.
- root progression by step is also used, but in classical style the chords will be in first inversion some refer to this as 'fauxbourdon', root position chords can also move by step but it is probably more common with pop styles
bVI bVII i is one example.
That isn't a complete list of patterns. It's just a starting point. But even from that short list certain things can be seen.
iii ii is considered a weak progression compared to a strong progression like roots by descending fifths. But, in the context of root movement by step it's a fairly common pattern.
Of course we need more than two chords to establish a clear pattern.
And that is what I think the potential pitfall of the chart is. It doesn't explain how some of those potential progressions fit into common patterns.
Nearly any two chords could could be used in succession depending on the surrounding musical context. In that sense the chart is both obvious and meaningless, because it doesn't explain how to create the context that gives chord progressions meaning. It's a kind of musical anti-pattern!
Some might say the chart is a kind of 'harmonic training wheels' for a beginner, but I actually think it will just lead to a beginner becoming confused.
Without some knowledge of common patterns there is the risk of the chart producing weak, meandering progressions like...
I ii viio iii ii IV iii ii.